GDA Models Results - Effects Tab

Select the Effects tab of the GDA Models Results dialog to access options to review the statistical significance of the predictor effects in the current model. As described in the Introductory Overview, the GDA module applies the general linear model to the discriminant function analysis problem, after (internally) recoding the class (group) memberships recorded in the categorical dependent variable into multiple (dummy-) coded dependent variables.

All effects. Click the All effect button to display a spreadsheet containing the ANOVA (MANOVA) table for all effects. If the design is univariate in nature, then the univariate results ANOVA table will be displayed; if the design is multivariate in nature, then the multivariate results MANOVA table will be displayed, showing the statistics as selected in the Multiv. tests box. For a discussion of the different types of designs, and how the respective ANOVA/MANOVA tables are computed, see the GRM Introductory Overview.

Design terms

Click the Design terms button to display a spreadsheet containing all the labels for each column in the design matrix (see GLM Introductory Overview). This spreadsheet is useful in conjunction with the Coefficients button (see below) to unambiguously identify how the categorical predictors in the design were coded, that is, how the model was parameterized, and how, consequently, the parameter estimates can be interpreted. Since the categorical predictor variables were coded according to the sigma-restricted parameterization, this spreadsheet will show the two levels of the respective factors that were contrasted in each column of the design matrix.

Within SSCP inv

Click the Within SSCP inv. button to display a spreadsheet containing information about the relationships among the variables in the analysis. The spreadsheet will display the G2 inverse of the pooled within-class sums of squares and cross products matrix for each vector in the design matrix for the factors.

Total SSCP inv

Click the Total SSCP inv. button to display a spreadsheet containing information about the relationships among the variables in the analysis. The spreadsheet will display the G2 inverse of the sums of squares and cross products matrix for each vector in the design matrix for the factors.

Coefficients

Click the Coefficients button to display a spreadsheet containing the current parameter estimates (b), standardized parameter estimates (beta), their standard errors, significance levels, and related statistics. In complex or incomplete designs, a Comment column may also be shown in the spreadsheet. The cells in this column may either be blank, or contain the designations Biased, Zeroed, or Dropped.

Biased parameters

Whenever during the initial computations of the generalized inverse of the variance/covariance matrix of the design matrix (see GLM Introductory Overview) a column is found to be redundant, it is zeroed out (i.e., all elements in the variance/covariance matrix for that column are set to zero; this check is performed during the so-called sweeping operation, where the diagonal elements are checked against a small constant delta; as specified via the SDelta keyword or in the Sweep delta field on the GDA Quick Specs Dialog - Advanced tab). Whenever a column in the design matrix is thus dropped from the analysis, the parameter estimates for the remaining columns belonging to the same effect are biased, because different orderings of the factor levels or columns in the design matrix for the respective effect will yield different parameter estimates for the respective columns. Thus, those parameter estimates are labeled as Biased in the coefficients spreadsheet.

Zeroed

Parameters labeled as Zeroed indicate that the respective columns in the design matrix are completely redundant with other columns in the design matrix, and hence, those columns were "dropped" or "zeroed out" from the design matrix. Usually, the parameter estimates for the remaining columns in the design matrix belonging to the same effect (as the one from which a column was zeroed) are labeled as Biased (see the description in the previous paragraph for additional details).

Pooled

This designation is only used in conjunction with the stepwise or best subset regression model building method. Pooled effects are those that were excluded from the final model because they did not qualify for inclusion given the current model building method and criteria for inclusion. Refer to Model Building in GRM in the Introductory Overview for a description of the stepwise and best subset regression methods.

Univariate results

Click the Univariate results button to display a spreadsheet containing the standard univariate ANOVA table for each dependent variable.

Model building results

The options in the Model building results group box will display summary spreadsheets for the stepwise regression analysis or the best subset regression analysis respectively. See GDA Models Results - Quick tab for a complete description of these buttons. Also, see Model Building in GRM in the Introductory Overview for details concerning the available model building procedures.

Multiv. tests. In the Multiv. test group box you can select the specific multivariate test statistics that are to be reported in the respective results spreadsheets. For description of the different multivariate tests statistics, refer to Multivariate Designs in the GLM Introductory Overview. These options are only available if the current design is multivariate in nature, i.e., if there are multiple dependent measures, or a within-subject (repeated measures) design with effects that have more than 2 levels (and hence, multivariate tests for those effects can be computed).

Alpha values

The values in the Alpha values group box are used in all results spreadsheets and graphs, whenever a confidence limit is to be computed, or a particular result to be highlighted based its statistical significance.

Confidence limits

Enter a value in the Confidence limits field to be used for constructing confidence limits in the respective results spreadsheets or graphs (e.g., spreadsheet of parameter estimates, graph of means); by default 95% confidence limits will be constructed.

Significant level

Enter a value in the Significant level field to be used for all spreadsheets and graphs, where statistically significant results are to be highlighted (e.g., in the All effects spreadsheet); by default all results significant at the p < .05 level will be highlighted.