Training Seminars

SPSS Inc. provides both public and onsite training seminars. All seminars feature hands-on workshops. Seminars will be offered in major cities on a regular basis. For more information on these seminars, contact your local office, listed on the SPSS Web site at http://www.spss.com/worldwide.

Technical Support

The services of SPSS Technical Support are available to registered customers. Customers may contact Technical Support for assistance in using SPSS products or for installation help for one of the supported hardware environments. To reach Technical Support, see the SPSS Web site at http://www.spss.com, or contact your local office, listed on the SPSS Web site at http://www.spss.com/worldwide. Be prepared to identify yourself, your organization, and the serial number of your system.

Additional Publications

Additional copies of SPSS product manuals may be purchased directly from SPSS Inc. Visit our Web site at http://www.spss.com/estore, or contact your local SPSS office, listed on the SPSS Web site at http://www.spss.com/worldwide. For telephone orders in the United States and Canada, call SPSS Inc. at 800-543-2185. For. telephone orders outside of North America, contact your local office, listed on the SPSS Web site. The SPSS Statistical Procedures Companion, by Marija Noruis, is being prepared for publication by Prentice Hall. It contains overviews of the procedures in the SPSS Base, plus Logistic Regression, General Linear Models, and Linear Mixed Models. Further information will be available on the SPSS Web site at http://www.spss.com (click Store, select your country, and click Books).

Tell Us Your Thoughts

Your comments are important. Please send us a letter and let us know about your experiences with SPSS products. We especially like to hear about new and interesting applications using the SPSS system. Please send e-mail to suggest@spss.com or write to SPSS Inc., Attn.: Director of Product Planning, 233 South Wacker Drive, 11th Floor, Chicago, IL 60606-6412.

About This Manual

This manual documents the graphical user interface for the procedures included in the Advanced Models module. Illustrations of dialog boxes are taken from SPSS for Windows. Dialog boxes in other operating systems are similar. The Advanced Models command syntax is included in the SPSS 12.0 Command Syntax Reference, available on the product CD-ROM.

2 Chapter 1

Residuals, predicted values, Cook's distance, and leverage values can be saved as new variables in your data file for checking assumptions. Also available are a residual SSCP matrix, which is a square matrix of sums of squares and cross-products of residuals, a residual covariance matrix, which is the residual SSCP matrix divided by the degrees of freedom of the residuals, and the residual correlation matrix, which is the standardized form of the residual covariance matrix. WLS Weight allows you to specify a variable used to give observations different weights for a weighted least-squares (WLS) analysis, perhaps to compensate for different precision of measurement.
Example. A manufacturer of plastics measures three properties of plastic film: tear
resistance, gloss, and opacity. Two rates of extrusion and two different amounts of additive are tried, and the three properties are measured under each combination of extrusion rate and additive amount. The manufacturer finds that the extrusion rate and the amount of additive individually produce significant results but that the interaction of the two factors is not significant.
Methods. Type I, Type II, Type III, and Type IV sums of squares can be used to
evaluate different hypotheses. Type III is the default.
Statistics. Post hoc range tests and multiple comparisons: least significant
difference, Bonferroni, Sidak, Scheff, Ryan-Einot-Gabriel-Welsch multiple F, Ryan-Einot-Gabriel-Welsch multiple range, Student-Newman-Keuls, Tukey's honestly significant difference, Tukey's-b, Duncan, Hochberg's GT2, Gabriel, Waller Duncan t test, Dunnett (one-sided and two-sided), Tamhane's T2, Dunnett's T3, Games-Howell, and Dunnett's C. Descriptive statistics: observed means, standard deviations, and counts for all of the dependent variables in all cells; the Levene test for homogeneity of variance; Box's M test of the homogeneity of the covariance matrices of the dependent variables; and Bartlett's test of sphericity.
Plots. Spread-versus-level, residual, and profile (interaction).
GLM Multivariate Data Considerations
Data. The dependent variables should be quantitative. Factors are categorical and
can have numeric values or string values of up to eight characters. Covariates are quantitative variables that are related to the dependent variable.
3 GLM Multivariate Analysis
Assumptions. For dependent variables, the data are a random sample of vectors from a multivariate normal population; in the population, the variance-covariance matrices for all cells are the same. Analysis of variance is robust to departures from normality, although the data should be symmetric. To check assumptions, you can use homogeneity of variances tests (including Box's M) and spread-versus-level plots. You can also examine residuals and residual plots. Related procedures. Use the Explore procedure to examine the data before doing an

Sums of Squares

For the model, you can choose a type of sum of squares. Type III is the most commonly used and is the default.
Type I. This method is also known as the hierarchical decomposition of the
sum-of-squares method. Each term is adjusted only for the term that precedes it in the model. The Type I sum-of-squares method is commonly used for: A balanced ANOVA model in which any main effects are specified before any first-order interaction effects, any first-order interaction effects are specified before any second-order interaction effects, and so on. A polynomial regression model in which any lower-order terms are specified before any higher-order terms. A purely nested model in which the first-specified effect is nested within the second-specified effect, the second-specified effect is nested within the third, and so on. (This form of nesting can be specified only by using syntax.)
Type II. This method calculates the sums of squares of an effect in the model adjusted for all other appropriate effects. An appropriate effect is one that corresponds to all effects that do not contain the effect being examined. The Type II sum-of-squares method is commonly used for:
A balanced ANOVA model. Any model that has main factor effects only.

6 Chapter 1

Any regression model. A purely nested design. (This form of nesting can be specified by using syntax.)
Type III. This method, the default, calculates the sums of squares of an effect in the
design as the sums of squares adjusted for any other effects that do not contain it and orthogonal to any effects (if any) that contain it. The Type III sums of squares have one major advantage in that they are invariant with respect to the cell frequencies as long as the general form of estimability remains constant. Therefore, this type is often considered useful for an unbalanced model with no missing cells. In a factorial design with no missing cells, this method is equivalent to the Yates' weighted-squares-of-means technique. The Type III sum-of-squares method is commonly used for: Any models listed in Type I and Type II. Any balanced or unbalanced model with no empty cells.
Type IV. This method is designed for a situation in which there are missing cells. For any effect F in the design, if F is not contained in any other effect, then Type IV = Type III = Type II. When F is contained in other effects, Type IV distributes the contrasts being made among the parameters in F to all higher-level effects equitably. The Type IV sum-of-squares method is commonly used for:
Any models listed in Type I and Type II. Any balanced model or unbalanced model with empty cells.

Tests displayed. Pairwise comparisons are provided for LSD, Sidak, Bonferroni,
Games and Howell, Tamhane's T2 and T3, Dunnett's C, and Dunnett's T3. Homogeneous subsets for range tests are provided for S-N-K, Tukey's-b, Duncan, R-E-G-W F, R-E-G-W Q, and Waller. Tukey's honestly significant difference test, Hochberg's GT2, Gabriel's test, and Scheff's test are both multiple comparison tests and range tests.

GLM Multivariate Save

Figure 1-7 Multivariate Save dialog box
You can save values predicted by the model, residuals, and related measures as new variables in the Data Editor. Many of these variables can be used for examining assumptions about the data. To save the values for use in another SPSS session, you must save the current data file.
Predicted Values. The values that the model predicts for each case. Unstandardized predicted values and the standard errors of the predicted values are available. If a WLS variable was chosen, weighted unstandardized predicted values are available.

12 Chapter 1

Diagnostics. Measures to identify cases with unusual combinations of values for the independent variables and cases that may have a large impact on the model. Available are Cook's distance and uncentered leverage values. Cook's Distance. A measure of how much the residuals of all cases would
change if a particular case were excluded from the calculation of the regression coefficients. A large Cook's D indicates that excluding a case from computation of the regression statistics, changes the coefficients substantially.
Leverage Value. The relative influence of each observation on the model's fit. Residuals. An unstandardized residual is the actual value of the dependent variable
minus the value predicted by the model. Standardized, Studentized, and deleted residuals are also available. If a WLS variable was chosen, weighted unstandardized residuals are available.
Unstandardized Residuals. The difference between an observed value and the
value predicted by the model.
Weighted Residuals. Weighted unstandardized residuals. Available only if a
WLS variable was previously selected.
Standardized. The residual divided by an estimate of its standard error.
Standardized residuals are also known as Pearson residuals.
Studentized Residual. The residual divided by an estimate of its standard deviation
that varies from case to case, depending on the distance of each case's values on the independent variables from the means of the independent variables.

Example. In a weight-loss study, suppose the weights of several people are measured
each week for five weeks. In the data file, each person is a subject or case. The weights for the weeks are recorded in the variables weight1, weight2, and so on. The gender of each person is recorded in another variable. The weights, measured for each subject repeatedly, can be grouped by defining a within-subjects factor. The factor could be called week, defined to have five levels. In the main dialog box, the variables weight1,., weight5 are used to assign the five levels of week. The variable in the data file that groups males and females (gender) can be specified as a between-subjects factor to study the differences between males and females.
Measures. If subjects were tested on more than one measure at each time, define the
measures. For example, the pulse and respiration rate could be measured on each subject every day for a week. These measures do not exist as variables in the data file but are defined here. A model with more than one measure is sometimes called a doubly multivariate repeated measures model.

21 GLM Repeated Measures

Defining Factors for GLM Repeated Measures
E From the menus choose: Analyze General Linear Model Repeated Measures. Figure 2-1 Repeated Measures Define Factor(s) dialog box
E Type a within-subject factor name and its number of levels. E Click Add. E Repeat these steps for each within-subjects factor.
To define measure factors for a doubly multivariate repeated measures design:
E Type the measure name. E Click Add.
After defining all of your factors and measures:

E Click Define.

22 Chapter 2
Obtaining GLM Repeated Measures Tables
Figure 2-2 Repeated Measures dialog box
E Select a dependent variable that corresponds to each combination of within-subjects
factors (and optionally, measures) on the list. To change positions of the variables, use the up and down arrows. To make changes to the within-subjects factors, you can reopen the Repeated Measures Define Factor(s) dialog box without closing the main dialog box. Optionally, you can specify between-subjects factor(s) and covariates.

23 GLM Repeated Measures

GLM Repeated Measures Model
Figure 2-3 Repeated Measures Model dialog box
Specify Model. A full factorial model contains all factor main effects, all covariate main effects, and all factor-by-factor interactions. It does not contain covariate interactions. Select Custom to specify only a subset of interactions or to specify factor-by-covariate interactions. You must indicate all of the terms to be included in the model. Between-Subjects. The covariates are listed with (C) for covariate. Model. The model depends on the nature of your data. After selecting Custom, you
can select the within-subjects effects and interactions and the between-subjects effects and interactions that are of interest in your analysis.

Example. At an agriculture school, weight gains for pigs in six different litters are
measured after one month. The litter variable is a random factor with six levels. (The six litters studied are a random sample from a large population of pig litters.) The investigator finds out that the variance in weight gain is attributable to the difference in litters much more than to the difference in pigs within a litter.

36 Chapter 3

Variance Components Data Considerations
Data. The dependent variable is quantitative. Factors are categorical. They can have numeric values or string values of up to eight characters. At least one of the factors must be random. That is, the levels of the factor must be a random sample of possible levels. Covariates are quantitative variables that are related to the dependent variable. Assumptions. All methods assume that model parameters of a random effect have zero means and finite constant variances and are mutually uncorrelated. Model parameters from different random effects are also uncorrelated. The residual term also has a zero mean and finite constant variance. It is uncorrelated with model parameters of any random effect. Residual terms from different observations are assumed to be uncorrelated. Based on these assumptions, observations from the same level of a random factor are correlated. This fact distinguishes a variance component model from a general linear model. ANOVA and MINQUE do not require normality assumptions. They are both robust to moderate departures from the normality assumption. ML and REML require the model parameter and the residual term to be normally distributed. Related procedures. Use the Explore procedure to examine the data before doing variance components analysis. For hypothesis testing, use GLM Univariate, GLM Multivariate, and GLM Repeated Measures.
Obtaining Variance Components Tables
E From the menus choose: Analyze General Linear Model Variance Components.
37 Variance Components Analysis Figure 3-1 Variance Components dialog box
E Select a dependent variable. E Select variables for Fixed Factor(s), Random Factor(s), and Covariate(s), as
appropriate for your data. For specifying a weight variable, use WLS Weight.

38 Chapter 3

Variance Components Model
Figure 3-2 Variance Components Model dialog box
Specify Model. A full factorial model contains all factor main effects, all covariate
main effects, and all factor-by-factor interactions. It does not contain covariate interactions. Select Custom to specify only a subset of interactions or to specify factor-by-covariate interactions. You must indicate all of the terms to be included in the model.
Factors and Covariates. The factors and covariates are listed with (F) for a fixed factor,
(R) for a random factor, and (C) for a covariate.

a custom model.

78 Chapter 7
Logit Loglinear Analysis Options
Figure 7-3 Logit Loglinear Analysis Options dialog box
The Logit Loglinear Analysis procedure displays model information and goodness-of-fit statistics. In addition, you can choose one or more of the following options:
Display. Several statistics are available for display: observed and expected cell
Plot. Plots available for custom models include two scatterplot matrices (adjusted residuals or deviance residuals against observed and expected cell counts). You can also display normal probability and detrended normal plots of adjusted residuals or deviance residuals. Confidence Interval. The confidence interval for parameter estimates can be adjusted. Criteria. The Newton-Raphson method is used to obtain maximum likelihood
79 Logit Loglinear Analysis
Logit Loglinear Analysis Save
Figure 7-4 Logit Loglinear Analysis Save dialog box
Select the values you want to save as new variables in the working data file. The suffix n in the new variable names increments to make a unique name for each saved variable. The saved values refer to the aggregated data (to cells in the contingency table), even if the data are recorded in individual observations in the Data Editor. If you save residuals or predicted values for unaggregated data, the saved value for a cell in the contingency table is entered in the Data Editor for each case in that cell. To make sense of the saved values, you should aggregate the data to obtain the cell counts. Four types of residuals can be saved: raw, standardized, adjusted, and deviance. The predicted values can also be saved.

80 Chapter 7

Ordinal Regression allows you to model the dependence of a polytomous ordinal response on a set of predictors, which can be factors or covariates. The design of Ordinal Regression is based on the methodology of McCullagh (1980, 1998), and the procedure is referred to as PLUM in the syntax. Standard linear regression analysis involves minimizing the sum-of-squared differences between a response (dependent) variable and a weighted combination of predictor (independent) variables. The estimated coefficients reflect how changes in the predictors affect the response. The response is assumed to be numerical, in the sense that changes in the level of the response are equivalent throughout the range of the response. For example, the difference in height between a person who is 150 cm tall and a person who is 140 cm tall is 10 cm, which has the same meaning as the difference in height between a person who is 210 cm tall and a person who is 200 cm tall. These relationships do not necessarily hold for ordinal variables, in which the choice and number of response categories can be quite arbitrary.
Example. Ordinal Regression could be used to study patient reaction to drug dosage.

Iterations. You can customize the iterative algorithm. Maximum iterations. Specify a non-negative integer. If 0 is specified, the
procedure returns the initial estimates.
Maximum step-halving. Specify a positive integer. Log-likelihood convergence. The algorithm stops if the absolute or relative change
in the log-likelihood is less than this value. The criterion is not used if 0 is specified.
Parameter convergence. The algorithm stops if the absolute or relative change
in each of the parameter estimates is less than this value. The criterion is not used if 0 is specified.
Confidence interval. Specify a value greater than or equal to 0 and less than 100. Delta. The value added to zero cell frequencies. Specify a non-negative value less

than 1.

Singularity tolerance. Used for checking for highly dependent predictors. Select a
value from the list of options.

85 Ordinal Regression

Link. Choose among the Cauchit, Complementary Log-log, Logit, Negative Log-log, and Probit functions.
Ordinal Regression Output
The Output dialog box allows you to produce tables for display in the Viewer and save variables to the working file.
Figure 8-3 Ordinal Regression Output dialog box
Display. Produces tables for: Print iteration history. The log-likelihood and parameter estimates are printed for
the print iteration frequency specified. The first and last iterations are always printed.
Goodness-of-fit statistics. The Pearson and likelihood-ratio chi-square statistics.
They are computed based on the classification specified in the variable list.
Summary statistics. Cox and Snell's, Nagelkerke's, and McFadden's R2 statistics. Parameter estimates. Parameter estimates, standard errors, and confidence

intervals.

86 Chapter 8
Asymptotic correlation of parameter estimates. Matrix of parameter estimate

correlations.

Asymptotic covariance of parameter estimates. Matrix of parameter estimate

covariances.

Cell information. Observed and expected frequencies and cumulative frequencies,

96 Chapter 9

SURVIVAL Command Additional Features
The SPSS command language also allows you to: Specify more than one dependent variable. Specify unequally spaced intervals. Specify more than one status variable. Specify comparisons that do not include all the factor and all the control variables. Calculate approximate, rather than exact, comparisons. See the SPSS Command Syntax Reference for complete syntax information.
Kaplan-Meier Survival Analysis
There are many situations in which you would want to examine the distribution of times between two events, such as length of employment (time between being hired and leaving the company). However, this kind of data usually includes some censored cases. Censored cases are cases for which the second event isn't recorded (for example, people still working for the company at the end of the study). The Kaplan-Meier procedure is a method of estimating time-to-event models in the presence of censored cases. The Kaplan-Meier model is based on estimating conditional probabilities at each time point when an event occurs and taking the product limit of those probabilities to estimate the survival rate at each point in time.
Example. Does a new treatment for AIDS have any therapeutic benefit in extending
life? You could conduct a study using two groups of AIDS patients, one receiving traditional therapy and the other receiving the experimental treatment. Constructing a Kaplan-Meier model from the data would allow you to compare overall survival rates between the two groups to determine whether the experimental treatment is an improvement over the traditional therapy. You can also plot the survival or hazard functions and compare them visually for more detailed information.
Statistics. Survival table, including time, status, cumulative survival and standard
error, cumulative events, and number remaining; and mean and median survival time, with standard error and 95% confidence interval. Plots: survival, hazard, log survival, and one minus survival.
Kaplan-Meier Data Considerations
Data. The time variable should be continuous, the status variable can be categorical or continuous, and the factor and strata variables should be categorical.

survival curves.

Pairwise Over Strata. Compares each distinct pair of factor levels. Pairwise
trend tests are not available.
For Each Stratum. Performs a separate test of equality of all factor levels for each
stratum. If you do not have a stratification variable, the tests are not performed.
Pairwise for each Stratum. Compares each distinct pair of factor levels for each
stratum. Pairwise trend tests are not available. If you do not have a stratification variable, the tests are not performed.
Linear trend for factor levels. Allows you to test for a linear trend across levels of the
factor. This option is available only for overall (rather than pairwise) comparisons of factor levels.
Kaplan-Meier Save New Variables
Figure 10-4 Kaplan-Meier Save New Variables dialog box
You can save information from your Kaplan-Meier table as new variables, which can then be used in subsequent analyses to test hypotheses or check assumptions. You can save survival, standard error of survival, hazard, and cumulative events as new variables.
Survival. Cumulative survival probability estimate. The default variable name is
the prefix sur_ with a sequential number appended to it. For example, if sur_1 already exists, Kaplan-Meier assigns the variable name sur_2.

102 Chapter 10

Standard Error of Survival. Standard error of the cumulative survival estimate. The
default variable name is the prefix se_ with a sequential number appended to it. For example, if se_1 already exists, Kaplan-Meier assigns the variable name se_2.
Hazard. Cumulative hazard function estimate. The default variable name is the
prefix haz_ with a sequential number appended to it. For example, if haz_1 already exists, Kaplan-Meier assigns the variable name haz_2.
Cumulative Events. Cumulative frequency of events when cases are sorted by their
survival times and status codes. The default variable name is the prefix cum_ with a sequential number appended to it. For example, if cum_1 already exists, Kaplan-Meier assigns the variable name cum_2.

Change Contrast. Allows you to change the contrast method. Available contrast

methods are:

Indicator. Contrasts indicate the presence or absence of category membership.
The reference category is represented in the contrast matrix as a row of zeros.
Simple. Each category of the predictor variable except the reference category is
compared to the reference category.
Difference. Each category of the predictor variable except the first category is
compared to the average effect of previous categories. Also known as reverse Helmert contrasts.
Helmert. Each category of the predictor variable except the last category is
compared to the average effect of subsequent categories.
Repeated. Each category of the predictor variable except the first category is
compared to the category that precedes it.
Polynomial. Orthogonal polynomial contrasts. Categories are assumed to be
equally spaced. Polynomial contrasts are available for numeric variables only.
Deviation. Each category of the predictor variable except the reference category is
compared to the overall effect. If you select Deviation, Simple, or Indicator, select either First or Last as the reference category. Note that the method is not actually changed until you click Change. String covariates must be categorical covariates. To remove a string variable from the Categorical Covariates list, you must remove all terms containing the variable from the Covariates list in the main dialog box.
109 Cox Regression Analysis

Cox Regression Plots

Figure 11-3 Cox Regression Plots dialog box
Plots can help you to evaluate your estimated model and interpret the results. You can plot the survival, hazard, log-minus-log, and one-minus-survival functions.
Survival Plot. Displays the cumulative survival function on a linear scale. Hazard Plot. Displays the cumulative hazard function on a linear scale. Log-Minus-Log. The cumulative survival estimate after the ln(-ln) transformation
is applied to the estimate.
One Minus Survival. Plots one-minus the survival function on a linear scale.
Because these functions depend on values of the covariates, you must use constant values for the covariates to plot the functions versus time. The default is to use the mean of each covariate as a constant value, but you can enter your own values for the plot using the Change Value control group. You can plot a separate line for each value of a categorical covariate by moving that covariate into the Separate Lines For text box. This option is available only for categorical covariates, which are denoted by (Cat) after their names in the Covariate Values Plotted At list.

110 Chapter 11

Cox Regression Save New Variables
Figure 11-4 Cox Regression Save New Variables dialog box
You can save various results of your analysis as new variables. These variables can then be used in subsequent analyses to test hypotheses or to check assumptions.
Survival. Allows you to save the survival function, standard error, and log-minus-log
estimates as new variables.
Diagnostics. Allows you to save the hazard function, partial residuals, and DfBeta(s) for the regression as new variables. Hazard Function. Saves the cumulative hazard function estimate (also called the

Cox-Snell residual).

Partial Residuals. You can plot partial residuals against survival time to test
the proportional hazards assumption. One variable is saved for each covariate in the final model. Parital residuals are available only for models containing at least one covariate.
DfBetas. Estimated change in a coefficient if a case is removed. One variable
is saved for each covariate in the final model. DfBetas are only available for models containing at least one covariate. If you are running Cox with a time-dependent covariate, DfBeta(s) are the only variables that you can save. You can also save the linear predictor variable X*Beta.
X*Beta. Linear predictor score. The sum of the product of mean-centered
covariate values and their corresponding parameter estimates for each case.
111 Cox Regression Analysis

Cox Regression Options

Figure 11-5 Cox Regression Options dialog box
You can control various aspects of your analysis and output.
Model Statistics. You can obtain statistics for your model parameters, including confidence intervals for exp(B) and correlation of estimates. You can request these statistics either at each step or at the last step only. Probability for Stepwise. If you have selected a stepwise method, you can specify the
probability for either entry or removal from the model. A variable is entered if the significance level of its F-to-enter is less than the Entry value, and a variable is removed if the significance level is greater than the Removal value. The Entry value must be less than the Removal value.
Maximum Iterations. Allows you to specify the maximum iterations for the model, which controls how long the procedure will search for a solution. Display baseline function. Allows you to display the baseline hazard function and

132 Index

descriptive statistics, 13, 32, 55 in GLM Multivariate, 13 in GLM Repeated Measures, 32 in Linear Mixed Models, 55 effect-size estimates, 13, 32 in GLM Multivariate, 13 in GLM Repeated Measures, 32 estimated marginal means, 13, 32 in GLM Multivariate, 13 in GLM Repeated Measures, 32 in Linear Mixed Models, 56 eta-squared, 13, 32 in GLM Multivariate, 13 in GLM Repeated Measures, 32 expected frequencies, 85 in Ordinal Regression, 85 factor-level information, 55 in Linear Mixed Models, 55 Fisher scoring, 53 in Linear Mixed Models, 53 fixed effects, 48 in Linear Mixed Models, 48 fixed predicted values in Linear Mixed Models, 57 frequencies, 63 in Model Selection Loglinear Analysis, 63 full factorial models, 23, 38 in GLM Repeated Measures, 23 in Variance Components, 38 Gehan test, 95 in Life Tables, 95 generalized log-odds ratio, 65 in General Loglinear Analysis, 65 General Loglinear Analysis, 65, 66, 66, 66, 68, 69, 70, 71 assumptions, 66 cell covariates, 65 cell structures, 65 confidence intervals, 69 contrasts, 65 criteria, 69 display options, 69 distribution of cell counts, 65 factors, 65
model specification, 68 multinomial distribution, 66 plots, 69 Poisson distribution, 66 residuals, 70 saving predicted values, 70 saving variables, 70 generating class, 61 in Model Selection Loglinear Analysis, 61 GLM Multivariate, 1, 2, 3, 13, 14 assumptions, 2 covariates, 1 dependent variable, 1 diagnostics, 13 display, 13 estimated marginal means, 13 factors, 1 options, 13 GLM Repeated Measures, 17, 18, 20, 21, 22, 23, 30, 32, 32, 33 assumptions, 18 diagnostics, 32 display, 32 estimated marginal means, 32 model, 23 options, 32 saving variables, 30 GLOR, 65 in General Loglinear Analysis, 65 goodness of fit, 85 in Ordinal Regression, 85 hazard rate, 91 in Life Tables, 91 hierarchical decomposition in GLM, 40 hierarchical loglinear models, 59 homogeneity-of-variance tests, 13, 32 in GLM Multivariate, 13 in GLM Repeated Measures, 32 interaction terms, 48 in Linear Mixed Models, 48 iteration history, 53, 85 in Linear Mixed Models, 53 in Ordinal Regression, 85

133 Index

iterations, 63 in Model Selection Loglinear Analysis, 63 Kaplan-Meier, 97 assumptions, 97 command additional features, 103 comparing factor levels, 100 data, 97 defining events, 100 example, 97 linear trend for factor levels, 100 mean and median survival time, 102 plots, 102 quartiles, 102 related procedures, 97 saving new variables, 101 statistics, 97, 102 survival status variables, 100 survival tables, 102 Levene test, 13, 32 in GLM Multivariate, 13 in GLM Repeated Measures, 32 leverage values, 30 in GLM Repeated Measures, 30 Life Tables, 91 assumptions, 92 censored cases, 92 command additional features, 96 comparing factor levels, 95 data considerations, 92 example, 91 factor variables, 94 hazard rate, 91 plots, 95 related procedures, 92 statistics, 91 suppressing table display, 95 survival function, 91 survival status variables, 94 Wilcoxon (Gehan) test, 95 likelihood-ratio chi-square statistic, 85 in Ordinal Regression, 85 Linear Mixed Models, 43, 44, 46, 47, 48, 48, 49, 51, 53, 55, 56, 57, 58, 125 assumptions, 44 build terms, 48, 49