User manual SPSS CATEGORIES 13.0

[. . . ] Heiser SPSS Inc 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. [. . . ] Figure 8-9 Residuals versus package design The U-shape is more pronounced in the plot of the standardized residuals against package. Every residual for Design B* is negative, whereas all but one of the residuals is positive for the other two designs. Because the linear regression model fits one parameter for each variable, the relationship cannot be captured by the standard approach. 117 Categorical Regression A Categorical Regression Analysis The categorical nature of the variables and the nonlinear relationship between Preference and Package design suggest that regression on optimal scores may perform better than standard regression. The U-shape of the residual plots indicates that a nominal treatment of Package design should be used. Thus, recovering as many properties of its categories as possible in the quantifications is desirable. Using an ordinal or nominal scaling level ignores the differences between the response categories. However, linearly transforming the response categories preserves category differences. Consequently, scaling the response numerically is generally preferred and will be employed here. Running the Analysis E To run a Categorical Regression analysis, from the menus choose: Analyze Regression Optimal Scaling. . . 118 Chapter 8 Figure 8-10 Categorical Regression dialog box E Select Preference as the dependent variable. E Select Package design through Money-back guarantee as independent variables. Figure 8-11 Define Scale dialog box E Select Numeric as the optimal scaling level. E Click Continue. 119 Categorical Regression E Select Package design and click Define Scale in the Categorical Regression dialog box. Figure 8-12 Define Scale dialog box E Select Nominal as the optimal scaling level. E Select Brand name through Money-back guarantee and click Define Scale in the Categorical Regression dialog box. Figure 8-13 Define Scale dialog box E Select Numeric as the optimal scaling level. E Click Output in the Categorical Regression dialog box. 120 Chapter 8 Figure 8-14 Output dialog box E Select Correlations of original variables and Correlations of transformed variables. Figure 8-15 Save dialog box E Select Transformed variables and Residuals. 121 Categorical Regression E Click Continue. Figure 8-16 Plots dialog box E Choose to create transformation plots for package and price. E Click OK in the Categorical Regression dialog box. Intercorrelations The intercorrelations among the predictors are useful for identifying multicollinearity in the regression. Variables that are highly correlated will lead to unstable regression estimates. However, due to their high correlation, omitting one of them from the model only minimally affects prediction. The variance in the response that can be explained by the omitted variable is still explained by the remaining correlated variable. However, zero-order correlations are sensitive to outliers and also cannot identify multicollinearity due to a high correlation between a predictor and a combination of other predictors. 122 Chapter 8 Figure 8-17 Original predictor correlations Figure 8-18 Transformed predictor correlations The intercorrelations of the predictors for both the untransformed and transformed predictors are displayed. All values are near 0, indicating that multicollinearity between individual variables is not a concern. [. . . ] Graphical display of interaction in multiway contingency tables by use of homogeneity analysis. New York: AcademicPress, 277 ­296. 347 Bibliography Meulman, J. 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. [. . . ]