User manual SPSS CATEGORIES 14.0

[. . . ] SPSS Categories 14. 0 ® 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. [. . . ] Standardized coefficients are often interpreted as reflecting the importance of each predictor. However, regression coefficients cannot fully describe the impact of a predictor or the relationships between the predictors. Alternative statistics must be used in conjunction with the standardized coefficients to fully explore predictor effects. 120 Chapter 8 Correlations and Importance To interpret the contributions of the predictors to the regression, it is not sufficient to only inspect the regression coefficients. In addition, the correlations, partial correlations, and part correlations should be inspected. The following table contains these correlational measures for each variable. The zero-order correlation is the correlation between the transformed predictor and the transformed response. However, if you can explain some of the variation in either the predictor or the response, you will get a better representation of how well the predictor is doing. Figure 8-21 Zero-order, part, and partial correlations (transformed variables) Other variables in the model can confound the performance of a given predictor in predicting the response. The partial correlation coefficient removes the linear effects of other predictors from both the predictor and the response. This measure equals the correlation between the residuals from regressing the predictor on the other predictors and the residuals from regressing the response on the other predictors. The squared partial correlation corresponds to the proportion of the variance explained relative to the residual variance of the response remaining after removing the effects of the other variables. Removing the effects of the other variables, Package design explains (­0. 955)2 = 0. 91 = 91% of the variation in the preference rankings. Both Price and Good Housekeeping seal also explain a large portion of variance if the effects of the other variables are removed. As an alternative to removing the effects of variables from both the response and a predictor, you can remove the effects from just the predictor. The correlation between the response and the residuals from regressing a predictor on the other predictors is the part correlation. Squaring this value yields a measure of the proportion of variance explained relative to the total variance of response. If you remove the effects of Brand 121 Categorical Regression name, Good Housekeeping seal, Money back guarantee, and Price from Package design, the remaining part of Package design explains (­0. 733)2 = 0. 54 = 54% of the variation in preference rankings. Importance In addition to the regression coefficients and the correlations, Pratt's measure of relative importance (Pratt, 1987) aids in interpreting predictor contributions to the regression. Large individual importances relative to the other importances correspond to predictors that are crucial to the regression. Also, the presence of suppressor variables is signaled by a low importance for a variable that has a coefficient of similar size to the important predictors. In contrast to the regression coefficients, this measure defines the importance of the predictors additively--that is, the importance of a set of predictors is the sum of the individual importances of the predictors. Pratt's measure equals the product of the regression coefficient and the zero-order correlation for a predictor. These products add to R2, so they are divided by R2, yielding a sum of 1. The set of predictors Package design and Brand name, for example, have an importance of 0. 654. [. . . ] Graphical display of interaction in multiway contingency tables by use of homogeneity analysis. Points of view analysis revisited: Fitting multidimensional structures to optimal distance components with cluster restrictions on the variables. New features of categorical principal components analysis for complicated data sets, including data mining. Principal components analysis with nonlinear optimal scaling transformations for ordinal and nominal data. [. . . ]