GOODNESS-OF-FIT IN REGRESSION-ANALYSIS - R-2 AND G(2) RECONSIDERED

There has been considerable debate on how important goodness of fit is as a tool in regression analysis, especially with regard to the contr oversy on R-2 in linear regression. This article reviews some of the a rguments of this debate and its relationship to other goodness of fit measures. It attempts to clarify the distinction between goodness of f it measures and other model evaluation tools as well as the distinctio n between model test statistics and descriptive measures used to make decisions on the agreement between models and data. It also argues tha t the utility of goodness of fit measures depends on whether the analy sis focuses on explaining the outcome (model orientation) or explainin g the effect(s) of some regressor(s) on the outcome (factor orientatio n). In some situations a decisive goodness of fit test statistic exist s and is a central tool in the analysis. In other situations, where th e goodness of fit measure is not a test statistic but a descriptive me asure, it can be used as a heuristic device along with other evidence whenever appropriate. The availability of goodness of fit test statist ics depends on whether the variability in the observations is restrict ed, as in table analysis, or whether it is unrestricted, as in OLS and logistic regression on individual data. Hence, G(2) is a decisive too l for measuring goodness of fit, whereas R-2 and SEE are heuristic too ls.