User manual SPSS ADVANCED MODELS 11.5

[. . . ] SPSS Advanced Models 11. 5 TM For more information about SPSS® software products, please visit our Web site at http://www. spss. com or contact SPSS Inc. 233 South Wacker Drive, 11th Floor Chicago, IL 60606-6412 Tel: (312) 651-3000 Fax: (312) 651-3668 SPSS is a registered trademark and the other product names are the trademarks of SPSS Inc. No material describing such software may be produced or distributed without the written permission of the owners of the trademark and license rights in the software and the copyrights in the published materials. Use, duplication, or disclosure by the Government is subject to restrictions as set forth in subdivision (c)(1)(ii) of The Rights in Technical Data and Computer Software clause at 52. 227-7013. [. . . ] Also, parameter estimates and confidence intervals for fixed effects, Wald tests and confidence intervals for parameters of covariance matrices. Type I and Type III sums of squares can be used to evaluate different hypotheses. Factors should be categorical and can have numeric values or string values. The dependent variable is assumed to be linearly related to the fixed factors, random factors, and covariates. The random effects model the covariance structure of the dependent variable. Multiple random effects are considered independent of each other, and separate covariance matrices will be computed for each; however, model terms specified on the same random effect can be correlated. The repeated measures model the covariance structure of the residuals. The dependent variable is also assumed to come from a normal distribution. Use the Explore procedure to examine the data before running an analysis. If you do not suspect there to be correlated or non-constant variability, you can alternatively use the GLM Univariate or GLM Repeated Measures procedure. You can alternatively use the Variance Components Analysis procedure if the random effects have a variance components covariance structure and there are no repeated measures. Linear Mixed Models Select Subjects/Repeated Variables This dialog box allows you to select variables that define subjects and repeated observations and to choose a covariance structure for the residuals. Subjects. A subject is an observational unit that can be considered independent of other subjects. For example, the blood pressure readings from a patient in a medical study can be considered independent of the readings from other patients. Defining subjects becomes particularly important when there are repeated measurements per subject and you want to model the correlation between these observations. For example, you might expect that blood pressure readings from a single patient during consecutive visits to the doctor are correlated. Subjects can also be defined by the factor-level combination of multiple variables; for example, you can specify Gender and Age category as subject variables to model the belief that males over the age of 65 are similar to each other but independent of males under 65 and females. 43 Linear Mixed Models All of the variables specified in the Subjects list are used to define subjects for the residual covariance structure. You can use some or all of the variables to define subjects for the random-effects covariance structure. Repeated. The variables specified in this list are used to identify repeated observations. For example, a single variable Week might identify the 10 weeks of observations in a medical study, or Month and Day might be used together to identify daily observations over the course of a year. The available structures are as follows: Ante-Dependence: First Order AR(1) AR(1): Heterogeneous ARMA(1, 1) Compound Symmetry Compound Symmetry: Correlation Metric Compound Symmetry: Heterogeneous Diagonal Factor Analytic: First Order Factor Analytic: First Order, Heterogeneous Huynh-Feldt Scaled Identity Toeplitz Toeplitz: Heterogeneous Unstructured Unstructured: Correlations For more information, see the appendix Covariance Structures. 44 Chapter 4 Selecting Subjects/Repeated Variables for Linear Mixed Models From the menus choose: Analyze Mixed Models Linear. . . Figure 4-1 Linear Mixed Models: Specify Subjects/Repeated Variables dialog box Optionally, select one or more subjects variables. Click Continue. 45 Linear Mixed Models Obtaining a Linear Mixed Models Analysis Figure 4-2 Linear Mixed Models dialog box Select a dependent variable. Click Fixed or Random and specify at least a fixed-effects or random-effects model. Optionally, select a weighting variable. 46 Chapter 4 Linear Mixed Models Fixed Effects Figure 4-3 Linear Mixed Models: Fixed Effects dialog box Fixed Effects. [. . . ] The correlation between any two elements is equal to rho for adjacent elements, rho^2 for two elements separated by a third, and so on. Rho is constrained to lie between ­1 and 1. Ls Msr s M Ms r r s M rrr s Ns 2 1 2 1 1 3 1 1 2 4 1 1 2 s 2s 1 r 1 s 2 2 s 3s 1r 1r 2 s 4s 1r 1r 2 r 3 s 3s 2 r 2 s 2 3 s 4s 2 r 2 r 3 s 4s 3 r 3 s2 4 s 3s 2 r 2 3 s 4s 2 r 2 r 3 s 4s 3 r 3 O P P P P Q L1 M r sM M r M r N 2 2 3 r r2 r 1 r r 2 1 r O P rP rP P 1Q r3 2 Ls Ms r s M Mr ss Mr s Ns 2 1 2 1 3 4 1 1 s 2s 1r s 2 2 s 3s 1r 2 s 3s 2 r s2 3 s 4s 3 r 2 s 3s 2 r s 4s 2 r 2 3 O P ssrP s s rP P s Q s 4s 1r 3 2 4 2 4 3 2 4 119 120 Appendix B ARMA(1, 1). The correlation between two elements is equal to phi*rho for adjacent elements, phi*(rho^2) for elements separated by a third, and so on. Rho and phi are the autoregressive and moving average parameters, respectively, and their values are constrained to lie between ­1 and 1, inclusive. [. . . ]