GRM Whole Model R Results Spreadsheets

Building the Whole Model

This topic explains the series of spreadsheets that will be displayed when you click the Whole model R button on the GRM Results - Summary tab.

Element Name Description
Overall fit of the model First, a spreadsheet will be displayed reporting the R, R-square, adjusted R-square, and overall model ANOVA results, for each dependent variable. The statistics reported in this spreadsheet, thus, test the overall fit of all parameters in the current model.
Lack of fit If you selected the Lack of fit check box on the Quick Specs Dialog - Options tab or via the LACKOFFIT keyword in the GRM syntax, another spreadsheet will be displayed that compares, for each dependent variable, the residual sums of squares for the current model against the estimate of pure error. The pure error is computed from the sums of squares within each unique combination of treatment levels (for categorical predictors) or values (for continuous predictors). If this test is statistically significant, then it can be concluded that the current model does not satisfactorily explain all (random) error variability in the data, and hence, that the current model exhibits an overall lack-of-fit (models that provide a good fit to the data will explain most variability in the data, except for random or pure error). For additional details, see also the discussion on replicated design points and pure error in Experimental Design.
Overall fit of the model vs. pure error. Since the pure error (see Lack of fit above) provides an estimate of the random error variability in the data, you can test the overall fit of the model (see above) against this estimate. If you selected the Lack of fit option on the Quick Specs Dialog - Options tab or via the LACKOFFIT keyword in the GRM syntax, a third spreadsheet will be displayed reporting the results for this test.
Test of whole model, adjusted for the mean If the current model does not include an intercept term, then another spreadsheet will be displayed, reporting the results (for each dependent variable) for the test of the overall fit of the model, using the sums of squares residuals adjusted for the means as the error term. When the current model does not include an intercept, you can compute the multiple R-square value either based on the variability around the origin (zero), or based on the variability around the mean. The default R-square value reported in the Overall fit of the model spreadsheet (see above) pertains to the former, that is, it is the proportion of variability of the dependent variables around 0 (zero) that is accounted for by the predictor variables. In this spreadsheet, STATISTICA will report the ANOVA tables (for each dependent variable), including the sums of squares and R-square value, based on the proportion of variability around the mean for the dependent variables, explained by the predictor variables. These computations are common in the analysis of mixtures (see also the discussion of mixture designs and triangular surfaces in Experimental Design). For various other alternative ways for computing the R-square value, refer to Kvalseth (1985).