User manual SPSS ADVANCED MODELS 12.0

[. . . ] SPSS Advanced Models 12. 0 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. [. . . ] For example, a grocery store chain may follow the spending of their customers at several store locations. Since each customer frequents only one of those locations, the Customer effect can be said to be nested within the Store location effect. Additionally, you can include interaction effects or add multiple levels of nesting to the nested term. Limitations. Nested terms have the following restrictions: All factors within an interaction must be unique. Thus, if A is a factor and X is a covariate, then specifying A(X) is invalid. Sum of Squares For the model, you can choose a type of sums of squares. Type III is the most commonly used and is the default. 50 Chapter 4 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. Type I sums of squares are 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 III. This method 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. Hence, this type of sums of squares 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. Any balanced or unbalanced model with no empty cells. 51 Linear Mixed Models Linear Mixed Models Random Effects Figure 4-4 Linear Mixed Models Random Effects dialog box Random Effects. There is no default model, so you must explicitly specify the random effects. You can also choose to include an intercept term in the random-effects model. Each random-effect model is assumed to be independent of every other random-effect model; that is, separate covariance matrices will be computed for each. Terms specified in the same random-effect model can be correlated. 52 Chapter 4 Covariance type. [. . . ] 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. 125 126 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. Compound Symmetry. [. . . ]