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Chapter 21
EClick OK in the Complex Samples OrdinalRegression dialog box.
Pseudo R-Squares
Figure 21-6
Pseudo R-Squares
In the linear regressionmodel, the coefficient of determination, R2, summarizes the proportion of
variance in the dependent variable associated with the predictor (independent)variables, with
larger R2valuesindicating that more of the variation is explained by the model, to a maximum
of 1. For regression models with a categorical dependent variable, it is n ot possible to compute
asingleR2statistic that has all of the characteristics of R2in the linear regression model,so
these approximations are computedinstead. The following methods are used to estimatethe
coefficient of determination.
Cox and Snell’sR2(Cox an d Snell, 1989) is based on the log likelihood for the model
compared to the log likelihood for a baseline model. However, with categorical outcomes, it
has a theoretical maximum value of less than 1, even for a “perfect” model.
Nagelkerke’sR2(Nagelkerke, 1991) is an adjusted version of the Cox & Sn ell R-square that
adjusts the scale of the statistic to cover the full range from 0 to 1.
McFadden’sR2(McFadden, 1974) is another version, based on the log-likelihood kernels for
the intercept-only model and thefull estimated model.
What constitutes a “good” R2value varies between different areas of application. While these
statisticscan be suggestive on their own, they are most useful when comparing competing models
for the same data. The model with the largest R2statistic is “best” according to this measure.
Testsof Model Effects
Figure 21-7
Testsof model effects