Spss MISSING VALUE ANALYSIS 7.5 User Manual

SPSS Missing Value Analysis™ 7.5

MaryAnn Hill / SPSS Inc.

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Preface

SPSS is a powerful software package for data management and analysis. The Missing
Value Analysis option extends this power by giving you tools for discovering patterns
of missing data that occur frequently in survey and other types of data and for dealing
with data that contain missing values. Often in survey data, patterns become evident
that will affect analysis. For example, you might find that people living in certain areas
are reluctant to give their annual incomes, thus creating missing values in your data. If
you leave these values out, are your statistical conclusions valid? Another concern is
that the statistical algorithms being used make valid assumptions about the data distri­bution. With the Missing Value option, you can:

• Describe patterns of missing data.

• Estimate means, standard deviations, and correlations using a listwise, pairwise,

regression, or EM (expectation-maximization) method.

• Fill in (impute) missing values with estimates obtained using a regression or an
EM method.

The Missing Value procedure must be used with the SPSS Base system and is
completely integrated into that system. You can use results from this procedure (for
example, a correlation matrix) in other SPSS procedures.

About This Manual

This manual first presents the operation of the dialog box interface for Missing Value
Analysis. The operational section is followed by extensive examples illustrating appli­cations to various data configurations. Finally, the Syntax Reference section provides
complete command syntax for the

Compatibility

SPSS is designed to run on many computer systems. See the materials that came with
your system for specific information on minimum and recommended requirements.

Serial Numbers

Your serial number is your identification number with SPSS Inc. You will need this
serial number when you contact SPSS Inc. for information regarding support, payment,
or an upgraded system. The serial number was provided with your Base system.

MVA command.

iii

Customer Service and Technical Support

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help for one of the supported hardware environments. To reach Technical Support, see
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Contacting SPSS Inc.

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iv

Contents

1 Missing Value Analysis 1

To Obtain a Missing Value Analysis 2

Missing Value Analysis Patterns 3
Missing Value Analysis Descriptives 5
Missing Value Analysis Regression 6
Missing Value Analysis EM 7
Missing Value Analysis Variables for EM and Regression 8
MVA Command Additional Features 9

2 Missing Data: Descriptive Displays, Estimates of Statistics, and

Imputation of Values 11

Example 1:
A First Look at Patterns of Incompleteness 14

Example 2:
Pursuing Patterns Further 21

Example 3:
Patterns in a Large Survey 29

Example 4:
Estimating Means, Standard Deviations, Covariances, and Correlations 41

Example 5:
Estimating Replacement Values: Imputation 53

Syntax Reference

MVA 63

Bibliography 77

Subject Index 79

Syntax Index 81

vii

1

Missing Value Analysis

The Missing Value procedure performs three primary functions:

• Describes the pattern of missing data: where the missing values are located, how ex­tensive they are, whether pairs of variables tend to have values missing in different
cases, whether data values are extreme, and whether values are missing randomly.

• Estimates means, standard deviation, covariances, and correlations using a listwise,
pairwise, regression, or EM (expectation-maximization) method. The pairwise
method also displays counts of pairwise complete cases.

• Fills in (imputes) missing values with estimated values using regression or EM
methods.

Missing value analysis helps address several concerns caused by incomplete data.
Cases with missing values that are systematically different from cases without missing
values can obscure the results. Also, missing data may reduce the precision of
calculated statistics because there is less information than originally planned. Another
concern is that the assumptions behind many statistical procedures are based on com­plete cases, and missing values can complicate the theory required.

Example.

ever, not all measurements are available for every patient. The patterns of missing data
are displayed, tabulated, and found to be random. An EM analysis is used to estimate
the means, correlations, and covariances. Missing values are replaced by imputed
values and saved into a new data file to be used for further analysis.

Statistics. Univariate statistics, including number of nonmissing values, mean, stan-

dard deviation, number of missing values, and number of extreme values. Estimated
means, covariance matrix, and correlation matrix, using listwise, pairwise, EM, or re­gression methods. Little’s MCAR test with EM results. Summary of means by various
methods. For groups defined by missing versus nonmissing values: t tests. For all vari­ables: missing value patterns displayed cases-by-variables.

Data. Data can be categorical or quantitative. For each variable, missing values that are

not coded as system-missing must be defined as user-missing. For example, if a ques­tionnaire item has the response
ing, the item should have 5 coded as a user-missing value.

Assumptions. Listwise and pairwise estimation depends on the assumption that the pat-

tern of missing values does not depend on the data values. (This condition is known as

In evaluating a treatment for leukemia, several variables are measured. How-

Don’t know coded as 5 and you want to treat it as miss-

1

2 Chapter 1

missing completely at random, or MCAR.) Violation of this assumption can lead to
biased estimates. Regression and EM estimation depend on the assumption that the pat­tern of missing data is related to the observed data only. (This condition is called missing
at random, or MAR.) This assumption allows estimates to be adjusted using available
information.

Related procedures. Many procedures in SPSS allow you to use listwise or pairwise

estimation. Linear Regression and Factor allow replacement of missing values by the
mean values. In the SPSS Trends option, several methods are available to replace miss­ing values in time series. To code user-missing values, choose
Data menu.

To Obtain a Missing Value Analysis

 From the menus choose:

Statistics

Missing Value Analysis...

Figure 1.1 Missing Value Analysis dialog box

Define Variable from the

 Select at least one quantitative variable.

Optionally, you can:

• Select categorical variables (numeric or string) and enter a limit on the number of cat­egories (

• Click

Maximum).

Patterns or Descriptives for descriptions of missing values.

• Select a method for estimation of statistics and estimation of the missing values
themselves.

• If you select EM or Regression, click
estimation.

Missing Value Analysis Patterns

Figure 1.2 Missing Value Analysis Patterns dialog box

Missing Value Analysis 3

Variables to specify a subset to be used for the

Display. Three types of pattern tables are available, containing cases or numbers of cases

versus variables. Instead of values or counts, the cells of the table contain symbols that

4 Chapter 1

indicate the type of value. For Tabulated cases, X’s are used to indicate missing values.

All cases and Cases with missing values, the symbols in the display are:

For

+ Extremely high value
– Extremely low value
S System-missing value
A First type of user-missing value
B Second type of user-missing value
C Third type of user-missing value

• Tabulated cases. The frequency of each missing value pattern is tabulated. Counts

and variables are both sorted by similarity of patterns.

Omit patterns with less than n % of cases. Eliminates patterns that occur

infrequently.

• Cases with missing values. Case-by-variable patterns of missing and extreme values

are shown only for cases that have missing values. Cases and variables are both
sorted by similarity of patterns.

• All cases. For each case, the pattern of missing values and extreme values is dis-

played. Unless a sort variable is specified, cases are listed in the order in which they
appear in the data file.

Variables. You can specify variables for labeling and sorting the pattern displays.

• Missing Patterns for. Lists all quantitative and categorical variables from the Missing

Value Analysis dialog box.

• Additional information for.

Lists values for each case. For tabulated patterns, this op­tion lists the mean of quantitative variables or, for categorical variables, the number
of cases having the pattern in each category.

• Sort b y. Cases are listed according to the ascending or descending order of the values

of the specified variable. Available only for

All cases.

Missing Value Analysis Descripti ves

Figure 1.3 Missing Value Analysis Descriptives dialog box

Univariate statistics. For each variable, displays the number of nonmissing values, the

mean, the standard deviation, and the number and percentage of missing values. Also
displays counts and percentages of missing values and counts of extremely high and low
values. (Means, standard deviation, and extreme value counts are not reported for cate­gorical variables.)

Missing Value Analysis 5

Indicator Variable S tatistics. For each variable, SPSS creates a missing indicator variable

that indicates whether the value of the variable is present or missing. The indicator vari­ables are not displayed but are used in creating the mismatch, t test, and frequency ta­bles. To reduce table size, you can omit statistics that are computed for only a small
number of cases.

• Percent mismatch. For each pair of variables, displays the percentage of cases in

which one variable has a missing value and the other variable has a nonmissing value.
Each diagonal element in the table contains the percentage of missing values for a
single variable.

6 Chapter 1

• t tests with groups formed by indicator variables. The means of two groups are com-

pared for each quantitative variable, using Student’s t statistic. The groups are deter­mined by whether the indicator variable is coded present or missing. The t statistic,
degrees of freedom, counts of missing and nonmissing values, and means of the two
groups are displayed. You can also display any two-tailed probabilities associated
with the t statistics, although interpretation of these probabilities can be problematic.

• Crosstabulations of categorical and indicator variables. A table is displayed for each

categorical variable. For each category, the table shows the frequency and percentage
of nonmissing values for the other variables. The percentages of each type of missing
value are also displayed.

Missing Value Analysis Regression

Figure 1.4 Missing Value Analysis Regression dialog box

Regression estimates missing values using multiple linear regression. The means, the
covariance matrix, and the correlation matrix of the predicted variables are displayed.

Estimation Adjustment.

sion estimates. You can select residuals, normal variates, Student’s t variates, or no
adjustment.

Maximum number of predictors. Sets a maximum limit on the number of predictor (inde-

pendent) variables used in the estimation process.

Save completed data. Writes an SPSS data file, with missing values replaced by values

estimated by the regression method.

The regression method can add a random component to regres-

Missing Value Analysis EM

Figure 1.5 Missing Value Analysis EM dialog box

EM estimates the means, the covariance matrix, and the correlation of quantitative vari­ables with missing values, using an iterative process.

Missing Value Analysis 7

Distribution.

normal, and Student’s t. For a mixed normal assumption, you can specify the proportion
and the standard deviation ratio. For Student’s t distribution, you must specify the de­grees of freedom.

Maximum iterations. Sets the maximum number of iterations. The procedure stops when

this number of iterations is reached, even if the estimates have not converged.

Save completed data. Writes an SPSS data file, with missing values replaced by values

estimated by the EM method.

Various assumptions can be made for distribution of data: normal, mixed

8 Chapter 1

Missing Value Analysis Variables for EM and Regression

Figure 1.6 Missing Value Analysis Variables for EM and Regression dialog box

Variables. Quantitative variables were selected in the Missing Value Analysis dialog

box. Variables in the Categorical list are not available here. Quantitative variables can
be copied to either Predicted Variables, Predictor Variables, or both.

MVA Command Additional Features

The SPSS command language also allows you to:

• Specify separate descriptive variables for missing value patterns, data patterns, and
tabulated patterns using the

TPATTERN subcommands.

• Specify more than one sort variable for the data patterns table, using the DPATTERN

subcommand.

• Specify tolerance and convergence, using the EM subcommand.

• Specify tolerance and F-to-enter, using the REGRESSION subcommand.

• Specify different variable lists for EM and Regression, using the EM and

REGRESSION subcommands.

• Specify different percentages for suppressing cases displayed for TTEST, TABULATE,

MISMATCH.

and

See the Syntax Reference section of this manual for complete syntax information.

Missing Value Analysis 9

DESCRIBE keyword on the MPATTERN, DPATTERN, or

Missing Data:
Descriptive Displays, Estimates of

2

Statistics, and Imputation of Values

Even in the best designed and monitored study, observations can be missing—a subject
inadvertently skips a question, a blood sample is ruined, or the recording equipment
malfunctions. Because many classical statistical analyses require complete cases (no
missing values), when data are incomplete it may be hard “to get off the ground.” That
is, if the analyst wants to explore a new data set by, say, using a factor analysis to identify
redundant variables or sets of related variables, a cluster analysis to check for distinct
subpopulations, or a stepwise discriminant analysis to see which variables differ among
subgroups, there may be too few complete cases for an analysis. For example, there are
no complete cases in the survey data with 61 variables and 1500 cases, described below.

The features in the Missing Value procedure address three tasks:

• Description of patterns. How many missing values are there? Where are they located

(specific cases and/or variables)? Are values missing randomly? For each variable,
the word pattern indicates the dichotomized version of the variable—that is, a binary
distribution where each value is missing or present. Also, when the same variables
are missing for several cases, cases are said to have the same pattern.

• Estimat ion of means, standa rd deviations, co variances, and correlation s. Statistics are

computed using one or more methods: all values, listwise, pairwise, EM (expectation
maximization), or regression. Several options are available for both the EM and re­gression methods.

• Imput ation of values. EM and regression methods are provided for estimating replace-

ment values for the missing data.

Methods for estimation and imputation are defined in the examples that follow. To us,
none of the approaches should be viewed as a magic black box when the data are non­randomly incomplete. While the EM and regression methods allow a specific way in
which the values of one variable may be related to another, a good data analyst will want
to ferret out possible problems in how the data are sampled, recorded, or otherwise fail
to conform to the study protocol—for example, which regions of a multivariate space
are sparse because data are missing? It is hard to separate the selection of an appropriate
method for estimation or imputation from the basic data screening process.

11

12 Chapter 2

Often it is necessary to run the Missing Value procedure several times. You should:

• First, see the extent and pattern of missing values, and determine if values are missing
randomly. At this point, you may want to delete cases and variables with large num­bers of missing data and, most importantly, screen variables with skewed distribu­tions for symmetrizing transformations before proceeding to the estimation or
imputation phases.

• Next, study various estimates of descriptive statistics, possibly making a side step to
check relations graphically when differences in estimates are found.

• Finally, impute values (estimate replacement values) and use graphics to assess the
suitability of the filled-in values.

The use of a data matrix with imputed values may not be acceptable for a final report of
results, but by using the approaches and methods described here, you may be able to find
a subset of variables with enough complete cases for a meaningful analysis. You may
omit variables simply because a large proportion of their values are missing; or, by mak­ing exploratory runs using the imputed data matrix, you may learn that some variables
are redundant or have little relation to the outcome variables of interest. For example:

• In a stepwise regression, you may find that some variables have no relation to your
outcome variable. Try rerunning the analysis with a smaller subset of candidate vari­ables that has many more complete cases.

• In a factor analysis, you may identify one or more redundant variables. You might also
learn this by examining an estimate of the correlation matrix in the MVA procedure.

Data. Two data sets are used in the examples below. We approach these data as consult-

ants contacted after the data were collected and recorded, not as collaborators involved
in designing a study.

For each of 109 countries in the world95m data file, 22 variables were culled from

several 1995 almanacs—including life expectancy, birth rate, the ratio of birth rate to
death rate, infant mortality, gross domestic product per capita, female and male literacy
rates, average calories consumed per day, the percentage of the population living in cit­ies, and so on. Because the values of some variables differed across sources, we are
unsure of their accuracy. Four percent of the data values are missing, yet only 58 cases
are complete (53% of the sample).

The General Social Survey (GSS) data contain a subset of 61 responses collected by

the National Opinion Research Center at the University of Chicago in 1993 for 1500 peo­ple, age 18 years or older. Variables include the respondent’s income in 1991 (rincom91),
the general household income (income91), years of school attendance (educ), sex, view
of life (dull, routine, or exciting), opinions about music (jazz, classical, rap), and so on.
Eighteen percent of the values are missing and there are no complete cases.

Missing Data 13

Example 1: A first look at patterns of incompleteness. After a univariate summary report

shows that the variable calories in the world95m data has the most values missing, rep­resentations, or pictures, of the data matrix displaying one character per variable are in­troduced (for example, an S represents a system-missing variable, and a blank represents
a value that is present). In one variation, cases and variables are ordered by the pattern
of incompleteness; in another, counts of cases with the most common patterns are re­ported. A tally of low and high values for each variable provides a clue that the distri­butions of three variables are skewed and need to be re-expressed.

Example 2: Pursuing patterns further. Using the missing value pattern of calories and

also male and female literacy rates as grouping variables, two-sample t tests are request­ed for all quantitative variables. The same patterns are also crosstabulated against the
categorical variables region2 and religion . As a check on whether pairs of variables tend
to have values missing for the same cases or whether they are mismatched (if one is
missing, the other is present), pairwise counts of values present and percentages of pair­wise mismatched cases are reported.

Example 3: Patterns in a large survey. In the 1993 General Social Survey, three subsets

of items are administered to different subsamples of two-thirds of the cases, so when
items are selected from each subset no complete cases remain. Our codebook provides
no identification of the subsets or subsamples. By using a display of the common pat­terns of missing data and information about pairwise mismatches, the subsets are iden­tified. Many of the items in this survey have two or more codes for missing values.
Boxplots and the crosstabulation of patterns against categorical variables highlight rela­tions among distributions in the categories and multiple missing value codes.

Example 4: Estimating means, standard deviations, covariances, and correlations. For

each quantitative variable, pairwise estimates of means and standard deviations are
computed for each subsample formed by pairing the variable with each other variable.
For easy comparison, estimates obtained by the listwise, all values, EM, and regression
methods are displayed in a summary panel. Correlations are estimated using each of the
default methods, and differences between elements in each pair of matrices are comput­ed and displayed using SPSS’s MATRIX procedure.

Example 5: Estimating replacement values: Impu tation . Replacements for missing values

are estimated by both the EM and regression methods. The filled-in data matrices are
saved and the identity of the observed and imputed values displayed in scatterplots. Es­timates from the two methods for the same variable are compared graphically.

14 Chapter 2, Example 1

Pivot table editing. In the examples below, we edited many of the SPSS output panels,

requesting fewer digits following the decimal point, omitting results for variables that
are similar to others, and so forth. Each task begins by clicking on the table to select it
and selecting

SPSS Pivot Table Object from the Edit menu (or double-click the table).

Then:

• To omit cases (rows) or columns of a table, press the Ctrl and Alt keys and simulta­neously click on the row(s) or columns(s) to highlight them, and then choose
or Delete from the Edit menu.

• To control the width of cells and digits following the decimal, first choose

Select/Table body on the Edit menu and then Cell Properties or Set Data Cell Width

from the Format menu.

• To transpose rows and columns, select
menu.

• To move elements in cells into “layers,” select
and drag the icons.

• To rotate column labels from horizontal to vertical or vice-versa, choose

Column Labels

from the Format menu.

Example 1:
A First Look at Patterns of Incompleteness

Clear

Transpose rows and columns from the Pivot

Pivoting Trays from the Pivot menu

Rotate Inner

Where are the missing values located? How extensive are they? If a value is missing for
one variable, does it tend to be missing for one or more other variables? Conversely, if
a value is present for one variable, do values tend to be missing for other specific vari­ables? Is the pattern of missing values related to values of another variable?

You may need to uncover patterns of incomplete data in order to:

• select enough complete cases for a meaningful analysis. If you omit a few variables,
or even just one, does the sample size of complete cases increase dramatically?

• select a method of estimation or imputation. If, for example, you plan to use complete
cases for a final analysis, you need to verify that values are missing completely at ran­dom, missing at random, or missing nonrandomly.

• understand how results may be biased or distorted because of a failure to meet nec­essary assumptions about randomness of the missing values.

Three items from the GSS survey described above form a good illustration of variables
that can not be used together in a multivariate procedure. The survey has three subsets
of questions administered to two-thirds of the sample. It is possible to include one item
from each set, with the result that no cases are complete. For example, look at the
crosstabulation of the patterns for questions about gun laws, marijuana, and euthanasia:

Missing Data 15

Table 2.1 Crosstabulation of patterns that shows no complete cases

LETDIE1

GUNLAW GRASS

missing missing 7 27

present 34 448

present missing 55 481

present 448 0

missing present

The sample sizes for the items are, respectively, 984, 930, and 956, and yet no subject
answered all three questions. The percents of pairwise mismatched cases are 65%, 68%,
and 66%! From the tabulated pattern display in Example 1, it is clear that the large
blocks of incomplete data occur for different subsets of the cases.

A study of burn victims provides an example of possibly distorted results. If the ulti­mate goal is a model to predict survival for burn victims using age, blood gasses, total
area burned, etc., as predictors, many would find it disconcerting that a sizable portion
of the healthiest part of the sample is missing—only 31% of the survivors had blood gas
determinations, but more than 90% of those who died had them. In addition, because of
pediatric hospital unit policy, blood gasses were measured for only 20% of the children
under the age of 7.

In this example, we explore the world95m data for patterns of how values are miss­ing. It begins to be clear in several displays that values of female and male literacy are
not missing randomly. In Example 2, we continue the search and description of patterns
after log-transforming some variables with skewed distributions.

To produce this output, from the menus choose:

Statistics

Missing Value Analysis...

 Quantitative Variables: populatn, density, urban, lifeexpf, lifeexpm, literacy,

pop_incr, babymort, gdp_cap, calories, birth_rt, death_rt, log_gdp, lg_aidsr, b_to_d,
fertilty, log_pop, lit_male, lit_fema

 Categorical Variables: region2, religion, climate

 Case Labels: country

Patterns...

Display

; Tabulated cases, grouped by missing value patterns
; Cases with missing values, sorted by missing value patterns
; All cases, optionally sorted by selected variable

Variables

; Additional information: region2, literacy, religion, babymort, gdp_cap
; Sort by: region2

16 Chapter 2, Example 1

Univariate statistics. This panel provides your first look, variable by variable, at the ex-

tent of incomplete data. The number of values present is reported in the second column;
the number missing, in the fifth column; and the percentage missing, in the sixth col­umn. For calories, 75 countries (cases) report a value, and 34 do not. That is, calories is
missing for 31.2% of the cases. The female and male literacy rates (lit_fema and
lit_male) are each missing for 22% of the cases. Ten variables have no missing values,
and nine others have from 0.9% to 2.8% missing values.

Because means and standard deviations are computed using all available data for
each variable, the sample sizes vary from variable to variable. Statistics are not com­puted for region2, religion, and climate because they are specified as categorical
variables.

POPULATN
DENSITY
URBAN
LIFEEXPF
LIFEEXPM
LITERACY
POP_INCR
BABYMORT
GDP_CAP
CALORIES

BIRTH_RT
DEATH_RT
LOG_GDP
LG_AIDSR
B_TO_D
FERTILTY
LOG_POP
LIT_MALE
LIT_FEMA
REGION2
RELIGION
CLIMATE

a.

Number of cases outside the range (Q1 - 1.5*IQR, Q3 + 1.5*IQR).

Univariate Statistics

No. of

N Mean

109 47723.88 146726.36 0 .0 0 11
109 203.415 675.705 0 .0 0 13
108 56.53 24.20 1 .9 0 0
109 70.16 10.57 0 .0 9 0
109 64.92 9.27 0 .0 6 0
107 78.34 22.88 2 1.8 0 0
109 1.682 1.198 0 .0 0 0
109 42.313 38.079 0 .0 0 1
109 5859.98 6479.84 0 .0 0 13

75 2753.83 567.83 34 31.2 0 0
109 25.923 12.361 0 .0 0 0
108 9.56 4.25 1 .9 0 9
109 3.4218 .6201 0 .0 0 0
106 1.3800 .7094 3 2.8 0 0
108 3.2035 2.1250 1 .9 0 2
107 3.563 1.902 2 1.8 0 0
109 4.1140 .6542 0 .0 2 2

85 78.73 20.45 24 22.0 0 0

85 67.26 28.61 24 22.0 0 0
107 2 1.8
108 1 .9
107 2 1.8

Std.

Deviation

Missing

Count Percent

Extremes

Low High

a

For each variable, Tukey’s robust boxplot criterion for “outside values” is used to define
extreme values. (For larger files the criterion is the sample mean plus or minus two stan­dard deviations.) The extremes are tabulated in the last two columns. Use these counts
to identify possible outliers and/or skewed distributions. Symmetry is important if one’s
goal is to estimate means, standard deviations, covariances, or correlations. More than
10% of the population, density, and GDP per capita values are high (the counts are 11,

Missing Data 17

13, and 13) and none are low. Boxplots of these distributions show that they are right­skewed; thus, for estimation and imputation, we log-transform them.

The first three boxplots in Figure 2.1 use the data as recorded. In the last three box­plots, each variable is log-transformed. In order to display the six distributions within a
single frame, the variables are transformed to z scores before plotting. The shape of each
distribution is emphasized because the maximum value is set as 4.0, eliminating the out­liers China and India for population and Hong Kong and Singapore for density in the
first three boxplots.

Figure 2.1 Boxplots of population, density, and GDP per capita

4

2

0

-2

before and after log transformation

-4

109109109109109109N =

ZLOG_GDPZLOG_DENZLOG_POPZGDP_CAPZDENSITYZPOPULAT

Casewise patterns of incomplete data. The display Data Patterns (all cases) is a picture

of the data file that highlights the location of missing observations and extreme values.
Each column in the display represents the values of a variable; each row represents the
data for one country or subject. (To save space, the Eastern European, African, and Latin
American countries are omitted.) Countries are ordered by geographical region, because
region2 is specified as the Sort variable. The values of region2 for Canada and the USA
are missing, so they are listed first.

A single print character is allowed for each variable: a blank when the value is present
and not extreme, a plus sign (+) for an extremely large value, a minus sign (–) for an
extremely small value, an S for system missing (for example, a blank in the data), and
up to three user-defined missing codes, denoted by A, B, and C. This display is used to
see if particular cases and/or variables have too little complete data to use and also to see
if variables (or groups of variables) have values missing nonrandomly.

18 Chapter 2, Example 1

Data Patterns (all cases)

Case

Canada
USA
Austria
Belgium

Denmark
Finland

France
Germany
Greece

Iceland
Ireland

Italy
Netherlands
Norway

Portugal
Spain
Sweden

Switzerland
UK

Afghanistan
Australia
Bangladesh

Cambodia
China

Hong Kong
India
Indonesia

Japan
Malaysia
N. Korea

New Zealand
Pakistan

Philippines
S. Korea
Singapore

Taiwan
Thailand

Vietnam
Armenia
Azerbaijan

Bahrain
Egypt
Iran

Iraq
Israel

Jordan
Kuwait
Lebanon

Libya
Oman

Saudi Arabia
Syria
Turkey

U.Arab Em.
Uzbekistan

Missing and Extreme Value Patterns

# Missing

% Missing

URBAN

DENSITY

LIFEEXPF

POPULATN

3 13.6 + S S S 97 6.8 19904 . Catholic

1 4.5 + + S 97 8.1 23474 . Protstnt
2 9.1 + S S 99 6.7 18396 Europe Catholic
3 13.6 + + S S S 99 7.2 17912 Europe Catholic

2 9.1 + S S 99 6.6 18277 Europe Protstnt
2 9.1 S S 100 5.3 15877 Europe Protstnt

2 9.1 + S S 99 6.7 18944 Europe Catholic
2 9.1 + S S 99 6.5 17539 Europe Protstnt
0 .0 93 8.2 8060 Europe Orthodox

3 13.6 + S - S S 100 4.0 17241 Europe Protstnt
2 9.1 S S 98 7.4 12170 Europe Catholic
0 .0 + 97 7.6 17500 Europe Catholic

2 9.1 + + S S 99 6.3 17245 Europe Catholic
2 9.1 + S S 99 6.3 17755 Europe Protstnt

1 4.5 S 85 9.2 9000 Europe Catholic
0 .0 95 6.9 13047 Europe Catholic
2 9.1 S S 99 5.7 16900 Europe Protstnt

2 9.1 + S S 99 6.2 22384 Europe Catholic
2 9.1 S S 99 7.2 15974 Europe Protstnt

1 4.5 - + S + 29 168.0 205 Pacific/Asia Muslim
0 .0 100 7.3 16848 Pacific/Asia Protstnt
0 .0 + + 35 106.0 202 Pacific/Asia Muslim

0 .0 35 112.0 260 Pacific/Asia Buddhist
0 .0 + + 78 52.0 377 Pacific/Asia Taoist
1 4.5 + S 77 5.8 14641 Pacific/Asia Buddhist

0 .0 + + + 52 79.0 275 Pacific/Asia Hindu
0 .0 + 77 68.0 681 Pacific/Asia Muslim

2 9.1 + + + S S 99 4.4 19860 Pacific/Asia Buddhist
0 .0 78 25.6 2995 Pacific/Asia Muslim
1 4.5 S 99 27.7 1000 Pacific/Asia Buddhist

2 9.1 S S 99 8.9 14381 Pacific/Asia Protstnt
1 4.5 + S 35 101.0 406 Pacific/Asia Muslim

0 .0 90 51.0 867 Pacific/Asia Catholic
1 4.5 + S 96 21.7 6627 Pacific/Asia Protstnt
0 .0 + 88 5.7 14990 Pacific/Asia Taoist

8 36.4 + S S S S S S S S 91 5.1 7055 Pacific/Asia Buddhist
0 .0 93 37.0 1800 Pacific/Asia Buddhist
0 .0 88 46.0 230 Pacific/Asia Buddhist

2 9.1 S S 98 27.0 5000 Middle East Orthodox
2 9.1 S S 98 35.0 3000 Middle East Muslim

1 4.5 + S 77 25.0 7875 Middle East Muslim
0 .0 48 76.4 748 Middle East Muslim
0 .0 54 60.0 1500 Middle East Muslim

0 .0 60 67.0 1955 Middle East Muslim
1 4.5 S 92 8.6 13066 Middle East Jewish

0 .0 80 34.0 1157 Middle East Muslim
0 .0 + 73 12.5 6818 Middle East Muslim
1 4.5 + S 80 39.5 1429 Middle East Muslim

0 .0 64 63.0 5910 Middle East Muslim
4 18.2 S S S S . 36.7 7467 Middle East Muslim
0 .0 62 52.0 6651 Middle East Muslim

1 4.5 S 64 43.0 2436 Middle East Muslim
0 .0 81 49.0 3721 Middle East Muslim

1 4.5 S + 68 22.0 14193 Middle East Muslim
1 4.5 S 97 53.0 1350 Middle East Muslim

LIFEEXPM

LITERACY

POP_INCR

GDP_CAP

BIRTH_RT

CALORIES

BABYMORT

B_TO_D

LIT_MALE

FERTILTY

LOG_GDP

DEATH_RT

LOG_POP

LG_AIDSR

CLIMATE

REGION2

LIT_FEMA

RELIGION

LITERACY

BABYMORT

Variable Values

GDP_CAP

REGION2

RELIGION

Missing Data 19

The S’s show that when female literacy is missing, male literacy is missing too. Lit_male
and lit_fema are missing frequently for European countries, but calories is missing more
often for Middle Eastern countries. In the complete sample, 36.4% of Taiwan’s data are
missing, 22.7% of Bosnia’s data are missing (not shown), and so forth. A “+” indicates
that China’s and India’s populations, for example, are extremely large. Some analysts
recommend treating a value that is an extreme outlier (and not a recording error) as a
missing value.

The user can opt to display values of variables with the patterns. Here, values of the
categorical variables region2 and religion are displayed along with the values of the
quantitative variables literacy, infant mortality (babymort), and GDP. For the European
countries, the literacy and GDP per capita values appear higher than those for most of
the other countries, while infant mortality (babymort) is lower. Variability appears
greatest within the Pacific/Asia region.

Sorted casewise patterns. In Missing Patterns (cases with missing values), cases and

variables are sorted by the patterns of the missing data. The last three columns are
lit_male, lit_fema, and calories, and the two last cases are Bosnia and Taiwan, because
they have the most values missing. Complete cases are not included. To shorten the out­put, we omit countries with one missing value and no extreme values (calories is miss­ing for most of the omitted cases).

20 Chapter 2, Example 1

Missing Patterns (cases with missing values)

Case

Afghanistan
Bahrain
Barbados
Hong Kong
Lebanon
Pakistan
Russia
S. Korea
U.Arab Em.
Armenia
Azerbaijan
USA
Canada
Denmark
Netherlands
New Zealand
Norway
Austria
Finland
France
Romania
Japan
Sweden
Switzerland
Germany
UK
Ireland
Bulgaria
Belgium
Croatia
Iceland
Oman
Czech Rep.
South Africa
Bosnia
Taiwan

Missing and Extreme Value Patterns

# Missing

% Missing

DENSITY

LIFEEXPF

POPULATN

1 4.5 - + + S 29 168.0 205 Pacific/Asia Muslim
1 4.5 + S 77 25.0 7875 Middle East Muslim
1 4.5 + - S 99 20.3 6950 Latn America Protstnt
1 4.5 + S 77 5.8 14641 Pacific/Asia Buddhist
1 4.5 + S 80 39.5 1429 Middle East Muslim
1 4.5 + S 35 101.0 406 Pacific/Asia Muslim
1 4.5 + S 99 27.0 6680 East Europe Orthodox
1 4.5 + S 96 21.7 6627 Pacific/Asia Protstnt
1 4.5 + S 68 22.0 14193 Middle East Muslim
2 9.1 S S 98 27.0 5000 Middle East Orthodox
2 9.1 S S 98 35.0 3000 Middle East Muslim
1 4.5 + + S 97 8.1 23474 . Protstnt
3 13.6 + S S S 97 6.8 19904 . Catholic
2 9.1 + S S 99 6.6 18277 Europe Protstnt
2 9.1 + + S S 99 6.3 17245 Europe Catholic
2 9.1 S S 99 8.9 14381 Pacific/Asia Protstnt
2 9.1 + S S 99 6.3 17755 Europe Protstnt
2 9.1 + S S 99 6.7 18396 Europe Catholic
2 9.1 S S 100 5.3 15877 Europe Protstnt
2 9.1 + S S 99 6.7 18944 Europe Catholic
2 9.1 S S 96 20.3 2702 East Europe Orthodox
2 9.1 + + + S S 99 4.4 19860 Pacific/Asia Buddhist
2 9.1 S S 99 5.7 16900 Europe Protstnt
2 9.1 + S S 99 6.2 22384 Europe Catholic
2 9.1 + S S 99 6.5 17539 Europe Protstnt
2 9.1 S S 99 7.2 15974 Europe Protstnt
2 9.1 S S 98 7.4 12170 Europe Catholic
3 13.6 S S S 93 12.0 3831 East Europe Orthodox
3 13.6 + + S S S 99 7.2 17912 Europe Catholic
3 13.6 S S S 97 8.7 5487 East Europe Catholic
3 13.6 + - S S S 100 4.0 17241 Europe Protstnt
4 18.2 S S S S . 36.7 7467 Middle East Muslim
4 18.2 S S S S . 9.3 7311 East Europe Catholic
4 18.2 A S S S 76 47.1 3128 Africa
5 22.7 S S S S S 86 12.7 3098 East Europe Muslim
8 36.4 + S S S S S S S S 91 5.1 7055 Pacific/Asia Buddhist

LIFEEXPM

POP_INCR

GDP_CAP

BIRTH_RT

BABYMORT

LOG_GDP

B_TO_D

LOG_POP

DEATH_RT

FERTILTY

URBAN

CLIMATE

LG_AIDSR

LITERACY

REGION2

RELIGION

LIT_MALE

LIT_FEMA

CALORIES

LITERACY

BABYMORT

Variable Values

GDP_CAP

REGION2

RELIGION

It is easy to see that when calories is missing, the literacy rates tend to be present. For
larger data files, the most common patterns may be less apparent; so, in the next display,
common patterns are tabulated.

Common patterns of missing data. In the Tabulated Patterns display, variables are listed

in the same order as in the Missing Pattern display, and the common patterns are tabu­lated. We hid columns for the first 10 variables because they are empty. The first row in
the display represents the pattern for 58 cases and has blanks for all 22 variables—that
is, 58 cases have no values missing. For 24 cases, calories is the only missing value; for
14 others, the male and female literacy rates are missing; and for 4 cases, all three vari­ables are missing. The sum of 58, 24, 14, and 4 does not equal the total sample size (109)
because patterns unique to a single case are not displayed. By default, the pattern is
omitted if less than 1% of the cases have it, but you can change the percentage.

Missing Data 21

The column labeled Complete if... reports the number of complete cases if the vari­able(s) marked by X in that pattern are omitted. Thus, if calories is eliminated, the
number of complete cases increases from 58 to 82; if only the male and female literacy
rates are omitted, the number is 72; and if all three variables are removed, it jumps to 100.

Tabulated Patterns

Missing Patterns

B_TO_D

BABYMORT

# of
cases

58 69.1 58.6 2757 3 1 11 16 8 19 1 0 1 15 2 4 28 3 3 1

58

X 82 81.6 37.1 5272 1 8 5 2 6 2 0 1 0 9 0 0 4 4 2 4

24

X X 72 98.8 7.5 16315 11 1 2 0 0 0 0 0 0 0 0 0 5 7 1 1

14

X X X 100 97.3 8.0 11118 2 2 0 0 0 0 0 0 0 0 0 0 2 1 0 1

4

URBAN

CLIMATE

FERTILTY

LG_AIDSR

RELIGION

LITERACY

For each pattern, the user can request frequency counts of categorical variables and/or
means of quantitative variables. From the tabulation of region2, literacy rates are miss­ing for at least 13 (11 + 2) European countries, while calories is missing for at least 10
(8 + 2) Eastern European countries. Infant mortality is much higher for the 58 complete
cases (an average of 58.6 deaths during infancy for every 1000 live births) than for the
countries where male and female literacy are missing (means of 7.5 and 8.0). The aver­age gdp_cap for the 14 countries where lit_fema and lit_male are missing is $16,315,
while it is only $2,757 for the 58 countries with no missing data. It is hard to believe that
values are missing randomly!

Example 2:
Pursuing Patterns Further

In this example, we investigate the nonrandom pattern of incomplete data further by us­ing the patterns of missing data for calories and the male and female literacy rates as
grouping variables in two-sample t tests and also in crosstabulations with the categorical
variables region2 and rel igion. We also examine which pairs of variables have values
that are jointly missing or mismatched (if one is present, the other is missing).

After viewing the output in Example 1, we decided that population, density, and
GDP per capita should be re-expressed in log units. Here we transform density and omit
the untransformed versions of the three variables.

REGION2

LITERACY

Complete if ...

REGION2

LIT_MALE

LIT_FEMA

CALORIES

GDP_CAP

BABYMORT

Europe

Africa

Pacific/Asi a

East Europe

Hindu

Middle East

Latn America

RELIGION

Tribal

Jewish

Taoist

Muslim

Animist

Protstnt

Catholic

Buddhist

Orthodox

22 Chapter 2, Example 2

To create this example, start by computing the log of each density value. From the

menus choose:

Transform

Compute...

log_den = LG10(density)

Recall the Missing Value Analysis dialog box from Example 1, and add log_den to the
list of Quantitative variables. Remove populatn, density, and gdp_cap, and deselect the
requests for the pattern displays shown in Example 1, as follows:

Statistics

Missing Value Analysis...

 Quantitative Variables: urban, lifeexpf, lifeexpm, literacy, pop_incr, babymort,

calories, birth_rt, death_rt, log_gdp, lg_aidsr, b_to_d, fertilty, log_pop, lit_male,
lit_fema, log_den

 Categorical Variables: region2, religion, climate

 Case Labels: country

Estimation
; Pairwise

Patterns...

Display

 Tabulated cases, grouped by missing value patterns (deselect)
 Cases with missing values, sorted by missing value patterns (deselect)
 All cases, optionally sorted by selected variable (deselect)

Descriptives...

Indicator Variable Statistics

; Percent mismatch
; t tests with groups formed by indicator variables
; Crosstabulations of categorical and indicator variables

Pairwise frequency counts. The Tabulated Patterns display in Example 1 on p. 21 pro-

vides one picture of the pattern of incomplete data, and a table of frequency counts for
each pair of variables gives another view. This panel of pairwise frequencies is printed
when you select

Pairwise under Estimation in the Missing Value Analysis dialog box.

Other results produced by this option are described in Example 4.

Pairwise Frequencies

Missing Data 23

LIFEEXPF
LIFEEXPM
POP_INCR
BABYMORT
BIRTH_RT
LOG_GDP
LOG_POP
LOG_DEN
DEATH_RT
B_TO_D
FERTILTY
LG_AIDSR
CLIMATE
URBAN
LITERACY
RELIGION
REGION2
LIT_FEMA
LIT_MALE
CALORIES

LIFEEXPF

LIFEEXPM

POP_INCR

109
109 109
109 109 109
109 109 109 109
109 109 109 109 109
109 109 109 109 109 109
109 109 109 109 109 109 109
109 109 109 109 109 109 109 109
108 108 108 108 108 108 108 108 108
108 108 108 108 108 108 108 108 108 108
107 107 107 107 107 107 107 107 107 107 107
106 106 106 106 106 106 106 106 106 106 106 106
107 107 107 107 107 107 107 107 107 107 106 105 107
108 108 108 108 108 108 108 108 107 107 106 105 106 108
107 107 107 107 107 107 107 107 106 106 105 104 105 107 107
108 108 108 108 108 108 108 108 107 107 106 105 106 107 106 108
107 107 107 107 107 107 107 107 106 106 105 104 105 106 105 106 107

85 85 85 85 85 85 85 85 85 85 85 84 84 85 85 85 84 85
85 85 85 85 85 85 85 85 85 85 85 84 84 85 85 85 84 85 85
75 75 75 75 75 75 75 75 75 75 75 75 75 74 74 75 73 59 59 75

BIRTH_RT

BABYMORT

LOG_POP

LOG_GDP

LOG_DEN

DEATH_RT

B_TO_D

FERTILTY

LG_AIDSR

URBAN

CLIMATE

LITERACY

RELIGION

REGION2

LIT_MALE

LIT_FEMA

CALORIES

The sample size for each variable is reported on the diagonal of the table; sample sizes
for complete pairs of cases, off the diagonal. Calories alone has 75 values, but when
paired with male or female literacy, the count of cases with both values drops to 59. If
you need a set of variables for a multivariate analysis, it would be wise to omit calories
or the male and female literacy rates. Otherwise, if these variables are essential to your
analysis, be concerned that results may be biased due to the fact they are not missing
randomly.

Pairwise mismatched patterns. For each pair of calorie and female literacy values, 50

cases (from the previous display, 109 total cases minus 59 cases that have both lit_fema
and calories present) are not complete; both values or just one or the other may be miss­ing (that is, the pattern is mismatched for the latter). If you need to omit variables in or­der to increase the number of complete cases, it helps to know which pairs of variables
seldom occur together. From the Percent Mismatch of Indicator Variables table, the en­try for calories paired with lit_fema is 38.5%. Almost 40% of the cases have either cal-
ories or a female literacy rate, but not both. The percentage missing for each variable
individually is reported on the diagonal. If the percentage missing is less than 5%, the
variable is not included in this display.You can change this cutoff for percentage missing
in the Descriptives dialog box. Notice that here, by default, the variables are ordered by
percentage missing. You can deselect this option on the same dialog box.

24 Chapter 2, Example 2

Percent Mismatch of Indicator

Variables

LIT_MALE

LIT_FEMA

LIT_MALE
LIT_FEMA
CALORIES

22.02
.00 22.02

38.53 38.53 31.19

CALORIES

Identifying nonrandom patterns with t tests. A two-sample t test is one way to check if

data are missing completely at random (called MCAR by Little and Rubin). If the val­ues of a variable are MCAR, then other quantitative variables should have roughly the
same distribution for cases separated into two groups based on pattern (missing or
present). In Figure 2.2, the pattern of female literacy groups infant mortality. Results of
the t tests below confirm that average infant mortality is significantly higher when female
literacy is present than when it is missing.

Figure 2.2 Boxplots of infant mortality grouped by pattern of female literacy

175

150

125

Afghanis tan

Infant mortality (deaths per 1000 live births)

100

75

50

25

0

PAT_LITF

South Afr ica

Oman

Romania

8524N =

presentmissing

Missing Data 25

For each quantitative variable, the Separate Variances t Tests display has a column of
two-sample t tests that compare its means for pattern variables (rows) with at least 5%
missing data. (When only a few values are missing, t statistics are not informative.) The
5% limit can be changed in the Descriptives dialog box.

We show the t test results in two ways: first, the t statistics alone (the cell statistics
are pivoted into layers) and then the default output layout (we hid lifeexpm and lit_male).
For larger data files, it helps first to scan the display of t statistics looking for large values
(positive or negative) and then refer to the complete table for more information.

Separate Variance t Tests

URBAN

CALORIES

LIT_MALE

LIT_FEMA

LIFEEXPF

-1.2 -2.3 -2.0 -2.0 1.7 2.0 . 2.1 1.2 -2.0 4.5 .4 1.8 2.5 -2.3 -2.5 -2.2

-3.1 -7.8 -7.6 -8.1 6.7 8.7 -8.6 7.2 .3 -9.2 -1.8 4.5 5.7 .9 . . -.2

-3.1 -7.8 -7.6 -8.1 6.7 8.7 -8.6 7.2 .3 -9.2 -1.8 4.5 5.7 .9 . . -.2

LIFEEXPM

LITERACY

POP_INCR

BABYMORT

CALORIES

BIRTH_RT

DEATH_RT

LOG_GDP

The t values greater than 2.0 or less than –2.0 are highlighted if you choose
Edit menu, then choose

_Create

.

Scripts, and select MVA_Table_TOUT_MATRIXOFTSTATISTICS

B_TO_D

LG_AIDSR

FERTILTY

LIT_MALE

LOG_POP

LIT_FEMA

Options on the

Both the size and location of the highlighted t’s confirm our earlier observation that
the literacy rates and calories have different nonrandom patterns of missing data. The
absolute values of the t statistics are considerably larger for the literacy rates than for
calories, so the departure from randomness is greater; and only 2 of the 11 variables with
highlighted t’s for the literacy rates are highlighted for calories (lifeexpf and birth_rt).

LOG_DEN

26 Chapter 2, Example 2

Separate Variance t Tests

t

df

# Present

# Missing

Mean(Present)

Mean(Missing)

CALORIESLIT_MALELIT_FEMA

t

df

# Present

# Missing

Mean(Present)

Mean(Missing)

t

df

# Present

# Missing

Mean(Present)

Mean(Missing)

URBAN

LIFEEXPF

LITERACY

POP_INCR

BABYMORT

-1.2

72.7 90.3 66.5 58.1 70.3 . 68.7 72 85.9 67.3 58.6 65.0 59.8 44.7 62.9

74 75 74 75 75 75 75 75 75 75 75 75 75 59 75

34 34 33 34 34 0 34 33 34 31 33 32 34 26 34

54.7 68.8 75 1.82 47.0 2754 27.5 9.9 3.35 1.55 3.26 3.8 4.22 62 1.70

60.6 73.1 85 1.38 31.9 . 22.3 8.9 3.58 .97 3.07 3.1 3.88 79 1.97

-3.1 -7.8 -8.1 6.7 8.7 -8.6 7.2

40.9 105 105 49.9 106.9 53.7 64.7 90 73.4 63.7 47.8 54.2 41.2 . 35.6

85 85 85 85 85 59 85 85 85 84 85 85 85 85 85

23 24 22 24 24 16 24 23 24 22 23 22 24 0 24

53.2 67.8 74 1.99 51.3 2589 29.0 9.6 3.24 1.34 3.58 3.9 4.14 67 1.78

68.8 78.5 96 .610 10.6 3362 15.2 9.4 4.05 1.55 1.81 2.1 4.02 . 1.80

-3.1 -7.8 -8.1 6.7 8.7 -8.6 7.2

40.9 105 105 49.9 106.9 53.7 64.7 90 73.4 63.7 47.8 54.2 41.2 . 35.6

85 85 85 85 85 59 85 85 85 84 85 85 85 85 85

23 24 22 24 24 16 24 23 24 22 23 22 24 0 24

53.2 67.8 74 1.99 51.3 2589 29.0 9.6 3.24 1.34 3.58 3.9 4.14 67 1.78

68.8 78.5 96 .610 10.6 3362 15.2 9.4 4.05 1.55 1.81 2.1 4.02 . 1.80

-2.0 1.7 2.0 .

-2.3

BIRTH_RT

CALORIES

2.1

DEATH_RT

1.2 -2.0

.3

-9.2

.3

-9.2

LOG_GDP

4.5

-1.8

-1.8

LG_AIDSR

B_TO_D

.4 1.8

4.5 5.7

4.5 5.7

FERTILTY

2.5 -2.5 -2.2

Each cell in the second panel of separate variances t tests includes both the sample sizes
and means of the present and missing groups, and the degrees of freedom for the sepa-
rate variances two-sample t test. When the latter is markedly smaller than the sample
size, the variances of the two groups differ. The sample size for the first five variables
is 108 or 109, but the df for pop_incr are only 58.You can request the probability asso­ciated with each t statistic in the Descriptives dialog box. However, don’t use these prob-
abilities for significance testing because they are appropriate only when a single test is
made and not in this situation of multiple tests.

Using the pattern of female literacy to separate the values of infant mortality into two
groups, the t is 8.7. When female literacy is present, average babymort is 51.3 babies;
when missing, it is 10.6 babies. The t’s are large for several other variables in the same
row. Figure 2.3 shows a profile of these mean differences (before plotting, the variables
were transformed to z scores). When female literacy is missing, the means of the first
five variables (b_to_d through birth_rt) are lower than when it is present; the opposite
is true for the last five variables (urban through log_gdp). That is, female literacy tends
to be missing for the more developed countries!

LOG_POP

LIT_FEMA

.9 . -.2

.9 . -.2

LOG_DEN

Missing Data 27

Figure 2.3 Profile of means for the female literacy pattern

1.5

ZB_TO_D

1.0

.5

0.0

-.5

-1.0

-1.5

Mea n

presentmis s i ng

ZBABYMOR

ZFERTILT

ZPOP_INC

ZBIRTH_R

ZURB A N

ZLIFEEXP

ZLITERAC

ZCALORIE

ZLOG_GDP

PAT_LITF

In Figure 2.4, relationships between pairs of variables are displayed in scatterplots. The
missing data pattern for female literacy is highlighted in the left plot; that for calories,
in the right plot.

Figure 2.4 Patterns for female literacy and calories

200

100

BABYMORT

LIT_FEMA

present

0

LOG_GD P

missi ng

5432

LG_AIDSR

4

3

2

1

-1

LOG_P OP

CALORIES

present

miss ing

765432

Within the scatterplot, regression lines are drawn for each group. In the plot on the right,
the pattern for calories separates the values of population and AIDS rate into two groups.
The top regression line fits the countries where calories is present; the lower line, where
calories is missing.

28 Chapter 2, Example 2

Crosstabulating patterns against categorical variables. The user can specify categorical

variables against which the predominant pattern variables are crosstabulated. Here, we
request tables for region2 and religion.

REGION2

Missing

Latn America

SysMis

CALORIES

LIT_MALE

LIT_FEMA

Present

Present

Present

Count
Percent
% SysMisMissing
Count
Percent
% SysMisMissing
Count
Percent
% SysMisMissing

Total

Europe

East Europe

75 14 3 13 16 8 19 2

68.8 82.4 21.4 68.4 84.2 47.1 90.5 100.0

31.2 17.6 78.6 31.6 15.8 52.9 9.5 .0
85 4 9 16 18 16 21 1

78.0 23.5 64.3 84.2 94.7 94.1 100.0 50.0

22.0 76.5 35.7 15.8 5.3 5.9 .0 50.0
85 4 9 16 18 16 21 1

78.0 23.5 64.3 84.2 94.7 94.1 100.0 50.0

22.0 76.5 35.7 15.8 5.3 5.9 .0 50.0

Pacific/Asia

Africa

Middle East

The count of values present for each category is given in the first row of each pattern
variable (for example, of the 75 calories values that are present, 14 are in the Europe
category). The percentage each count is of the total sample size is given in the next row
(75 is 68.8% of 109 countries and 14 is 82.4% of the 17 European countries). The per­centage missing for individual categories can be contrasted with the overall percentage
missing reported in the Total column. Overall, 31.2% of the values of calories are miss­ing, but the variable is missing for more than three-fourths (78.6%) of the Eastern Eu­ropean and half (52.9%) the Middle Eastern countries. The information for lit_fema is
missing for three-fourths (76.5%) of the European countries. Across the region2 catego­ries, the Latin American countries have many fewer missing values.

RELIGION

Missing Data 29

CALORIES

LIT_MALE

LIT_FEMA

Present

Present

Present

Count
Percent

% SysMisMissing
Count
Percent

% SysMisMissing
Count

Percent
% SysMisMissing

In the crosstabulation of patterns with religion, values of lit_fema and lit_male are miss­ing for half of the countries (50%) that are predominantly Protestant—this is consider­ably more than that found for the other religions. Overall, only 22% of the values are
missing.

Example 3:
Patterns in a Large Survey

Sometimes data are missing by design. The General Social Survey has been adminis­tered yearly since 1972. Each survey is an independently drawn sample of people over
18 years of age living in non-institutional arrangements. Each year, permanent items are
included; but starting in 1988, a subset of items appears on two-thirds of the cases each
year. Actually, there are three subsets of items, and each is asked of a different two-thirds
subsample of the respondents. The codebook we received does not identify which items
are in what subset, nor which respondents received them. In the crosstabulation of pat­tern variables for questions about gun laws, marijuana, and euthanasia (Table 2.1), we
show that there are no cases that are complete across the three items. We used the Tab­ulated Pattern display in this example to identify the three subsets of items and then se­lected one item from each as table factors.

The responses for many survey items have dichotomous or ordered categories. For a
first look at the survey, we treat these items as quantitative variables. If we were to pur­sue these data further, we would identify them as categorical variables for some
purposes—for example, when crosstabulating patterns against categorical variables.

Total

Hindu

75 1 0 1 15 2 4 35 11 4 2 0

68.8 100.0 .0 100. 0 55.6 100.0 100.0 85.4 68.8 57. 1 25.0 .0

31.2 .0 100.0 .0 44.4 .0 .0 14.6 31.3 42. 9 75.0 100.0

85 1 1 1 25 2 4 32 8 5 6 0

78.0 100.0 100.0 100.0 92.6 100.0 100.0 78.0 50.0 71.4 75.0 .0

22.0 .0 .0 .0 7.4 .0 .0 22.0 50.0 28.6 25.0 100.0
85 1 1 1 25 2 4 32 8 5 6 0

78.0 100.0 100.0 100.0 92.6 100.0 100.0 78.0 50.0 71.4 75.0 .0

22.0 .0 .0 .0 7.4 .0 .0 22.0 50.0 28.6 25.0 100.0

Tribal

Jewish

Taoist

Muslim

Animist

Protstnt

Catholic

Buddhist

Orthodox

Missing

30 Chapter 2, Example 3

Because the gss93mva data file is considerably larger than that used in the first exam­ples, the allocation for memory needs to be increased. To do this, from the menus
choose:

Edit
Options...

Special Workspace Memory Limit

1250 K Bytes

(When you are finished working with the large file, reset the memory limit to 512K.)

Now you are ready to run the Missing Value procedure. To produce the following output,
from the menus choose:

Statistics

Missing Value Analysis

 Quantitative Variables: childs, age, educ, degree, padeg, madeg, sex, income91,

rincom91, size, vote92, polviews, natenvir, natheal, natcity, natcrime, natdrug,
nateduc, cappun, gunlaw, grass, life, sathobby, drink, fework, pillok, spanking,
letdie1, news, tvhours, bigband, blugrass, country, blues, musicals, classicl, folk,
jazz, opera, rap, hvymetal, attsprts, visitart, tvshows, tvnews, tvpbs, partners,
sexfreq, sei

 Categorical Variables: wrkstat, marital, birthmo, zodiac, race, region, xnorcsiz,

partyid, relig, aged, sexeduc, dwelown

Estimation
; Pairwise

Patterns...

Display
; Tabulated cases, grouped by missing value patterns

Descriptives...

Indicator Variable Statistics

; Percent mismatch
; t tests with groups formed by indicator variables
; Crosstabulations of categorical and indicator variables

Omit variables missing less than 20% of cases

Note: You may wish to run Tabulated cases under Patterns separately because it could
take a good bit of time.

Missing Data 31

Univariate statistics. For this display, we pasted the syntax and rearranged the variables

list to reflect the order in the file. This univariate panel provides an overview of the ex­tent of incomplete data. Because the panel is long, we split it into two sections. Nine
variables are missing roughly half (from 49.5% to 56.7%) of their values, starting with

region and ending with the nation items (whether the nation is spending too little, about
right, or too much for the environment, health, etc.). Fourteen variables are missing

about one-third of their values. Among these must be the items given to only two-thirds
of the sample. In the Tabulated Patterns display, we will try to distinguish the three sub­sets of items.

For this larger data set, the criterion for identifying extreme values is now the mean
plus or minus two standard deviations. If the product of the number of variables times
the number of cases times the base 10 log of the number of cases is less than 150,000,
the robust measure defined in Example 1 is used; otherwise, the rule here is used.

For age, there are 41 “high” extreme values. If you run the Frequencies procedure
with a histogram, you will find there are 41 respondents older than 81 years (46.23 +
2*17.42) and that the age distribution is right-skewed. Watch out for outliers, however,
when the data are coarse (each variable has only a few unique values). For example, the
responses for degree, padeg, and madeg (father’s and mother’s degrees) have five codes
with 3 meaning bachelor’s degree and 4, a graduate degree. From the Frequencies pro­cedure, you will find that the 113 high values for degree are the count of graduate
degrees and the 125 high values for madeg include 96 bachelor degrees and 29 graduate
degrees.

32 Chapter 2, Example 3

WRKSTAT
MARITAL
CHILDS
AGE
BIRTHMO
ZODIAC
EDUC
DEGREE
PADEG
MADEG
SEX
RACE
INCOME91
RINCOM91
REGION
XNORCSIZ
SIZE
PARTYID
VOTE92
POLVIEWS
NATENVIR
NATHEAL
NATCITY
NATCRIME
NATDRUG
NATEDUC
CAPPUN
GUNLAW
GRASS
RELIG
LIFE
SATHOBBY
AGED
DRINK

Univariate Statistics

No. of

Std.

N Mean

1500 0 .0
1499 1 .1
1495 1.85 1.68 5 .3 0 42
1495 46.23 17.42 5 .3 0 41
1487 13 .9
1487 13 .9
1496 13.04 3.07 4 .3 40 25
1496 1.41 1.18 4 .3 0 113
1207 .93 1.19 293 19.5 0 72
1352 .84 .94 148 9.9 0 125
1500 1.57 .49 0 .0 0 0
1500 0 .0
1434 14.68 5.46 66 4.4 59 0

994 12.80 5.62 506 33.7 26 0
757 743 49.5
757 743 49.5

757 360.63 1225.20 743 49.5 0 42
1491 9 .6
1492 1.34 .54 8 .5 0 40
1443 4.17 1.36 57 3.8 30 41

710 1.51 .67 790 52.7 0 69

720 1.33 .61 780 52.0 0 54

650 1.52 .72 850 56.7 0 88

717 1.32 .57 783 52.2 0 38

707 1.44 .64 793 52.9 0 57

724 1.37 .59 776 51.7 0 43
1388 1.23 .42 112 7.5 0 0

984 1.18 .38 516 34.4 0 173

930 1.77 .42 570 38.0 0 0
1492 8 .5

997 2.41 .61 503 33.5 65 0

970 2.65 1.52 530 35.3 0 63

967 533 35.5

981 1.31 .46 519 34.6 0 0

Deviation

Missing

Count Percent

Extremes

Low High

Std.

FEWORK
PILLOK
SEXEDUC
SPANKING
LETDIE1
NEWS
TVHOURS
BIGBAND
BLUGRASS
COUNTRY
BLUES
MUSICALS
CLASSICL
FOLK
JAZZ
OPERA
RAP
HVYMETAL
ATTSPRTS
VISITART
TVSHOWS
TVNEWS
TVPBS
PARTNERS
SEXFREQ
DWELOW N
SEI

a.

Number of cases outside the range (Mean-2*SD,Mean+2*SD).

N Mean

992 1.20 .40 508 33.9 0 198
974 2.34 1.07 526 35.1 0 0
984 516 34.4
997 2.11 .83 503 33.5 0 67

956 1.32 .47 544 36.3 0 0
1010 2.02 1.21 490 32.7 0 58
1489 2.90 2.24 11 .7 0 63
1337 2.45 1.09 163 10.9 0 52
1335 2.66 1.02 165 11.0 0 56
1468 2.32 1.09 32 2.1 0 63
1434 2.51 1.03 66 4.4 0 57
1412 2.60 1.09 88 5.9 0 64
1425 2.66 1.22 75 5.0 0 0
1414 2.76 1.04 86 5.7 0 85
1451 2.62 1.11 49 3.3 0 66
1410 3.49 1.13 90 6.0 66 0
1431 3.93 1.12 69 4.6 41 0
1423 4.13 1.11 77 5.1 45 0
1489 1.47 .50 11 .7 0 0
1488 1.60 .49 12 .8 0 0
1490 2.52 1.19 10 .7 0 94
1492 1.60 1.00 8 .5 0 118
1486 2.71 1.25 14 .9 0 0
1367 1.02 .93 133 8.9 0 83
1330 2.88 1.98 170 11.3 0 0
1012 488 32.5
1419 47.206 18.760 81 5.4 0 56

Deviation

Missing

Count Percent

No. of

Extremes

Low High

Missing Data 33

a

Common patterns of missing data. In the Tabulated Patterns display, the order of the vari-

ables results from simultaneously sorting the rows and columns of the data matrix by
their missing value patterns. If 15 (1% of 1500) or fewer cases have the same pattern,
they are not tabulated here. The last 22 variables are the ones identified in the Univariate
Statistics panel as having one-third or more of their values missing.

34 Chapter 2, Example 3

Q

Tabulated Patterns

Missing Pa tterns

SEX

AGE

RACE

EDUC

RELIG

VOTE92

PARTYID

TVNEWS

TVSHOWS

TVPBS

VISITART

TVHOURS

ATTSPRTS

CHILDS

DEGREE

# of
cases
0

34

33

44

33

23

26

44

47

36

39

35

29

MARITAL

WRKSTAT

X X

X X X X X

X X X X X X X X X X X

X X X X X X X X

X X X X

X X X X X X X

X X X X X X X X X X X X X

X X X X X X X X X X

X X X X X X X X X X X X X

X X X X X X X X X X X X X X X X

X X X X X X X

X X X X X X X X X X

RAP

JAZZ

BLUES

ZODIAC

BIRTHMO

COUNTRY

HVYMETAL

SEI

FOLK

OPERA

MUSICALS

POLVIEWS

INCOME91

CAPPUN

SEXFRE

PARTNERS

MADEG

BIGBAND

BLUGRASS

PADEG

RINCOM91

NEWS

SEXEDUC

DWELOWN

PILLOK

FEWORK

SPANKING

LETDIE1

NATHEAL

NATEDUC

NATDRUG

NATENVIR

NATCRIME

AGED

DRINK

GRASS

NATCITY

SATHOBBY

To collect cases that may have a few other values missing in addition to those here, let’s
digress and rerun the same analysis using only the last 22 variables.

Tabulated Patterns

Missing Patterns

Number
of Cases

82
90

108

95

124

86
86

109

89

87
102

123

NEWS

SPANKING

DWELOWN

0

0

FEWORK

PILLOK

SEXEDUC

LETDIE1

NATCRIME

NATHEAL

NATEDUC

NATENVIR

NATCITY

NATDRUG

GRASS

DRINK

AGED

SATHOBBY

X X 82
X X X X X X X X 157

X X X X X X X X X X X 341
X X X X X 177
X X X X X X X X X X 184
X X X X 86

X X X X X X X 172
X X X X X X X X X X X X X 363
X X X X X X X 89
X X X X X X X X X X 176

X X X X X X X X X X X X X X X X 363
X X X X X X X X X X X X X 192

REGION

SIZE

XNORCSIZ

REGION

XNORCSIZ

LIFE

LIFE

SIZE

GUNLAW

34

67

137

62

23

49

126

60

63

129

35

64

GUNLAW

Complete if ...

0

Complete if ...

In the Tabulated Patterns display restricted to 22 variables, we highlight three sets of
variables that are missing independently of the others: 1) dwelown, news, spanking,

Missing Data 35

fework, sexeduc, pillok, letdie1; 2) grass, drink, sathobby, aged; and 3) life and gunlaw.
Each of these sets is sometimes missing with the “nat” set of six variables or with the
set that includes region, but not simultaneously with another of these sets. We will look
for these sets in the Percent Mismatch table below.

Pairwise mismatched patterns. Only variables that have 20% or more of their values

missing are included in the Percent Mismatch table. Diagonal entries are the percentage
missing for each variable individually; off the diagonal, the entries are the percentage
with one member of the pair missing and the other present. We highlight pairs combin­ing the three sets of variables identified above:

Percent Mismatch of Indicator Variables.

DRINK

SATHOBBY

AGED

XNORCSIZ

RINCOM91
SEXEDUC
DWELOWN
NEWS

SPANKING
FEWORK
PILLOK

LETDIE1
NATCRIME
NATEDUC

NATHEAL
NATENVIR
NATDRUG

NATCITY
GRASS
DRINK

SATHOBBY
AGED

XNORCSIZ
REGION
SIZE

LIFE
GUNLAW

NEWS

SEXEDUC

RINCOM91

DWELOWN

34
43 34

44 2 33
44 2 0 33
44 3 1 1 34

44 3 2 2 2 34
45 4 3 3 3 4 35
45 5 4 4 5 5 5 36

51 50 51 50 50 50 50 50 52
51 50 51 51 50 51 51 50 2 52
51 50 51 51 50 51 51 50 2 2 52

51 50 51 51 50 50 50 50 3 2 3 53
50 51 52 51 51 51 51 51 3 3 3 3 53
52 51 52 51 51 51 51 50 6 7 7 7 7 57

46 66 66 66 66 67 65 66 50 49 50 49 50 50 38
45 67 67 67 67 68 66 67 50 49 50 50 50 51 3 35
45 66 67 67 66 67 66 66 50 49 49 49 50 50 4 1 35

45 66 66 67 66 67 66 66 50 49 50 50 50 51 4 1 1 36
50 51 51 51 51 51 51 51 51 51 51 51 51 51 51 51 51 51 50
50 51 51 51 51 51 51 51 51 51 51 51 51 51 51 51 51 51 0 50

50 51 51 51 51 51 51 51 51 51 51 51 51 51 51 51 51 51 0 0 50
45 65 66 65 65 65 66 65 51 52 51 52 51 54 68 68 68 68 48 48 48 34
44 65 65 65 66 65 66 65 51 51 51 52 51 53 68 68 68 67 48 48 48 2 34

PILLOK

LETDIE1

FEWORK

SPANKING

NATCRIME

NATEDUC

NATHEAL

NATENVIR

NATDRUG

GRASS

NATCITY

REGION

LIFE

SIZE

GUNLAW

When a variable is paired with a variable from one of the other sets, roughly two-thirds
of the cases are mismatched. For example, 34% of the gunlaw values and 38% of the

grass values are missing—yet, when paired together, 68% of the cases have either gun-
law or grass missing, but not both.

Identifying nonrandom patterns with t tests. As in Example 2, we pivot the results of the

separate variances two-sample t tests into layers displaying the panel of t statistics alone
(drag the statistics icon into the Layer tray). In addition, we transpose the rows and col-
umns for a better fit on the page. Thus, the pattern variables that form groups for the two-

36 Chapter 2, Example 3

sample t tests are columns and the measures tested, the rows. The panel shown here has
already been pivoted into layers and transposed.

t

Separate Variance t Tests

CHILDS

AGE

EDUC

DEGREE

PADEG

MADEG

SEX

INCOME91

RINCOM91

SIZE

VOTE92

POLVIEWS

NATENVIR

NATHEAL

NATCITY

NATCRIME

NATDRUG

NATEDUC

CAPPUN

GUNLAW

GRASS

LIFE

SATHOBBY

DRINK

FEWORK

PILLOK

SPANKING

LETDIE1

NEWS

TVHOURS

BIGBAND

BLUGRASS

COUNTRY

BLUES

MUSICALS

CLASSICL

FOLK

JAZZ

OPERA

RAP

HVYMETAL

ATTSPRTS

VISITART

TVSHOWS

TVNEWS

TVPBS

PARTNERS

SEXFREQ

SEI

SIZE

RINCOM91

1.3 -2.2 -1.7 -2.3 -1.8 -1.4 -1.5 -1.4 -.8 -1.4 -.8 -.5 1. 2 1.6 2.2 1.6 1.8

-6.7

3.5 -1.8 -1.7 -2.9 -1.9 -2.1 -1.9 -.4 -.1 .3 -1.0 -.3 -.5 -1.3 -.2 -.4 -.2

-15.9

-.4 1.3 .7 2.2 .6 .5 .8 .5 .6 .1 1.2 .8 -.2 -. 1 -.9 -.1 -.8

12.0

.0 1.0 .8 2.2 .7 .6 .7 .5 .8 -.1 .8 .5 .2 -.1 -.6 .5 -.3

11.4

-2.9 3.0 3.0

6.2

-1.8 2.0 1.8 2.5 1.9 1.7 1.6 1.2 -.9 .9 -.2 -.4 .3 .0 -.1 .5 -.1

6.3

-.3 -2.4 -1.7 -2.9 -2.3 -2.0 -1.9 -.5 1.8 .0 1.9 2.2 -2.8 -2.1 -2.1 -2.7 -2.4

-6.6

.3 -.3 -.5 .6 -.2 -.4 -.4 -.2 1.0 .0 1.3 1.3 -.8 -1.5 -1.3 -.9 -1.3

12.6

. 1.5 1.2 .9 2.0 1.2 .7 1.3 .9 .3 1.1 -.3 .0 -1.1 -1.9 -1.6 -.5 -1.3

1.8 . .6 .9 1.1 1.0 .8 .4 .6 -.6 .5 .2 .1 -.6 -.4 -.3 -1.0 -.4

-2.4 -1.0 -.1 .2 -1.0 -.6 .4 .1 -2.1 -.3 -1.8 .3 .5 .0 .3 .5 .6 1.0

-3.3 1.5 .0 .1 .3 .3 .1 .2 -.7 1.3 -.6 .9 .9 -.7 .0 -.5 -.8 -.4

2.2 . -.6 -1.4 .5 -2.1 -.9 -.7 -.8 -.8 -1.1 -.8 1.2 .6 1.5 1.6 1.6

-4.4

-2.8 .5 -.2 . .3 3.2 -.9 -.6 .5 -.2 .2 -.7 -.4 .1 -.5 -.1 .3 -.1

-1.0 1.1 -.5 -.6 . -.1 -1.2 -.7 -.8 .7 -.6 .9 1.0 -.6 -.5 -.3 -.5 -.4

-.2 -.8 -.6 -1.2 .4 . -.7 -.1 2.6 -.2 2.1 -.8 -.7 -1.6 -1.5 -1.5 -1.2 -1.8

1.6 .2 -1.4 -1.4 -.9 -.7 . -.1 .5 .6 .5 .5 .6 -1.6 -1.8 -1.2 -1.2 -1.2

-3.0 -.3 -2.1 -.4 -.9 -1.3 -2.7 . -. 1 -2.0 -.1 -1.8 -1.7 1.7 1.2 2.1 1.6 1.7

-1.4 -1.3 -.4 -.7 -.8 -.8 -.7 -.6 -1.4 1.1 -1.4 1.0 .9 .4 1.0 .7 .7 .6

-1.1 1.2 3.2 3.0 2.6 3.2 3.3 3.1 . 1.0 -.1 .3 .6 -.6 .2 -.5 -.3 -.5

-2.7 3.2 -1.1 -1.4 -1.6 -1.4 -1.2 -1.2 -.2 . .0

.2 -.9 -1.1 -.2 -.8 -1.3 -.7 2.8 -.3 . -.3 -.6 .7 .5 .6 .5 .6

4.8

-3.3 -2.5 1.1 1.3 1.8 1.0 1.7 1.1

.3 -1.6 -1.7 -2.0 -1.4 -1.8 -1.5 .0 1.7 .4

-6.4

1.8 -1.8 -1.8 -1.5 -1.8 -1.9 -1.9 .4 -.3 .4 -.7 -.3 . -.3 .1 .5 -.2

-4.7

1.5 -2.4 -2.2 -2.1 -2.6 -2.5 -2.6 -1.1 1.5 -.9 .6 1.0 -.2 . 1.0 -2.1 -2.3

-3.8

1.8 1.1 1.4 1.2 1.8 1.1 1.2 1.4 -1.6 1.8 -1.8 1.9 1.8 1.8 -.6 . -1.0

2.5 -.2 -.2 -.4 -.1 -.2 -.5 2.0 -1.9 2.5 -2.4 -2.4 -.9 .4 -.3 . .0

-3.8

-1.2 1.8 -.3 .0 -1.3 .0 .6 .0 -1.0 .8 -.9 .7 .9 -1.8 -.2 .7 .0 .

-.4 -.6 -.9 -1.2 -.7 -.5 -1.2 -.3 -.8 -.3 -.5 -.6 .8 .8 .9 .6 .9

-9.3

2.6 -2.0 .6 .6 .3 .5 1.0 1.1 -. 7 .1 -.8 -.2 -.1 1.0 .5 1.1 1.3 .9

.4 -2.1 -1.2 -.5 -.4 -1.1 -1.1 -1.0 -.3 1.0 -.6 1.3 1.5 -1.5 -1.0 -.9 -.7 -1.0

.5 -2.1 1.1 1. 4 1.1 .8 .9 .9 -.1 .3 -.2 .7 .8 -1.0 -.7 -.6 .2 -.7

.9 -1.8 -1.9 -2.4 -2.0 -1.8 -1.9 -1.5 -.9 -1.3 -.8 -.7 1.6 1.2 2. 3 1.8 2.1

-3.6

-.4 -.6 .0 -.4 -.1 .0 .0 -.1 -1.0 -.4 -1.0 -.3 -.2 .9 1.1 1.6 1.9 1.3

-2.6 -.5 -.4 -.7 -.6 -.2 -.3 -.4 -.7 -.7 -.6 -.8 -.9 1.0 .7 1.8 1.5 1.5

-.6 -2.3 -.6 -.3 .5 -.4 -.4 -.3 -1.9 .5 -1.8 1.5 1.4 -.1 -.2 .4 .5 .4

.6 -1.4 -1.2 -2.0 -1.6 -1.6 -1.0 -.2 -1.0 .2 -1.8 -1.5 1.4 1.0 1.7 1.4 1.4

-4.4

1.5 -.2 1.0 .9 1.0 1.2 1. 2 1.0 -.7 -.7 -.6 -1.1 -1.0 1. 7 1.2 2.0 2.0 1.7

-.8 -1.2 -.2 -.5 -.5 -.1 -.4 -.7 -.4 1.1 -.7 .9 .8 .0 -.4 -.2 .1 -.1

1.8 .6 .7 .5 .9 .8 .6 1.7 .0 1.5 -.4 -.3 -1.4 -1.7 -1.2 -1.7 -1.2

-5.2

.0 -1.3 -1.1 -2.4 -1.4 -.9 -1.1 .1 .0 .4 -.5 .0 -1.2 -1.2 -.8 -.9 -. 8

-9.5

1.4 -1.2 -1.4 -2.3 -1.1 -.9 -1.4 -1.0 -.3 -.7 -.4 -.3 .4 .4 1.3 .5 .9

-6.3

.4 .9 -.3 .4 -.1 -.2 -.2 .4 2.2 .8 2.6 .2 .7

3.0 .1 -1.2 -.3 -.7 -.9 -.3 -.4 -.4 -.6 .1 -.5 -.4 -.3 .3 .2 .0 .2

1.1 .8 .2 .0 -.7 .6 .6 .6 .1 -.4 .5 -.6 -.4 -.7 -.5 .1 -.3 -.2

-3.0 2.1 1.7 1.9 1.5 1.9 1.9 -. 5 .1 -.5 .3 .0 .8 1.1 .9 1.2 .7

8.9

-2.2 1.9 1.1 2.1 1.6 1.7 1.7 -2.5 1.0 -2.7 2.1 1.6 1.5 1.9 1.4 1. 7 1.2

11.8

.9 -.3 -.5 .5 -.5 -.9 -.5 .8 .8 .5 .7 .6 -.5 -1.1 -.8 .1 -.8

6.8

NATCITY

NATHEAL

NATENVIR

NATCRIME

3.2 3.1 3.0 .6 -1.0 .4 -.9 -1.0 1.2 1.3 1. 1 1.3 .9

3.8

NATDRUG

NATEDUC

GUNLAW

-3.6

GRASS

.2

-3.8

LIFE

DRINK

FEWORK

SATHOBBY

. -.1 -.1 .2 -.4 .0

-16.5

. . 3.0

. -1.1 -.5 -.3 -1.0 -. 7

-4.2

-3.7

PILLOK

SPANKING

3.4 2.8

3.5

-3.3 -3.5 -3.1

LETDIE1

NEWS

3.7

4.0

-3.5

Missing Data 37

RI NCOM9 1

presentmissi ng

AGE

90

70

50

30

10

The most extreme t value is –16.5 for the grass item split into groups based on the
pattern of sathobby (the respondents satisfaction with nonworking activities, or hob­bies). In the full table with all layers displayed (not shown), we find that only eight cases
have values of sathobby missing when grass is present; so we do not pursue this relation
further. These variables belong to the same subset identified above and, if missing, tend
to be missing together.

The tests based on the pattern of rincom91 (respondent’s income on the 1991–93 sur­veys) are more interesting. The t statistics are sizable for more than 20 items, including
income91 (total family income from all sources). See Figure 2.5 for boxplots of four of
these distributions: age, education, income, and political views grouped by the pattern
of rincom91.

Figure 2.5 Boxplots of age, education, family income, and political views grouped by the

pattern of rincom91

25

20

15

EDUC

10

5

0

presentmissing

RINC OM91

25

20

15

10

INCOME91

5

0

presentmissi ng

RI NCOM9 1

8

7

6

5

4

3

POLVIEW S

2

1

0

presentmis sing

RINC OM91

The 34% of the respondents for whom rincom91 is missing tend to be older, have less
education, have a lower total family income, and are more conservative (low values of

polviews indicate liberal political views) than the 66% who do report rincom91. If
rincom91 is crosstabulated against wrkstat (this variable’s eight codes define job status),
more than 80% of the respondents with missing rincom91 values report they are retired,
in school, or a homemaker.

38 Chapter 2, Example 3

A Look at Multiple Missing Value Codes

When the pattern variable has a few distinct categories, it is easy to use SPSS’s boxplots
to compare distributions of a measure within valid categories against those for one or
more types of missing values.

In the previous two-sample t tests, each pattern variable had to have at least 20% of
its values missing. Lowering this cutoff to the default value of 5%, would add the big
band and heavy metal music items as pattern variables. The two-sample t statistics for
testing differences in average age for the groups formed by the two patterns are respec­tively, –6.95 and 6.24. The average age for the 163 subjects with missing big band
values is 37.9 years; the average age for the 77 people with missing heavy metal values
is 60.4 years. The variables bigband and hvymetal have two missing value codes: 8 for
don’t know much and 9 for no answer. Figure 2.6 and Figure 2.7 examine the age distri­bution within each of these missing value categories.

Figure 2.6 People who “don’t know much” about big band music are younger

100

80

582
591

709

1089

894651
704

9665901467

530

425554

159

436
1349420

60

40

20

0

Age of Respondent

Like very much

Like it

Mixed feelings

Dislike very much

Dislike it

Don’t know much

1215152216268544252N =

NA

Bigband Music

In both Figure 2.6 and Figure 2.7, the age distribution of the few subjects with no answer
(NA) differs from that for the don’t know much group.

Missing Data 39

Figure 2.7 People who “don’t know much” about heavy metal music are older

100

333

80

60

40

20

0

Age of Respondent

346

323

1246

381

Like very much

Like it

1349
1056

929
11121096
115
411464

Mixed feelings

407744
189
1139
1379

948
1478
956

1148
474

Dislike very much

Dislike it

106771736517511645N =

NA

Don’t know much

Heavy Metal Music

The Missing Value feature for crosstabulating pattern variables against categorical vari­ables is useful for studying relationships among categories with different missing value
codes. Here we define polviews (Where do you place yourself on a scale of political
views ranging from Extremely liberal to Extremely conservative?) as a categorical vari-
able and show how the categories relate to selected patterns. To produce the output, we
specify:

Descriptives...

Indicator Variable Statistics
; Crosstabulation of categorical and indicator variables
Omit variables missing less than 5% of cases

The pattern variables include cappun (Do you favor or oppose the death penalty for per­sons convicted of murder?), letdie1 (If a person is in an advanced stage of a terminal ill-
ness, should doctors be allowed to end the patient’s life if he and his family request it?),
and the respondent’s preference for big band and heavy metal music.

40 Chapter 2, Example 3

Overall, 7.1% of the respondents answered that they don’t know about capital punish­ment, but this response is spread unevenly across the seven categories. Almost 10% of the
moderates say they don’t know, while the percentages for those in the three liberal and
three conservative categories are collectively closer to 5%. Among those who don’t know
(DK) where they belong on the political scale, 18.8% also don’t know where they stand
regarding capital punishment (this is considerably higher than the overall 7.1% rate).

POLVIEWS

CAPPUN

LETDIE1

BIGBAND

HVYMETAL

Present

Missing

Present

Missing

Present

Missing

Present

Missing

Count
Percent
% DK
% NA
Count
Percent
% NAP
% DK
% NA
Count
Percent
% Don’t know
% NA
Count
Percent
% Don’t know
% NA

Total

1388 29 152 184 473 238 228 39 39 6

92.5 96.7 93.3 95.3 89.8 96.0 94.6 95.1 81.3 66.7

7.1 3.3 5.5 4.7 9.9 3.6 5.4 4.9 18.8 22.2
.4 .0 1.2 .0 .4 .4 .0 .0 .0 11.1

956 22 103 125 344 161 148 26 25 2

63.7 73.3 63.2 64.8 65.3 64.9 61.4 63.4 52.1 22.2

32.3 26.7 35.6 32.1 29.4 33.1 34.4 31.7 41.7 44.4

3.7 .0 1.2 3.1 4.9 2.0 4.1 4.9 6.3 11.1
.3 .0 .0 .0 .4 .0 .0 .0 .0 22.2

1337 25 145 167 465 227 224 39 40 5

89.1 83.3 89.0 86.5 88.2 91.5 92.9 95.1 83.3 55.6

10.1 13.3 10.4 13.0 11.6 8.1 6.2 4.9 12.5 11.1
.8 3.3 .6 .5 .2 .4 .8 .0 4.2 33.3

1423 28 160 182 508 238 229 38 35 5

94.9 93.3 98.2 94.3 96.4 96.0 95.0 92.7 72.9 55.6

4.5 3.3 1.2 5.2 3.6 3.6 4.6 7.3 22.9 11.1
.7 3.3 .6 .5 .0 .4 .4 .0 4.2 33.3

Extremely liberal

Liberal

Slightly liberal

Moderate

Conservative

Slightly conservative

In the Extremely liberal and Liberal categories, there are fewer folks (0.0% and 1.2%)
who are uncertain (DK) about euthanasia than there are in the conservative groups (4.1%
and 4.9%). With respect to big band music, there is a linear decrease in the percentage
answering don’t know across the seven political categories (13.3%, 10.4%, 13%, 11.6%,

8.1%, 6.2%, and 4.9%)—conservatives are less apt to report that they don’t know about
big band music. The opposite is true for heavy metal music.

Missing

Extremely conservative

DK

NA

Example 4:
Estimating Means, Standard Deviations, Covariances, and Correlations

In the Missing Value procedure, the user can choose to estimate means, standard devia­tions, covariances, and correlations using listwise (complete cases only), pairwise, EM,
and/or regression methods. The Missing Value procedure also provides all values esti­mates of means and standard deviations plus several options for the EM and regression
methods. When more than one method is requested, the estimates of the means are dis­played in one summary panel, and the estimates of the standard deviations are displayed
in another (see p. 46).

Over the years, many software users approached the missing data problem by using
a pairwise complete method to compute a covariance or correlation matrix and then
using this matrix as input for, say, a factor analysis. However, such a matrix may have
eigenvalues less than 0, and some correlations may be computed from substantially dif­ferent subsets of the cases. Other analysts use EM (expectation-maximization) or
regression methods to estimate statistics or to impute data (estimate replacement
values). Simulation studies indicate that pairwise estimates are often more distorted than
estimates obtained via the EM method. In most algorithms, they are simply the first iter­ation of the EM method. A few analysts use multiple imputation, a computationally
complex method that is not commonly available. For a variation of this method, see
“Multiple Imputation” on p. 59.

Missing Data 41

Listwise method. This method uses complete cases only. That is, if among the variables

you select as quantitative or categorical there are one or more values missing, the case
is omitted from the computations.

Pairwise method. Estimates are computed separately for each pair of variables, using all

cases that have both values.

EM method. For the EM procedure, a distribution is assumed for the partially missing

data, and inferences are based on the likelihood under that distribution. Each iteration
consists of an E step and an M step. The E step finds the conditional expectation of the
“missing” data, given the observed values and current estimates of the parameters.
These expectations are then substituted for the “missing” data. In the M step, maximum
likelihood estimates of the parameters are computed as though the missing data had been
filled in. “Missing” is enclosed in quotation marks because the missing values are not
being directly filled, but, rather, functions of them are used in the log-likelihood.

By default for the EM method, the Missing Value procedure assumes that the data
follow a normal distribution. If you know that the tails of the distributions are longer
than those of a normal distribution, you can request that a t distribution with n degrees
of freedom be used in constructing the likelihood function (n is specified by the user).
A second option also provides a distribution with longer tails. You specify the ratio of
standard deviations of a mixed normal distribution and the mixture proportion of the two

42 Chapter 2, Example 4

distributions. This assumes that only the standard deviations of the distributions differ,
not the means.

The default is to use all variables on the Quantitative Variables list in the Missing
Value Analysis dialog box for estimation. However, in the Variables for EM and
Regression dialog box, you can specify that specific variables are predictor variables or
predicted variables. Of course, a given variable can be in both lists, but there are situa­tions in which you might want to restrict the use of a variable. For example, some
analysts are uncomfortable estimating values of outcome variables. Or, if, for each sub­ject, you have a set of items that are nurses’ ratings and another set that are doctors’
ratings, you may want to make one run using the nurses’ items to estimate missing
nurses’ items and another run for estimates of the doctors’ items.

Regression method. To estimate means, standard deviations, covariances, or correla-

tions, the regression method computes multiple linear regression estimates and has op­tions for augmenting the estimates with random components. To each predicted value,
the Missing Value procedure can add a residual from a randomly selected complete case,
a random normal (0, RMS) deviate, or a random deviate (scaled by the square root of
the residual mean square) from the t distribution with n degrees of freedom (the user can
specify n or use the default value of 5). To add nothing, select
dialog box. The default is to add a randomly selected residual. However, if the number
of complete cases is less than half the total sample size, a normal deviate is added.

All quantitative variables specified as predictors are available as candidates for esti­mation (see the discussion of the EM method about use of variables). In addition, since
in multiple regression the use of a large subset of independent variables can produce
poorer predicted values than a smaller subset, a variable must achieve an F-to-enter limit
of 4.0 to be used. This limit can be changed with syntax.

None in the Regression

Assumptions. If data are missing completely at random (called MCAR by Little and

Rubin), complete cases, pairwise, EM, and regression methods give consistent and un­biased estimates of correlations and covariances. The pairwise, EM, and regression
methods may still provide good estimates if the data are conditionally missing at
random (MAR). For example, in a study of education and income, the subjects with
low education may have more missing income values. If education is MCAR and if,
for a given level of education, income is MCAR, pairwise, EM, and regression meth­ods may still give good estimates. In other words, for MAR, the probability that in­come is recorded depends on the subject’s level of education, so the probability may
vary by education but not by income within that level of education. Besides MCAR
and MAR patterns, the probability that income is present could vary by the value of
income within each level of education (for example, people with high incomes don’t
report them). The last situation is not an unusual pattern for real-world applications,
but, alas, current methods are not appropriate.

Missing Data 43

If the data are MAR and the assumption that the distributions are normal, mixed nor­mal, or t with specific degrees of freedom is met, the EM methods yield maximum
likelihood estimates of means, standard deviations, covariances, and correlations. Be
sure to check the data for outliers and to determine whether symmetrizing transforma­tions are required.

Roderick J. A. Little’s chi-square statistic for testing whether values are missing
completely at random is printed with EM matrices (see p. 48). The separate variances
two-sample t tests introduced in Example 2 are also useful for identifying departures
from randomness. However, be aware that while a sizable t statistic does indicate a
departure from randomness, a small t may be no confirmation that values are missing
randomly (see the discussion with Figure 2.9). Sadly, there is no magic test for MAR.

In this example, we continue to use the world95m data used in Example 2, now
requesting estimates of statistics. Even though we established that values are nonran­domly missing, we request listwise (complete cases) estimates so that they can be
compared later with estimates obtained by the pairwise, EM, and regression methods.
Estimates of means and standard deviations obtained by using all available data for each
variable are displayed automatically.

To produce this output, from the menus choose:

Statistics

Missing Value Analysis...

 Quantitative Variables: urban, lifeexpf, lifeexpm, literacy, pop_incr, babymort,

calories, birth_rt, death_rt, log_gdp, lg_aidsr, b_to_d, fertilty, log_pop, lit_male,
lit_fema, log_den

 Categorical Variables: region2, religion, climate

 Case Labels: country

Estimation

; Listwise
; Pairwise
; EM
; Regression

Pairwise means and standard deviations. If a variable has missing data, how much do

means and standard deviations of other variables change when the incomplete cases are
omitted from the sample? The following panels display estimates of means and standard
deviations and also provide additional information about how the pattern of missing
values of one variable relates to that of other variables.

44 Chapter 2, Example 4

Pairwise Means

URBAN
LIFEEXPF
LIFEEXPM
LITERACY
POP_INCR
BABYMORT
CALORIES
BIRTH_RT
DEATH_RT
LOG_GDP
LG_AIDSR
B_TO_D
FERTILTY
LOG_POP
LIT_MALE
LIT_FEMA
LOG_DEN
REGION2
RELIGION
CLIMATE

URBAN

LIFEEXPF

LITERACY

POP_INCR

BABYMORT

56.5

70.1 78.3 1.70 42.6 2742 26.0 9.5 3.418 1.39 3.22 3.6 4.115 67.3 1.781

56.5

56.5 70.2 78.3 1.68 42.3 2754 25.9 9.6 3.422 1.38 3.20 3.6 4.114 67.3 1.784

57.0 70.1

56.5 70.2 78.3

56.5 70.2 78.3 1.68

54.7 68.8 75.5 1.82 47.0

56.5 70.2 78.3 1.68 42.3 2754

56.4 70.1 78.2 1.69 42.7 2754 26.0

56.5 70.2 78.3 1.68 42.3 2754 25.9 9.6

56.6 70.0 78.0 1.70 43.0 2754 26.2 9.6 3.417

56.4 70.1 78.2 1.69 42.7 2754 26.0 9.6 3.418 1.38

56.6 70.0 78.1 1.70 42.9 2754 26.1 9.6 3.417 1.38 3.21

56.5 70.2 78.3 1.68 42.3 2754 25.9 9.6 3.422 1.38 3.20 3.6

53.2 67.8 73.6 1.99 51.3 2589 29.0 9.6 3.245 1.34 3.58 3.9 4.142 67.3 1.779

53.2 67.8 73.6 1.99 51.3 2589 29.0 9.6 3.245 1.34 3.58 3.9 4.142

56.5 70.2 78.3 1.68 42.3 2754 25.9 9.6 3.422 1.38 3.20 3.6 4.114 67.3

56.2 70.0 78.0 1.70 43.0 2731 26.1 9.6 3.405 1.36 3.23 3.6 4.099 66.9 1.800

56.6 70.2 78.4 1.67 42.3 2754 25.8 9.6 3.421 1.38 3.19 3.6 4.109 67.3 1.786

56.3 70.0 78.0 1.69 42.8 2754 26.0 9.6 3.415 1.39 3.20 3.6 4.117 66.9 1.772

78.3 1.68 42.3 2754 25.9 9.6 3.422 1.38 3.20 3.6 4.114 67.3 1.784

70.2

1.68 42.7 2742 25.9 9.6 3.413 1.39 3.18 3.6 4.123 67.3 1.789

78.3

42.3 2754 25.9 9.6 3.422 1.38 3.20 3.6 4.114 67.3 1.784

1.68

2754 25.9 9.6 3.422 1.38 3.20 3.6 4.114 67.3 1.784

42.3
2754

BIRTH_RT

CALORIES

27.5 9.9 3.350 1.55 3.26 3.8 4.219 62.1 1.698

25.9

LOG_GDP

DEATH_RT

9.6 3.422 1.38 3.20 3.6 4.114 67.3 1.784

3.418 1.38 3.20 3.6 4.112 67.3 1.775

9.6

1.38 3.20 3.6 4.114 67.3 1.784

3.422

1.38

B_TO_D

FERTILTY

LG_AIDSR

3.21 3.6 4.119 66.9 1.772

3.20

LOG_POP

3.6 4.112 67.3 1.775

4.116 67.3 1.773

3.6

4.114

LIT_FEMA

67.3 1.784

1.779

67.3

1.784

In the Pairwise Means display, the mean of each column variable is reported for the
cases in which the row variable is present (lifeexpm and lit_male are not shown). The
means in which all available values are used are highlighted if you choose
the Edit menu, then choose

Scripts, and select MVA_Table_MOUT_MEAN_Create before

Options on

you run the analysis. While means are computed only for quantitative variables, the
row variables can be quantitative or categorical. Canada and the United States are the
only countries for which region2 has missing codes. Thus, in the

REGION2 row of the

table, when these two countries are omitted from the sample, the mean of urban drops
from 56.5% to 56.2%, average female life expectancy (lifeexpf) drops from 70.2 years
to 70 years, the average literacy rate drops from 78.3% to 78%, etc. The average of all
infant mortality values (babymort) is 42.3. Using only the babymort values where cal-
ories is also present, the mean increases to 47. For the subsample of countries that re­port both female literacy and infant mortality, the average infant mortality is even
greater, 51.3.

LOG_DEN

Pairwise Standard Deviations

Missing Data 45

URBAN
LIFEEXPF
LIFEEXPM
LITERACY
POP_INCR
BABYMORT
CALORIES
BIRTH_RT
DEATH_RT
LOG_GDP
LG_AIDSR
B_TO_D
FERTILTY
LOG_POP
LIT_MALE
LIT_FEMA
LOG_DEN
REGION2
RELIGION
CLIMATE

URBAN

LIFEEXPF

LITERACY

POP_INCR

BABYMORT

24.2

10.6 22.9 1.19 38.1 562 12.4 4.27 .621 .711 2.13 1.90 .657 28.6 .626

24.2 10.6 22.9 1.20 38.1 568 12.4 4.25 .620 .709 2.12 1.90 .654 28.6 .624

24.2 10.6 22.9 1.20 38.1 568 12.4 4.25 .620 .709 2.12 1.90 .654 28.6 .624

23.9 10.7 22.9 1.19 38.3 562 12.3 4.27 .623 .714 2.08 1.89 .655 28.6 .623

24.2 10.6 22.9 1.20 38.1 568 12.4 4.25 .620 .709 2.12 1.90 .654 28.6 .624

24.2 10.6 22.9 1.20 38.1 568 12.4 4.25 .620 .709 2.12 1.90 .654 28.6 .624

25.1 11.4 23.1 1.14 38.7 568 12.5 4.45 .664 .693 2.10 1.94 .623 27.0 .610

24.2 10.6 22.9 1.20 38.1 568 12.4 4.25 .620 .709 2.12 1.90 .654 28.6 .624

24.3 10.6 23.0 1.20 38.1 568 12.4 4.25 .622 .709 2.12 1.90 .657 28.6 .619

24.2 10.6 22.9 1.20 38.1 568 12.4 4.25 .620 .709 2.12 1.90 .654 28.6 .624

24.4 10.7 23.1 1.21 38.3 568 12.4 4.27 .627 .709 2.14 1.91 .661 28.6 .625

24.3 10.6 23.0 1.20 38.1 568 12.4 4.25 .622 .709 2.12 1.90 .657 28.6 .619

24.3 10.6 23.1 1.20 38.2 568 12.4 4.26 .624 .709 2.13 1.90 .659 28.6 .622

24.2 10.6 22.9 1.20 38.1 568 12.4 4.25 .620 .709 2.12 1.90 .654 28.6 .624

24.2 10.7 23.3 1.11 38.3 516 11.9 4.70 .571 .765 2.12 1.88 .671 28.6 .619

24.2 10.7 23.3 1.11 38.3 516 11.9 4.70 .571 .765 2.12 1.88 .671 28.6 .619

24.2 10.6 22.9 1.20 38.1 568 12.4 4.25 .620 .709 2.12 1.90 .654 28.6 .624

24.3 10.6 23.0 1.20 38.1 558 12.4 4.29 .613 .700 2.13 1.91 .647 28.6 .615

24.3 10.6 23.0 1.20 38.3 568 12.4 4.27 .623 .713 2.13 1.91 .655 28.6 .626

24.4 10.6 23.0 1.21 38.2 568 12.4 4.26 .624 .708 2.13 1.91 .658 28.6 .621

CALORIES

BIRTH_RT

DEATH_RT

LOG_GDP

LG_AIDSR

B_TO_D

FERTILTY

LIT_FEMA

LOG_POP

LOG_DEN

The table of Pairwise Standard Deviations has the same structure as that for Pairwise
Means. Using all available values, the standard deviation for urban is 24.2; restricting
the sample to only those countries that also have values of calories, the standard devia­tion increases to 25.1.

Summary panels of mean and standard deviation estimates. Following are the default

summary panels of means and standard deviations computed using the listwise, all
values, EM, and regression methods. (Results are displayed for requested methods
only.)

46 Chapter 2, Example 4

Summary of Estimates of Means

Listwise

All Values

EM

Regression

URBAN

LIFEEXPF

LITERACY

POP_INCR

BABYMORT

49.3 65.6 69.1 2.23 58.6 2570 31.8 9.9 3.107 1.503 3.81 4.3 4.217 61.5 1.665

56.5 70.2 78.3 1.68 42.3 2754 25.9 9.6 3.422 1.380 3.20 3.6 4.114 67.3 1.784

56.6 70.2 78.4 1.68 42.3 2804 25.9 9.5 3.422 1.377 3.20 3.5 4.114 72.6 1.784

56.9 70.2 78.5 1.68 42.3 2808 25.9 9.5 3.422 1.369 3.20 3.5 4.114 72.1 1.784

BIRTH_RT

CALORIES

DEATH_RT

LOG_GDP

B_TO_D

FERTILTY

LOG_POP

LG_AIDSR

LIT_FEMA

As might be expected, since values are not missing randomly, the listwise estimates
stand apart from the others. For urban, the listwise estimate is 49.3%, and for the other
methods, the estimates are over 56%; for literacy, the listwise estimate is 69.1%, and for
the other methods, the estimates are over 78%; for infant mortality, the listwise estimate
is 58.6, and for the other methods, the estimates are under 43, and so on. For most of the
variables, the all values, EM, and regression estimates agree fairly well. However, for
calories and lit_fema, the variables with the most values missing, the EM and regression
estimates are slightly larger than the all values estimates.

Summary of Estimates of Standard Deviations

Listwise

All Values

EM

Regression

URBAN

LIFEEXPF

LITERACY

POP_INCR

BABYMORT

25.2 11.0 22.2 .955 36.7 500.2 11.0 5.0 .542 .745 2.085 1.84 .639 26.85 .617

24.2 10.6 22.9 1.20 38.1 567.8 12.4 4.3 .620 .709 2.125 1.90 .654 28.61 .624

24.2 10.6 22.8 1.20 38.1 538.3 12.4 4.2 .620 .707 2.117 1.90 .654 28.03 .624

24.3 10.6 22.7 1.20 38.1 544.0 12.4 4.2 .620 .709 2.116 1.90 .654 27.76 .624

BIRTH_RT

CALORIES

DEATH_RT

LOG_GDP

B_TO_D

FERTILTY

LOG_POP

LG_AIDSR

LIT_FEMA

LOG_DEN

LOG_DEN

As is true for the previous panel of mean estimates, the listwise estimates shown here
differ considerably from the others. The all values, EM, and regression estimates for cal­ories and female literacy fluctuate a little, but there is no definite pattern (that is, neither
the EM nor regression estimates appear to reduce the spread more than the other). A re­gression estimate without random augmentation would undesirably reduce the variance.

Estimates of correlations. By default, when you request the listwise, pairwise, EM,

and/or regression methods, the Missing Value procedure, for each method, prints three
pivot tables: a panel of means, the covariance matrix, and the correlation matrix. In this
section, we omit the means and covariances and display the correlation matrices for the
four methods requested.

Listwise Correlations

Missing Data 47

URBAN
LIFEEXPF
LIFEEXPM
LITERACY
POP_INCR
BABYMORT
CALORIES
BIRTH_RT
DEATH_RT
LOG_GDP
LG_AIDSR
B_TO_D
FERTILTY
LOG_POP
LIT_MALE
LIT_FEMA
LOG_DEN

URBAN
LIFEEXPF
LIFEEXPM
LITERACY
POP_INCR
BABYMORT
CALORIES
BIRTH_RT
DEATH_RT
LOG_GDP
LG_AIDSR
B_TO_D
FERTILTY
LOG_POP
LIT_MALE
LIT_FEMA
LOG_DEN

URBAN

LIFEEXPF

1.00
.74 1.00
.71 .99 1.00
.61 .82 .78 1.00

-.17 -.38 -.31 -.55 1.00

-.70 -.95 -.93 -.89 .40 1.00
.67 .71 .70 .56 -.37 -.69 1.00

-.56 -.81 -.77 -.82 .77 .80 -.64 1.00

-.59 -.85 -.87 -.62 .01 .77 -.45 .55 1.00
.79 .76 .73 .63 -.33 -.74 .79 -.66 -.52 1.00

-.13 -.30 -.37 -.01 -.13 .15 -.24 .14 .50 -.04 1.00
.28 .30 .35 .07 .68 -.26 .08 .17 -.58 .13 -.31 1.00

-.52 -.78 -.74 -.81 .75 .78 -.57 .97 .57 -.57 .16 .13 1.00

-.18 .00 .02 .04 -.27 .03 .08 -.18 -.07 -.23 -.34 -.25 -.21 1.00
.59 .75 .72 .94 -.53 -.80 .56 -.75 -.55 .57 -.09 .05 -.75 .15 1.00
.63 .81 .77 .96 -.57 -.85 .53 -.80 -.59 .59 -.03 .06 -.81 .07 .96 1.00

-.22 .01 .03 .01 -.22 -.05 .00 -.15 .01 -.21 -.18 -.08 -.15 .30 .11 .08 1.00

URBAN

LIFEEXPF

1.00
.74 1.00
.73 .98 1.00
.65 .87 .81 1.00

-.37 -.58 -.50 -.70 1.00

-.72 -.96 -.94 -.90 .60 1.00
.69 .78 .77 .68 -.61 -.78 1.00

-.63 -.86 -.80 -.87 .86 .87 -.76 1.00

-.48 -.70 -.74 -.49 -.04 .63 -.35 .37 1.00
.75 .83 .80 .73 -.56 -.82 .85 -.77 -.40 1.00

-.06 -.15 -.17 -.01 -.07 .04 -.07 .05 .34 .06 1.00

-.03 -.09 -.01 -.27 .80 .12 -.24 .48 -.51 -.21 -.22 1.00

-.62 -.84 -.78 -.87 .84 .83 -.70 .98 .40 -.69 .07 .45 1.00

-.14 -.09 -.08 -.05 -.08 .11 .05 -.03 .01 -.22 -.21 -.15 -.06 1.00
.59 .78 .72 .95 -.62 -.81 .58 -.79 -.49 .61 -.14 -.15 -.80 .08 1.00
.61 .82 .74 .97 -.64 -.84 .55 -.83 -.51 .63 -.10 -.15 -.84 .00 .96 1.00
.02 .13 .15 .08 -.25 -.15 .05 -.22 -.06 .00 -.14 -.11 -.22 .14 .14 .11 1.00

LITERACY

LIFEEXPM

LITERACY

LIFEEXPM

POP_INCR

POP_INCR

CALORIES

BABYMORT

Pairwise Correlations

CALORIES

BABYMORT

BIRTH_RT

BIRTH_RT

DEATH_RT

DEATH_RT

LOG_GDP

LOG_GDP

B_TO_D

LG_AIDSR

LG_AIDSR

FERTILTY

B_TO_D

FERTILTY

LIT_MALE

LOG_POP

LOG_POP

LIT_MALE

LIT_FEMA

LIT_FEMA

LOG_DEN

LOG_DEN

48 Chapter 2, Example 4

BIRTH_RT

DEATH_RT

a

B_TO_D

FERTILTY

LOG_POP

LIT_MALE

LOG_GDP

LG_AIDSR

LIT_FEMA

EM Correlations

URBAN

LIFEEXPF

URBAN
LIFEEXPF
LIFEEXPM
LITERACY
POP_INCR
BABYMORT
CALORIES
BIRTH_RT
DEATH_RT
LOG_GDP
LG_AIDSR
B_TO_D
FERTILTY
LOG_POP
LIT_MALE
LIT_FEMA
LOG_DEN

a.

Little’s MCAR test: Chisquare=157.252, df=108, Prob=.001

1.00
.74 1.00
.73 .98 1.00
.65 .86 .81 1.00

-.38 -.58 -.50 -.70 1.00

-.72 -.96 -.94 -.90 .60 1.00
.66 .75 .74 .64 -.58 -.76 1.00

-.63 -.86 -.80 -.87 .86 .87 -.74 1.00

-.48 -.70 -.74 -.47 -.04 .63 -.32 .37 1.00
.75 .83 .80 .73 -.56 -.82 .81 -.77 -.40 1.00

-.06 -.15 -.17 -.02 -.06 .05 -.08 .05 .34 .06 1.00

-.04 -.09 -.01 -.28 .80 .12 -.26 .48 -.51 -.21 -.22 1.00

-.61 -.84 -.79 -.86 .84 .83 -.67 .98 .40 -.69 .07 .45 1.00

-.14 -.09 -.08 -.04 -.08 .11 .00 -.03 .01 -.22 -.20 -.15 -.06 1.00
.63 .80 .75 .95 -.68 -.83 .64 -.82 -.41 .67 -.06 -.31 -.82 .07 1.00
.65 .84 .78 .97 -.70 -.86 .60 -.86 -.43 .68 -.03 -.31 -.86 .01 .96 1.00
.02 .13 .15 .09 -.25 -.15 .10 -.22 -.07 .00 -.14 -.11 -.23 .14 .16 .14 1.00

LITERACY

LIFEEXPM

POP_INCR

BABYMORT

CALORIES

Little’s chi-square test for missing completely at random is printed with EM results.
Here, the chi-square is 157.3 (df =108 and p value = 0.001), agreeing with the nonran­dom pattern of missing values identified in the displays above.

When the regression method of estimation is requested and the number of complete
cases is less than half the total number of cases, the Missing Value procedure augments
each estimated value with a normal deviate instead of the residual from a randomly
selected complete case. For these data, 53% of the cases are complete, and we would be
more comfortable if more cases were complete. In the next section, we will examine the
element-by-element differences between correlation matrices estimated with regression
methods using random normal deviates and random residuals.

LOG_DEN

Missing Data 49

Regression Correlations

URBAN

LIFEEXPF

LIFEEXPM

LITERACY

POP_INCR

BABYMORT

CALORIES

BIRTH_RT

URBAN
LIFEEXPF
LIFEEXPM
LITERACY
POP_INCR
BABYMORT
CALORIES
BIRTH_RT
DEATH_RT
LOG_GDP
LG_AIDSR
B_TO_D
FERTILTY
LOG_POP
LIT_MALE
LIT_FEMA
LOG_DEN

Residual of randomly picked case added to each estimate.a.

1.00
.74 1.00
.73 .98 1.00
.64 .87 .81 1.00

-.38 -.58 -.50 -.69 1.00

-.72 -.96 -.94 -.90 .60 1.00
.65 .76 .76 .62 -.54 -.76 1.00

-.63 -.86 -.80 -.86 .86 .87 -.73 1.00

-.48 -.70 -.74 -.48 -.04 .63 -.37 .37 1.00
.75 .83 .80 .73 -.56 -.82 .82 -.77 -.40 1.00

-.08 -.15 -.18 -.03 -.06 .05 -.07 .06 .34 .05 1.00

-.05 -.09 -.01 -.27 .80 .12 -.21 .48 -.51 -.21 -.22 1.00

-.61 -.84 -.79 -.85 .84 .83 -.67 .98 .40 -.69 .08 .46 1.00

-.14 -.09 -.08 -.05 -.08 .11 .00 -.03 .01 -.22 -.21 -.15 -.05 1.00
.57 .78 .73 .92 -.64 -.80 .56 -.78 -.43 .63 -.08 -.26 -.78 .05 1.00
.63 .83 .77 .96 -.69 -.84 .57 -.84 -.44 .67 -.03 -.29 -.85 .00 .96 1.00
.02 .13 .15 .09 -.25 -.15 .07 -.22 -.07 .00 -.15 -.11 -.23 .14 .13 .12 1.00

DEATH_RT

Comparing Estimates of Covariance and Correlation Matrices

a

LOG_GDP

LG_AIDSR

B_TO_D

FERTILTY

LOG_POP

LIT_MALE

LIT_FEMA

LOG_DEN

In a large study, it is difficult to compare two correlation matrices for differences (or to
determine whether they differ at all). We saved four correlation matrices shown above
and also a matrix of regression estimates augmented with random normal deviates. We
used SPSS’s MATRIX procedure to compute the difference between elements in each
pair of matrices.

50 Chapter 2, Example 4

You may not need to do this, but following are the steps we took to accomplish the task:

• In the Output Navigator, click on the first matrix to select it.

• To remove row and column labels choose:

Utilities

Run Script...

; Remove labels.sbs (or remlabel.sbs)

Click Run.

• Open the Syntax Editor:

File

New

Syntax

• Return to the Output Navigator and click and hold the matrix, and drag it to the open
Syntax Editor.

• Type the following syntax before the matrix:

MATRIX DATA VARIABLES = urban, lifeexpf, lifeexpm, literacy, pop_incr,
babymort, calories, birth_rt, death_rt,
log_gdp, lg_aidsr, b_to_d, fertility,
log_pop, lit_male, lit_fema, log_den.
BEGIN DATA.

• Type the following syntax after the matrix:

END DATA.
SAVE OUTFILE=corr_list.sav.

• Repeat the above steps for one or more other matrices, entering a SAVE command
after each. For example,

SAVE OUTFILE=corr_em.sav.
SAVE OUTFILE=corr_resid.sav.
SAVE OUTFILE=corr_norm.sav.

• After the last SAVE command, add syntax for the MATRIX procedure:

MATRIX.
GET list / FILE=corr_list.sav.
GET em / FILE=corr_em.sav.
GET resid / FILE=corr_resid.sav.
GET norm / FILE=corr_norm.sav.

PRINT (list - em) / FORMAT=’F4.2’ / TITLE="List - EM".
PRINT (resid - norm) / FORMAT=’F4.2’ / TITLE="Resid - Norm".

END MATRIX.

Missing Data 51

The matrix of element-by-element differences between the correlation matrices estimat­ed by the listwise and EM methods is displayed in Figure 2.8. (Two columns of zeros are
deleted.) The order of variables is the same as that in the preceding correlation matrices.
For example, differences for variables correlated with calories are in the seventh row and
the seventh column. Differences between correlations involving log_den are in the last
row, and those correlated with male and female literacy are in the two rows preceding
log_den. Babymort is in the sixth row and column.

Figure 2.8 Differences between listwise and EM estimates of correlations

.00

–.01 .00
–.02 .01 .00
–.04 –.04 –.03 .00

.20 .20 .20 .14 .00
.02 .01 .01 .01 –.20 .00
.01 – .05 –.04 –.08 .22 .07 .00
.07 .05 .04 .05 –.09 –.06 .10 .00

–.11–.16 –.13 –.15 .05 .14 –.13 .18 .00

.03 – .07 –.07 –.10 .22 .09 –.03 .11 –.11 .00

–.06 –.15 –.20 .01 –.07 .10 –.16 .09 .16 –.10 .00

.32 .39 .36 .35 –.11
.08 .05 .04 .05 –.09 –.06 .11–.01 .17 .12 .09 –.32 .00

–.04 .09 .10 .09 –.19 –.07 .08 –.16–.09 –.01 –.14 –.09 –.15 .00
–.04 –.05 –.03 –.01 .15 .02 –.07 .07 –.15–.10 –.02 .36 .07 .08 .00
–.03 –.03 –.01 –.01 .14 .00 –.07 .05 –.16–.10 .00 .36 .05 .07 –.01 .00
–.24 –.11 –.12 –.08 .03 .11 –.10 .07 .08 –.21–.04 .03 .08 .16 –.06 –.05 .00

babymort

–.38 .34 –.32 –.07 .34 –.10 .00

b_to_d

As might be expected, since values are not missing randomly, the estimates differ mark­edly, especially for b_to_d, the ratio of births to deaths, in the twelfth row and column.
For example, the listwise estimate of the correlation between b_to_d and babymort is

–0.26; the EM estimate is 0.12—making a difference of –0.38 (the pairwise and regres-

sion estimates are also 0.12). The data for babymort are complete; for b_to_d, one case
is missing. In the earlier search for nonrandom patterns, b_to_d was not noticed. The
plots in Figure 2.9 provide another view.

52 Chapter 2, Example 4

Figure 2.9 Scatterplots highlighting the pattern of listwise missing

4000

3000

2000

1000

0

Daily calorie intake

Birth to death ratio

LIST_PAT

1614121086420

200

150

100

50

present

missing listwise

Infant mortality (deaths per 1000 live births)

0

Birth to death ratio

LIST_PAT

1614121086420

In the plot on the left, we arbitrarily assigned 1000 to the values of calories that are miss-
ing (they fall below the horizontal line). It is easy to see that the distribution of b_to_d
values that exists when calories is missing differs little from that marked by X’s above
the line. Now look at the cluster of filled circles at the top of the plot—these are the
values of calories and b_to_d omitted by listwise deletion. They certainly are not a ran­dom subsample from the bivariate distribution of babymort and b_to_d. In the plot on
the right, the complete data for the pair (x’s) and those omitted by listwise deletion are
shown. If we add a line-of-best-fit to each group, the line for the missing listwise cases
has a positive slope, while that for the complete pairs has a negative slope.

Most of the differences (not shown) between correlations estimated by the EM and

pairwise methods are 0 except for the rows and columns involving correlations with cal­ories and the male and female literacy rates. Where differences exist, they are smaller
than those in Figure 2.8. The differences for correlations between b_to_d and the male
and female literacy rates (0.15) are two times as large as any other difference in the
matrix. All other differences involving b_to_d are 0 or 0.01.

The only differences (not shown) between correlations estimated by 1) EM and

regression with random residuals and 2) EM and regression with random normal vari­ates involve calories and the male and female literacy rates. Thus, it is not surprising to
see in Figure 2.10 that the differences between correlation estimates computed via the
two regression methods are small. We are unable to say which estimates are best
because we do not know the underlying truth. The values are gone. The only thing we
can conclude is that the listwise estimates are the worst because the data clearly are not
missing randomly. In the next example, we will examine values imputed via the differ­ent methods.

present

missing listwise

Missing Data 53

Figure 2.10 Differences between regression estimates augmented with random residuals and

.00
.00 .00
.00 .00 .00
.01 .00 .00 .00

–.01 .00 .00 .00 .00

.00 .00 .00 .00 .00 .00
.01 – .02 –.02 –.02 .02 .02 .00

–.01 .00 .00 .00 .00 .00 .02 .00

.01 .00 .00 .00 .00 .00 .00 .00 .00
.00 .00 .00 –.01 .00 .00 –.02 .00 .00 .00
.00 .02 .02 .02 –.02 –.02 –.06 –.02–.02 .01 .00

–.01 .00 .00 –.01 .00 .00 .02 .00 .00 .00 –.01 .00
–.01 .00 .00 –.01 .00 .00 .03 .00 .00 .00 –.03 .00 .00

.00 .00 .00 .01 .00 .00 .00 .00 .00 .00 .00 .00 .00 .00

–.05 .01 .01 .01 .03 –.01 .01 .02 –.03 .04 .05 .03 .02 –.01 .00

.01 .00 .01 .00 –.02 –.01 .00 –.01 .02 .02 .03 –.03 –.02 .00 –.03 .00
.00 .00 .00 .01 .00 .00 .02 .00 .00 .00 .03 .00 .00 .00 –.01 .01 .00

those with random normal deviates

babymort

Example 5:
Estimating Replacement Values: Imputation

The Missing Value procedure provides EM and regression methods for estimating (im­puting) replacement values, but this should not be done until the data have been screened
for recording errors and variables in need of a symmetrizing transformation.

To save the filled-in data, select
box when you specify the estimation procedure (estimation is described in Example 4).
In one run, you can save a file with completed data from an EM method and another file
from a regression method but not more than one file from a single method. For the exam­ples in this section, we use data files saved from the default EM and regression methods
described in the last example.

Values in the world95m data are not randomly missing (we’re sure that they are not
missing completely at random and also have doubts about satisfying the MAR condi­tion). So, how good are the imputed values? In this section, we display some plots that
you might create when evaluating your own filled-in data. You can:

• Display the variables with the most values missing in a pair of bivariate scatterplots
with the same plot scales—one using the observed data only and the other using the
imputed values. For our example, we use calories and lit_fema.

• For the same variable, plot the imputed values from one method against those from
another. For female literacy, we plot imputed values from the regression method with
random residuals against those from the EM method.

• Using knowledge of the subject matter, design displays that highlight the presence of
the observed and imputed values.

b_to_d

Save completed data in the EM or Regression dialog

54 Chapter 2, Example 5

Generating pattern variables. In the plots that follow, pattern variables are used as case

selection variables to group and identify observed and imputed values. To generate
pattern variables for calories and female literacy, we use
menu with its MISSING function to form two 0,1 variables (the values for each new
variable are 0 for missing and 1 for present). The SPSS statements for doing this are
pat_calr = 1 – MISSING(calories) and pat_litf = 1 – MISSING(lit_fema).

We also generate a third pattern variable that combines the missing/present informa­tion for calories and female literacy by specifying pat_both = 10*pat_calr + pat_litf.
The result of this transformation is four codes: 0, 1, 10, and 11. For example, if, for a
case, both values are present (pat_calr and pat_litf are both 1), the value of the new vari­able pat_both is 10*1 + 1 or 11. When only female literacy is missing, the code for
pat_both is 10; when only calories is missing, the code is 1; and when values of both
variables are missing, the code is 0.

Compute on the Transform

Scatterplots of observed and imputed values. In some plots below, we use

Select Cases

on the Data menu to select countries (cases) in which values of both calories and female
literacy are present (pat_both = 11), and in other plots, countries in which one variable
is missing or both are missing (pat_both is less than 11).

Following are some of the chart features we use (click on the graph and choose

Chart Object

• To set minimum and maximum limits, increments, and grids, use

on the Edit menu to access the Chart Editor):

Axis on the Chart

SPSS

menu in the Chart Editor.

• To set the position of a reference line, select

Reference Line on the Chart menu. For

literacy, we add a line at 100% to see how many imputed values fall above the valid

range.

• To select distinct symbols for cases missing literacy only, calories only, and both
variables, click on a plot point in the first group, select the
Editor toolbar, select the symbol and plot size you want, and, finally, select

Apply All. Then, repeat the selections for each group.

Marker button on the Chart

Apply, not

The observed values of female literacy and calories are plotted in the left frame in Figure

2.11. They are, of course, the same for both imputation methods.

Figure 2.11 Observed and imputed values of calories and female literacy

Missing Data 55

120

100

80

60

40

20

Ethiopia

0

Females who read (%)

Daily calorie intake

Boliv ia

Bots w ana

Chile

Ir aq

Australia

Singapore

Kuw ait

Libya

Egy p t

Spain

USA

Greece

400035003000250020001500

120

100

80

60

40

20

0

Females who read (%)

Daily calorie intake

400035003000250020001500

Values imputed via the EM method are displayed in the right frame in Figure 2.11. No­tice that the plot scales are the same, and when female literacy is missing (dark squares),
its imputed values tend to be high. Some of these imputed values even fall above 100%.
In Figure 0.5, by adding country names to identify these countries, we find Japan, UK,
and Germany.

Figure 2.12 EM imputed values with country names

120

UK

Germany

Lebanon

Morocco

Japan

Bosnia

U.Arab Em.

Syr ia

Portugal

Ireland

PAT_BOTH

400035003000250020001500

lit miss ing

cal missing

both missing

100

80

60

40

20

0

Females who read (%)

Daily calorie intake

Gambia

Af ghanistan

Uz be ki st an

PAT_BOTH

lit miss ing

cal missing

both missing

56 Chapter 2, Example 5

Values imputed by the regression method are plotted in Figure 2.13. Iceland’s estimated
female literacy is considerably above 100%.

Figure 2.13 Values imputed by the regression method

120

100

80

60

40

20

0

Females who read (%)

Daily calorie intake

400035003000250020001500

120

100

80

60

40

Gambia

20

0

Females who read (%)

Daily calorie intake

Uzbekistan

Afghanistan

South Africa

Bosnia

Lebanon

Morocco

Pakistan

Japan

Oman

Iceland

UK

Germany

France

Norway

U.Arab Em.

Syria

Portugal

Hong Kong

Israel

400035003000250020001500

Comparing values imputed by the EM and regression methods. In Figure 2.14, for female

literacy, values imputed by the EM method are compared with those imputed by the re­gression method with random residuals. The Add Variables dialog box under

Merge Files

on the Data menu was used to merge the two files of imputed values side-by-side.

Ideally, the plot points should fall along a line connecting the intersection of grid

lines for the same percentage (for example, 80% for EM with 80% for regression).
When both calories and female literacy are estimated (the plot symbol X marks Oman,
Bosnia, South Africa, and Iceland), the regression estimates tend to be higher than the
EM estimates. The points with estimated literacy values (small dark squares) are clus­tered together, making it difficult to identify them.

PAT_BOTH

lit missing

cal missing

both missing

Figure 2.14 EM and regression imputed values for female literacy

Missing Data 57

120

100

80

60

40

20

0

Female literacy via random residuals

Female literacy via EM

Oman

South Af rica

Bosnia

Iceland

Japa n

Nor w ay

120100806040200

120

110

100

90

Portugal

80

Female literacy via random residuals

Female literacy via EM

Iceland

Croatia

Cuba

Austria

Germany

Finland

Sw itzerland

Japan

France

Netherlands

UK

1201101009080

On the right side in Figure 2.14, we zoom in on this area of the plot, finding that the largest
discrepancies between the methods are for Iceland and the Netherlands. Iceland’s x-y plot
coordinates are (91%, 114%) and the Netherlands’ are (103%, 89%).

In Figure 2.15, we compare imputed values for calories. The regression filled-in

value for Israel is almost 700 calories larger than the EM value (3908 calories versus

3223). In general, when there is a difference, the regression estimates tend to be higher
more often than they are lower.

Figure 2.15 EM and regression imputed values for calories

Bahrain

Bosnia

Israel

Poland

Russia

Lithuania

Belarus

Estonia

Sw itzerland

Ireland

PAT_BOTH

400035003000250020001500

lit miss ing

cal missing

both missing

4000

3500

3000

2500

2000

1500

Calories via random residuals

Af ghanistan

Uzbekistan

Gambia

Calories via EM

Paki s ta n

Lebanon

PAT_BOTH

lit miss ing

cal missing

both missing

58 Chapter 2, Example 5

Using the subject matter to design displays. In Example 1 and Example 2, it was noted that

the pattern of missing data varied by geographical region. Neither imputation method
makes an adjustment for these subpopulation differences. The left frame in Figure 2.16 is a
scatterplot of the observed female literacy values (open circles) and the EM imputed values
(filled squares) against the code for geographical region (code 1 is Europe, ..., code 6 is

Latin America).

Figure 2.16 Observed and imputed values of female literacy and calories grouped by region

120

Netherlands

100

80

60

40

20

0

Females who read (%)

geographical region

Bosn ia

South Af rica

PAT_LITF

present

missing

76543210

4000

3500

3000

2500

2000

1500

Daily calo rie inta ke

geographical region

Bosnia

Hong Kong

South Af rica

Uzbekistan

PAT_CALR

present

missing

76543210

Instead of female literacy, observed and imputed values of calories are displayed in the
right frame in Figure 2.16. The estimate for Hong Kong is much higher than the observed
values in the Pacific/Asia group (code 3). Visually, Hong Kong looks as though it might
be a member of the European region (code 1). This is not as unreasonable as it might
seem at first, because Hong Kong’s infant mortality rate, female life expectancy, GDP per
capita, and high proportion of people living in cities are like those of European countries.

Figure 2.17 Female literacy versus literacy

120

Missing Data 59

100

80

60

40

20

0

Females who read (%)

People who read (%)

Nicaragua

Oman

Botswana

Bahrain

Ireland

PAT_BOTH

both present

lit missing

cal missing

both missing

120100806040200

Another internal cross-check is to compare observed and imputed values of female lit­eracy with the overall literacy rate (it has only two values missing). Look at Botswana
in Figure 2.17, where neither value is imputed. The original data screening was not
thorough enough. Several sources report that the literacy rate for this older and more
prosperous country among countries in Africa is 72% or 74%. Where did the value of
16% for female literacy come from? Is it a recording error? Did someone use total pop­ulation size when computing the rate instead of the number of females? Also, does the
presence of this outlier distort the other estimates?

Multiple Imputation

Multiple imputation is a technique that replaces each missing or deficient value with two
or more values simulated from a suitable distribution. Options with the regression method
that incorporate randomness allow you to perform a variation of multiple imputation. In
the Missing Value procedure, imputed data values can be augmented with a random nor­mal (0, RMS) deviate, a random t scaled by the square root of RMS (with 5 or a user­specified degrees of freedom), or a residual randomly selected from another case.

Multiple imputation is accomplished by generating m, say 7, data files via the regres­sion method (the seed for the random number generator changes for each file) and
performing the desired statistical analysis (for example, regression) with each com­pleted data set. The final estimate of each parameter is the average of the respective
estimates from the individual runs, and the multiple imputation estimate of the covari­ance matrix is the sum of the pooled within components plus a between component
obtained from deviations between the final parameter estimate and the individual
estimates.

Syntax Reference

MVA

MVA [VARIABLES=] {varlist}
{ALL }

[/CATEGORICAL=varlist]

**

[/MAXCAT={25
{n }

[/ID=varname]

Description:

[/NOUNIVARIATE]

[/TTEST [PERCENT={5}] [{T }] [{DF } [{PROB }] [{COUNTS }] [{MEANS }]]
{n} {NOT} {NODF} {NOPROB}] {NOCOUNTS} {NOMEANS}

[/CROSSTAB [PERCENT={5}]]
{n}

[/MISMATCH [PERCENT={5}] [NOSORT]]
{n}

[/DPATTERN [SORT=varname[({ASCENDING })] [varname ... ]]
{DESCENDING}
[DESCRIBE=varlist]]

[/MPATTERN [NOSORT] [DESCRIBE=varlist]]

[/TPATTERN [NOSORT] [DESCRIBE=varlist] [PERCENT={1}]]
{n}

}]

Estimation:

[/LISTWISE]

[/PAIRWISE]

[/EM [predicted_varlist] [WITH predictor_varlist]
[([TOLERANCE={0.001} ]
{value}
[CONVERGENCE={0.0001}]
{value }
[ITERATIONS={25} ]
{n }
[TDF=n ]
[LAMBDA=a ]
[PROPORTION=b ]
[OUTFILE=’file’ ])]

63

64 MVA

[/REGRESSION [predicted_varlist] [WITH predictor_varlist]
[([TOLERANCE={0.001} ]

{n }
[FLIMIT={4.0} ]
{N }
[NPREDICTORS=number_of_predictor_variables]
[ADDTYPE={RESIDUAL*} ]
{NORMAL }
{T[({5}) }
{n}
{NONE }
[OUTFILE=’file’ ])]]

* If the number of complete cases is less than half the number of cases, the default ADDTYPE specification
is NORMAL.

** Default if the subcommand is omitted.

Examples:

MVA VARIABLES=populatn density urban religion lifeexpf region
/CATEGORICAL=region
/ID=country
/MPATTERN DESCRIBE=region religion.

MVA VARIABLES=all
/EM males msport WITH males msport gradrate facratio.

Overview

MVA (Missing Value Analysis) describes the missing value patterns in a data file (data ma-

trix). It can estimate the means, the covariance matrix, and the correlation matrix by using
listwise, pairwise, regression, and EM estimation methods. Missing values themselves can
be estimated (imputed), and you can then save the new data file.

Options

Categorical variables. String variables are automatically defined as categorical. For a long

string variable, only the first eight characters are used to define categories. Quantitative vari­ables can be designated as categorical by using the

MAXCAT specifies the maximum number of categories for any categorical variable. If any

categorical variable has more than the specified number of distinct values,

CATEGORICAL subcommand.

MVA is not executed.

Analyzing patterns. For each quantitative variable, the TTEST subcommand produces a series

of t tests. Values of the quantitative variable are divided into two groups, based on the pres­ence or absence of other variables. These pairs of groups are compared using the t test.

Crosstabulating categorical varia bles. The CROSSTAB subcommand produces a table for each

categorical variable, showing, for each category, how many nonmissing values are in the oth­er variables and the percentages of each type of missing value.

Displaying patterns. DPATTERN displays a case-by-case data pattern with codes for system-

missing, user-missing, and extreme values.
missing values and sorts by the pattern formed by missing values.

MPATTERN displays only the cases that have

TPATTERN tabulates the

cases that have a common pattern of missing values. The pattern tables have sorting options.
Also, descriptive variables can be specified.

Labeling cases. For pattern tables, an ID variable can be specified to label cases.
Suppression of rows. To shorten tables, the PERCENT keyword suppresses missing value pat-

terns that occur relatively infrequently.

Statistics. Displays of univariate, listwise, and pairwise statistics are available.
Estimation. EM and REGRESSION use different algorithms to supply estimates of missing

values, which are used in calculating estimates of the mean vector, the covariance matrix,
and the correlation matrix of dependent variables. The estimates can be saved as replace­ments for missing values in a new data file.

Basic Specification

The basic specification depends on whether you want to describe the missing data pattern or
estimate statistics. Often, description is done first, and then, considering the results, an esti­mation is done. Alternatively, both description and estimation can be done by using the same

MVA command.

Descriptive analysis. A basic descriptive specification includes a list of variables and a statis-

tics or pattern subcommand. For example, a list of variables and the subcommand
would show missing value patterns for all cases with respect to the list of variables.

Estimation. A basic estimation specification includes a variable list and an estimation method.

For example, if the EM method is specified, SPSS estimates the mean vector, the covariance
matrix, and the correlation matrix of quantitative variables with missing values.

MVA 65

DPATTERN

Syntax Rules

• A variables specification is required directly after the command name. The specification
can be either a variable list or the keyword

• The

CATEGORICAL, MAXCAT, and ID subcommands, if used, must be placed after the vari-

ables list and before any other subcommand. These three subcommands can be in any order.

• Any combination of description and estimation subcommands can be specified. For exam­ple, both the

EM and REGRESSION subcommands can be specified in one MVA command.

• Univariate statistics are displayed unless the
Thus, if only a list of variables is specified, with no description or estimation subcom­mands, univariate statistics are displayed.

• If a subcommand is specified more than once, only the last one is honored.

• The following words are reserved as keywords or internal commands in the

dure:

VARI ABLES, SORT, NOSORT, DESCRIBE, and WITH. They cannot be used as vari-

able names in

MVA.

• The tables Summary of Estimated Means and Summary of Estimated Standard Deviations
are produced if you specify more than one way to estimate means and standard deviations.
The methods include univariate (default), listwise, pairwise, EM, and regression. For ex­ample, these tables are produced when you specify both

ALL.

NOUNIVARIATE subcommand is specified.

LISTWISE and EM.

MVA proce-

66 MVA

Symbols

The symbols displayed in the DPATTERN and MPATTERN table cells are:

+ Extremely high value

- Extremely low value

S System-missing value

A First type of user-missing value

B Second type of user-missing value

C Third type of user-missing value

• An extremely high value is more than 1.5 times the interquartile range above the 75th per-

centile, if , where n is the number of cases.

number of variables()nn150000≤log×

• An extremely low value is more than 1.5 times the interquartile range below the 25th per-

centile, if , where n is the number of cases.

• For larger files—that is, —extreme values are

number of variables()nn150000≤log×

number of variables()nn150000>log×

two standard deviations from the mean.

Missing Indicator Variables

For each variable in the VA RIA BLE S list, a binary indicator variable is formed (internal to

MVA), indicating whether a value is present or missing.

VARIABLES Subcommand

A list of variables or the keyword ALL is required.

• The order in which the variables are listed determines the default order in the output.

• The keyword

• If the keyword

VAR IAB LES is optional.

ALL is used, the default order is the order of variables in the working data

file.

• String variables specified in the variable list, whether short or long, are automatically de-

fined as categorical. For a long string variable, only the first eight characters of the values
are used to distinguish categories.

• The list of variables must precede all other subcommands.

• Multiple lists of variables are not allowed.

CATEGORICAL Subcommand

The MVA procedure automatically treats all string variables in the variables list as categorical.
You can designate numeric variables as categorical by listing them on the
subcommand. If a variable is designated categorical, it will be ignored if listed as a depen­dent or independent variable on the

REGRESSION or EM subcommand.

CATEGORICAL

MAXCAT Subcommand

The MAXCAT subcommand sets the upper limit of the number of distinct values that each cat-
egorical variable in the analysis can have. The default is 25. This limit affects string variables
in the variables list and also the categorical variables defined by the
mand. A large number of categories can slow the analysis considerably. If any categorical
variable violates this limit,

MVA does not run.

Example

MVA VARIABLES=populatn density urban religion lifeexpf region
/CATEGORICAL=region
/MAXCAT=30
/MPATTERN.

• The CATEGORICAL subcommand specifies that region, a numeric variable, is categorical.
The variable

• The maximum number of categories in
distinct values,

religion, a string variable, is automatically categorical.

region or religion is 30. If either has more than 30

MVA produces only a warning.

• Missing data patterns are shown for those cases that have at least one missing value in the
specified variables.

• The summary table lists the number of missing and extreme values for each variable, in­cluding those with no missing values.

CATEGORICAL subcom-

MVA 67

ID Subcommand

The ID subcommand specifies a variable to label cases. These labels appear in the patterns
tables. Without this subcommand, the SPSS case numbers are used.

Example

MVA VARIABLES=populatn density urban religion lifeexpf region
/CATEGORICAL=region
/MAXCAT=20
/ID=country
/MPATTERN.

• The values of the variable country are used as case labels.

• Missing data patterns are shown for those cases that have at least one missing value in the

specified variables.

NOUNIVARIATE Subcommand

By default, MVA computes univariate statistics for each variable—the number of cases with
nonmissing values, the mean, the standard deviation, the number and percentage of missing
values, and the counts of extreme low and high values. (Means, standard deviations, and ex­treme value counts are not reported for categorical variables.)

• To suppress the univariate statistics, specify

NOUNIVARIATE.

68 MVA

Examples

MVA VARIABLES=populatn density urban religion lifeexpf region
/CATEGORICAL=region
/CROSSTAB PERCENT=0.

• Univariate statistics (number of cases, means, and standard deviations) are displayed for

populatn, density, urban, and lifeexpf. Also, the number of cases, counts and percentages of

missing values, and counts of extreme high and low values are displayed.

• The total number of cases and counts and percentages of missing values are displayed for

region and religion (a string variable).

• Separate crosstabulations are displayed for

MVA VARIABLES=populatn density urban religion lifeexpf region
/CATEGORICAL=region.
/NOUNIVARIATE
/CROSSTAB PERCENT=0.

region and religion.

• Only crosstabulations are displayed, no univariate statistics.

TTEST Subcommand

For each quantitative variable, a series of t tests is computed to test the difference of means
between two groups defined by a missing indicator variable for each of the other variables
(see “Missing Indicator Variables” on p. 66). For example, a t test is performed on
between two groups defined by whether their values are present or missing for calories. An­other t test is performed on

density are present or missing, and so on for the remainder of the variable list.

PERCENT=n Omit indicator variables with less than the specified percentage of

populatn for the two groups defined by whether their values for

missing values. You can specify a percentage from 0 to 100. The de­fault is 5, indicating the omission of any variable with less than 5%
missing values. If you specify 0, all rows are displayed.

populatn

Display of Statistics

The following statistics can be displayed for a t test:

• The t statistic, for comparing the means of two groups defined by whether the indicator

variable is coded as missing or nonmissing (see “Missing Indicator Variables” on p. 66).

T Display the t statistics. This is the default.
NOT Suppress the t statistics.

degrees of freedom associated with the t statistic.

• The

DF Display the degrees of freedom. This is the default.
NODF Suppress the degrees of freedom.

MVA 69

• The probability (two-tailed) associated with the t test, calculated for the variable tested
without reference to other variables. Care should be taken when interpreting this
probability.

PROB Display probabilities.
NOPROB Suppress probabilities. This is the default.

• The number of values in each group, where groups are defined by values coded as miss-
ing and present in the indicator variable.

COUNTS Display counts. This is the default.
NOCOUNTS Suppress counts.

• The means of the groups, where groups are defined by values coded as missing and
present in the indicator variable.

MEANS Display means. This is the default.
NOMEANS Suppress means.

Example

MVA VARIABLES=populatn density urban religion lifeexpf region
/CATEGORICAL=region
/ID=country
/TTEST.

• The TTEST subcommand produces a table of t tests. For each quantitative variable named
in the variables list, a t test is performed, comparing the mean of the values for which the
other variable is present against the mean of the values for which the other variable is
missing.

• The table displays default statistics, including values of t, degrees of freedom, counts, and
means.

CROSSTAB Subcommand

CROSSTAB produces a table for each categorical variable, showing the frequency and per-

centage of values present (nonmissing) and the percentage of missing values for each cate­gory as related to the other variables.

• No tables are produced if there are no categorical variables.

• Each categorical variable yields a table, whether it is a string variable assumed to be cat-

egorical or a numeric variable declared on the

• The categories of the categorical variable define the columns of the table.

• Each of the remaining variables defines several rows—one each for the number of values

present, the percentage of values present, and the percentage of system-missing values;
and one each for the percentage of values defined as each discrete type of user-missing (if
they are defined).

CATEGORICAL subcommand.

70 MVA

PERCENT=n Omit rows for variables with less than the specified percentage of

missing values. You can specify a percentage from 0 to 100. The de­fault is 5, indicating the omission of any variable with less than 5%
missing values. If you specify 0, all rows are displayed.

Example

MVA VARIABLES=age income91 childs jazz folk
/CATEGORICAL=jazz folk
/CROSSTAB PERCENT=0.

• A table of univariate statistics is displayed by default.

• In the output are two crosstabulations, one for

plays, for each category of

income91, childs, and folk. It also displays, for each category of jazz, the percentage of each

jazz, the number and percentage of present values for age,

jazz and one for folk. The table for jazz dis-

type of missing value (system-missing and user-missing) in the other variables. The sec­ond crosstabulation shows similar counts and percentages for each category of

• No rows are omitted, since

PERCENT=0.

MISMATCH Subcommand

MISMATCH produces a matrix showing percentages of cases for a pair of variables in which

one variable has a missing value and the other variable has a nonmissing value (a mismatch).
The diagonal elements are percentages of missing values for a single variable, while the off­diagonal elements are the percentage of mismatch of the indicator variables (see “Missing
Indicator Variables” on p. 66). Rows and columns are sorted on missing patterns.

PERCENT=n Omit patterns involving less than the specified percentage of cases.

You can specify a percentage from 0 to 100. The default is 5, indicat­ing the omission of any pattern found in less than 5% of the cases.

NOSORT Suppress sorting of the rows and columns. The order of the variables

in the variables list is used. If
order is that of the data file.

ALL was used in the variables list, the

folk.

DPATTERN Subcommand

DPATTERN lists the missing values and extreme values for each case symbolically. For a list

of the symbols used, see “Symbols” on p. 66.

By default, the cases are listed in the order in which they appear in the file. The following

keywords are available:

SORT=varname [(order)] Sort the cases according to the values of the named variables. You

can specify more than one variable for sorting. Each sort variable
can be in

ASCENDING.

DESCRIBE=varlist List values of each specified variable for each case.

ASCENDING or DESCENDING order. The default order is

Example

MVA VARIABLES=populatn density urban religion lifeexpf region
/CATEGORICAL=region
/ID=country
/DPATTERN DESCRIBE=region religion SORT=region.

• In the data pattern table, the variables form the columns, and each case, identified by its
country, defines a row.

• Missing and extreme values are indicated in the table, and, for each row, the number miss­ing and percentage of variables that have missing values are listed.

• The values of

• The cases are sorted by

region and religion are listed at the end of the row for each case.

region in ascending order.

• Univariate statistics are displayed.

MPATTERN Subcommand

The MPATTERN subcommand symbolically displays patterns of missing values for cases that
have missing values. The variables form the columns. Each case that has any missing values
in the specified variables forms a row. The rows are sorted by missing value patterns. For use
of symbols, see “Symbols” on p. 66.

• The rows are sorted to minimize the differences between missing patterns of consecutive
cases.

• The columns are also sorted according to missing patterns of the variables.

The following keywords are available:

NOSORT Suppress the sorting of variables. The order of the variables in the

variables list is used. If
that of the data file.

DESCRIBE=varlist List values of each specified variable for each case.

ALL was used in the variables list, the order is

MVA 71

Example

MVA VARIABLES=populatn density urban religion lifeexpf region
/CATEGORICAL=region
/ID=country
/MPATTERN DESCRIBE=region religion.

• A table of missing data patterns is produced.

region and the religion are named for each case listed.

• The

72 MVA

TPATTERN Subcommand

The TPATTERN subcommand displays a tabulated patterns table, which lists the frequency of
each missing value pattern. The variables in the variables list form the columns. Each pattern
of missing values forms a row, and the frequency of the pattern is displayed.

• An X is used to indicate a missing value.

• The rows are sorted to minimize the differences between missing patterns of consecutive

cases.

• The columns are sorted according to missing patterns of the variables.

The following keywords are available:

NOSORT Suppress the sorting of the columns. The order of the variables in the

variables list is used. If
that of the data file.

DESCRIBE=varlist Display values of variables for each pattern. Categories for each

named categorical variable form columns in which the number of each
pattern of missing values is tabulated. For quantitative variables, the
mean value is listed for the cases having the pattern.

PERCENT=n Omit patterns that describe fewer than 1% of the cases. You can spec-

ify a percentage from 0 to 100. The default is 1, indicating the omis­sion of any pattern representing less than 1% of the total cases. If you
specify 0, all patterns are displayed.

ALL was used in the variables list, the order is

Example

MVA VARIABLES=populatn density urban religion lifeexpf region
/CATEGORICAL=region
/TPATTERN NOSORT DESCRIBE=populatn region.

• Missing value patterns are tabulated. Each row displays a missing value pattern and the

number of cases having that pattern.

DESCRIBE causes the mean value of populatn to be listed for each pattern. For the categories

•

in

region, the frequency distribution is given for the cases having the pattern in each row.

LISTWISE Subcommand

For each quantitative variable in the variables list, the LISTWISE subcommand computes the
mean, the covariance between the variables, and the correlation between the variables. The
cases used in the computations are listwise nonmissing; that is, they have no missing value
in any variable listed in the

Example

MVA VARIABLES=populatn density urban religion lifeexpf region
/CATEGORICAL=region
/LISTWISE.

• Means, covariances, and correlations are displayed for populatn, density, urban, and lifeexpf.

Only cases that have values for all of these variables are used.

VAR IA BLES subcommand.

PAIRWISE Subcommand

For each pair of quantitative variables, the PAI RWISE subcommand computes the number of
pairwise nonmissing values, the pairwise means, the pairwise standard deviations, the pairwise
covariance, and the pairwise correlation matrices. These results are organized as matrices. The
cases used are all cases having nonmissing values for the pair of variables for which each com­putation is done.

Example

MVA VARIABLES=populatn density urban religion lifeexpf region
/CATEGORICAL=region
/PAIRWISE.

• Frequencies, means, standard deviations, covariances, and the correlations are displayed
for

populatn, density, urban, and lifeexpf. Each calculation uses all cases that have values

for both variables under consideration.

EM Subcommand

The EM subcommand uses an EM (expectation-maximization) algorithm to estimate the
means, the covariances, and the Pearson correlations of quantitative variables. This is an itera­tive process, which uses two steps for each iteration. The E step computes expected values con­ditional on the observed data and the current estimates of the parameters. The M step calculates
maximum likelihood estimates of the parameters based on values computed in the E step.

• If no variables are listed in the
tative variables in the variables list.

• If you want to limit the estimation to a subset of the variables in the list, specify a subset
of quantitative variables to be estimated after the subcommand name
list, after the keyword

WITH, the quantitative variables to be used in estimating.

• The output includes tables of means, correlations, and covariances.

• The estimation, by default, assumes that the data are normally distributed. However, you

can specify a multivariate t distribution with a specified number of degrees of freedom or
a mixed normal distribution with any mixture proportion (
dard deviation ratio (

LAMBDA).

• You can save a data file with the missing values filled in. You must specify a filename
and its complete path in single or double quotation marks.

• Criteria keywords and
parentheses.

The criteria for the

TOLERANCE=value Numerical accuracy control. The tolerance helps eliminate predictor

EM subcommand are as follows:

variables that are highly correlated with other predictor variables and
would reduce the accuracy of the matrix inversions involved in the cal­culations. The smaller the tolerance, the more inaccuracy is tolerated.
The default value is 0.001.

EM subcommand, estimates are performed for all quanti-

EM. You can also

PROPORTION) and any stan-

OUTFILE specifications must be enclosed in a single pair of

MVA 73

74 MVA

CONVERGENCE=value Convergence criterion. Determines when iteration ceases. If the rela-

tive change in the likelihood function is less than this value, conver­gence is assumed. The value of this ratio must be between 0 and 1. The
default value is 0.0001.

ITERATIONS=n Maximum number of iterations. Limits the number of iterations in the

EM algorithm. Iteration stops after this many iterations even if the
convergence criterion is not satisfied. The default value is 25.

Possible distribution assumptions:

TDF=n Student’s t distribution with n degrees of freedom. The degrees of free-

dom must be specified if you use this keyword. The degrees of free­dom must be an integer greater than or equal to 2.

LAMBDA=a Ratio of standard deviations of a mixed normal distribution. Any pos-

itive real number can be specified.

PROPORTION=b Mixture proportion of two normal distributions. Any real number be-

tween 0 and 1 can specify the mixture proportion of two normal
distributions.

The following keyword produces a new data file:

OUTFILE=’file’ Specify the name of the file to be saved. Missing values for predicted

variables in the file are filled in by using the EM algorithm. Specify the
complete path in single or double quotation marks.

Examples

MVA VARIABLES=males to tuition
/EM (OUTFILE=’c:\colleges\emdata.sav’).

• All variables on the variables list are included in the estimations.

• The output includes the means of the listed variables, a correlation matrix, and a covari-

ance matrix.

• A new data file named

MVA VARIABLES=all
/EM males msport WITH males msport gradrate facratio.

emdata.sav with imputed values is saved in the c:\colleges directory.

• For males and msport, the output includes a vector of means, a correlation matrix, and a

covariance matrix.

• The values in the tables are calculated using imputed values for

ing observations for

males, msport, gradrate, and facratio are used to impute the values that

males and msport. Exist-

are used to estimate the means, correlations, and covariances.

MVA VARIABLES=males to tuition
/EM verbal math WITH males msport gradrate facratio
(TDF=3 OUTFILE=’c:\colleges\emdata.sav’).

• The analysis uses a t distribution with three degrees of freedom.

• A new data file named

emdata.sav with imputed values is saved in the c:\colleges directory.

REGRESSION Subcommand

n 0=

The REGRESSION subcommand estimates missing values using multiple linear regression.
It can add a random component to the regression estimate. Output includes estimates of
means, a covariance matrix, and a correlation matrix of the variables specified as predicted.

• By default, all of the variables specified as predictors (after
but you can limit the number of predictors (independent variables) by

• Predicted and predictor variables, if specified, must be quantitative.

• By default,

REGRESSION adds the observed residuals of a randomly selected complete

case to the regression estimates. However, you can specify that the program add random
normal, t, or no variates instead. The normal and t distributions are properly scaled, and
the degrees of freedom can be specified for the t distribution.

• If the number of complete cases is less than half the total number of cases, the default

ADDTYPE is NORMAL instead of RESIDUAL.

• You can save a data file with the missing values filled in. You must specify a filename
and its complete path in single or double quotation marks.

• The criteria and

OUTFILE specifications for the REGRESSION subcommand must be en-

closed in a single pair of parentheses.

The criteria for the

TOLERANCE=value Numerical accuracy control. The tolerance helps eliminate predictor

REGRESSION subcommand are as follows:

variables that are highly correlated with other predictor variables and
would reduce the accuracy of the matrix inversions involved in the cal­culations. If a variable passes the tolerance criterion, it is eligible for
inclusion. The smaller the tolerance, the more inaccuracy is tolerated.
The default value is 0.001.

FLIMIT=n F-to-enter limit. The minimum value of the F statistic that a variable

must achieve in order to enter the regression estimation. You may
want to change this limit, depending on the number of variables and
the correlation structure of the data. The default value is 4.

NPREDICTORS=n Maximum number of predictor variables. This specification limits the

total number of predictors in the analysis. The analysis uses the step­wise selected n best predictors, entered in accordance with the toler­ance. If , it is equivalent to replacing each variable with its
mean.

WITH) are used in the estimation,

NPREDICTORS.

MVA 75

76 MVA

ADDTYPE Type of distribution from which the error term is randomly drawn.

Random errors can be added to the regression estimates before the
means, correlations, and covariances are calculated. You can specify
one of the following types:

RESIDUAL. Error terms are chosen randomly from the observed residu-

als of complete cases to be added to the regression estimates.

NORMAL. Error terms are randomly drawn from a distribution with the

expected value 0 and the standard deviation equal to the square root of
the mean squared error term (sometimes called the root mean
squared error, or RMSE) of the regression.

T(n). Error terms are randomly drawn from the t(n) distribution and

scaled by the RMSE. The degrees of freedom can be specified in pa­rentheses. If T is specified without a value, the default degrees of free­dom is 5.

NONE. Estimates are made from the regression model with no error

term added.

The following keyword produces a new data file:

OUTFILE Specify the name of the new data file to be saved. Missing values for

the dependent variables in the file are imputed (filled in) by using the
regression algorithm. Specify the complete path in single or double
quotation marks.

Examples

MVA VARIABLES=males to tuition
/REGRESSION (OUTFILE=’c:\colleges\regdata.sav’).

• All variables in the variables list are included in the estimations.

• The output includes the means of the listed variables, a correlation matrix, and a covari-

ance matrix.

• A new data file named

MVA VARIABLES=males to tuition
/REGRESSION males verbal math WITH males verbal math faculty
(ADDTYPE = T(7)).

regdata.sav with imputed values is saved in the c:\colleges directory.

• The output includes the means of the listed variables, a correlation matrix, and a covari-

ance matrix.

• A t distribution with 7 degrees of freedom is used to produce the randomly assigned ad-

ditions to the estimates.

Bibliography

Azen, S. P., M. Van Guilder, and M. A. Hill. 1989. Estimation of parameters and miss-

ing values under a regression model with nonnormally distributed and
nonrandomly incomplete data. Statistics in Medicine, 8: 217–228.

Dempster, A. P., N. M. Laird, and D. B. Rubin. 1977. Maximum likelihood from

incomplete data via the EM algorithm. Journal of the Royal Statistical Society B:
Methodological, 39: 1–38.

Hill, M. A., and W. J. Dixon. 1981. Missing data: Search for patterns. In Proceedings

of the Statistical Computing Section, 57–60. American Statistical Association.

Little, R. J. A., and D. B. Rubin. 1987. Statistical analysis with missing data. New

York: John Wiley and Sons.

Little, R. J. A.

for the Social and Behavioral Sciences, G. Arminger, C. C. Clogg, and M. E. Sobel, eds.
New York: Plenum Press.

Rubin, D. B. 1987. Multiple imputation for nonresponse in surveys. New York: John

Wiley and Sons.

, and N. Schenker. 1995. Missing data. In Handbook of Statistical Modeling

77

Subject Index

chi-square test

in Missing Value Analysis, 48

correlation estimates

comparing, 49

correlations

in Missing Value Analysis, 6, 7, 46

covariance

in Missing Value Analysis

, 6, 7, 46, 49

covariance estimates

comparing, 49

crosstabulations

in Missing Value Analysis

data files
data patterns

, 12

, 17

, 28, 39, 69

data sets

large

, 31

EM estimates

comparing with regression, 56

in Missing Value Analysis, 7, 41, 73
expectation maximization. See EM estimates
extreme value counts

in Missing Value Analysis

, 5

extreme values

in Missing Value Analysis

, 16, 31, 66

filling in data. See imputation
frequency tables

in Missing Value Analysis

, 5

General Social Survey. See GSS data
GSS data

, 12

imputation

in Missing Value Analysis, 53
multiple, 59

imputed values

, 12

incomplete data. See missing data indicator variables

in Missing Value Analysis

, 5

listwise deletion

in Missing Value Analysis

, 1

listwise estimation

in Missing Value Analysis, 41
Little’s chi-square test. See chi-square test
Little’s MCAR test

in Missing Value Analysis

, 1

MAR test

in Missing Value Analysis

, 42

MATRIX procedue, 49
MCAR test

in Missing Value Analysis

, 1, 42

mean

in Missing Value Analysis

pairwise

, 43

, 5, 6, 7, 16

mismatch

in Missing Value Analysis

, 5, 70

missing at random. See MAR test
missing completely at random. See MCAR test
missing data

casewise patterns

correlations

, 11–59

, 17

, 46

covariance, 46.49

crosstabulations

crosstbulations

, 39

, 28

EM estimation, 41

estimation

, 41

imputation, 53

listwise estimation

, 41

79

80 Subject Index

mismatched patterns, 23
multiple codes
pairwise estimation

, 38

, 41

pairwise mismatched patterns
regression estimation
summaries
surveys
t tests

, 45

, 29

, 24, 35

univariate statistics

missing data patterns

, 42

, 16, 31

, 14, 19

missing indicator variables

in Missing Value Analysis

Missing Value Analysis

descriptive statistics

, 1–9, 63–76

, 5

EM, 7
expectation-maximization
extreme values

, 66

missing indicator variables, 66

, 3

patterns
regression

, 6

saving imputed data, 74
summary tables
symbols

, 65

, 66

univariate statistics, 5

missing value codes

, 38

missing value patterns

in Missing Value Analysis

multiple imputation, 59

normal variates

in Missing Value Analysis

, 35

, 5, 66

, 8

, 70–72

, 6

pairwise standard deviations

in Missing Value Analysis

patterns of missing data

, 14

regression estimates

comparing with EM, 56
in Missing Value Analysis

residuals

in Missing Value Analysis

separate variance t tests

, 25

sorted casewise patterns

in Missing Value Analysis

sorting cases

in Missing Value Analysis

standard deviation

in Missing Value Analysis

Student’s t test

in Missing Value Analysis, 6

survey data

, 29

t tests

in Missing Value Analysis
separate variance

, 25

tabulated patterns

in Missing Value Analysis

tabulating cases

in Missing Value Analysis, 3

, 45

, 6, 42, 75

, 6

, 19

, 3

, 5, 16, 45

, 5, 24, 35, 68

, 20, 33

omitting patterns

in Missing Value Analysis

pairwise estimation

in Missing Value Analysis

pairwise frequencies

in Missing Value Analysis, 22

pairwise means

in Missing Value Analysis

pairwise mismatched patterns

in Missing Value Analysis, 23, 35

, 3

, 1, 41

, 43

univariate statistics

in Missing Value Analysis

, 16, 31

Syntax Index

ADDTYPE (keyword)

MVA command, 76

CATEGORICAL (subcommand)

MVA command, 66

CONVERGE (keyword)

MVA command, 74

COUNTS (keyword)

MVA command, 69

CROSSTAB (subcommand)

MVA command, 69

DESCRIBE (keyword)

MVA command, 70, 71, 72

DF (keyword)

MVA command, 68

DPATTERN (subcommand)

MVA command, 70

EM (subcommand)

MVA command, 73

FLIMIT (keyword)

MVA command, 75

LISTWISE (subcommand)

MVA command, 72

MAXCAT (subcommand)

MVA command, 67
MEANS (keyword)

MVA command, 69
MISMATCH (subcommand)

MVA command, 70
MPATTERN (subcommand)

MVA command, 71
MVA (command), 63

CATEGORICAL subcommand, 66

CROSSTAB subcommand, 69

DPATTERN subcommand, 70

EM subcommand, 73

ID subcommand, 67

LISTWISE subcommand, 72

MAXCAT subcommand, 67

MISMATCH subcommand, 70

missing indicator variables, 66

MPATTERN subcommand, 71

NOUNIVARIATE subcommand, 67

PAIRWISE subcommand, 73

REGRESSION subcommand, 75

symbols, 66

TPATTERN subcommand, 72

TTEST subcommand, 68

VARIABLES subcommand, 66

ID (subcommand)

MVA command, 67

ITERATIONS (keyword)

MVA command, 74

LAMBDA (keyword)

MVA command, 74

NOCOUNTS (keyword)

MVA command, 69
NODF (keyword)

MVA command, 68
NOMEANS (keyword)

MVA command, 69
NOPROB (keyword)

MVA command, 69
NORMAL (keyword)

MVA command, 76

81

82 Syntax Index

NOSORT (keyword)

MVA command, 70, 71, 72

NOT (keyword)

MVA command, 68

NOUNIVARIATE (subcommand)

MVA command, 67

NPREDICTORS (keyword)

MVA command, 75

OUTFILE (keyword)

MVA command, 74, 76

PAIRWISE (subcommand)

MVA command, 73

PERCENT (keyword)

MVA command, 68, 70

PROB (keyword)

MVA command, 69

PROPORTION (keyword)

MVA command, 74

REGRESSION (subcommand)

MVA command, 75

RESIDUAL (keyword)

MVA command, 76

SORT (keyword)

MVA command, 70

T (keyword)

MVA command, 68, 76

TDF (keyword)

MVA command, 74

TOLERANCE (keyword)

MVA command, 73, 75

TPATTERN (subcommand)

MVA command, 72

TTEST (subcommand)

MVA command, 68

VARIABLES (subcommand)

MVA command, 66