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Comparison of Logistic Regression's Quality Indicators in the Case of Factors which Determine the Type of Alcohol Consumption among Students
The evaluation of the logistic regression model quality often perplexes the researchers: there are a lot of quality indicators (Likelihood ratio test, Goodness-of-fit test, Hosmer-Lemeshov test, classification table, ROC-curve, pseudo-R2 and their various modifications) meanwhile there is no consensus on the primacy of any indicator or even on the accurate interpretation of some of them. The research problem lies in the contradiction between theory and practice: there are certain statistical grounds for the utility of using pseudo-R2 indicators in assessing the quality of logistic regression models, but this approach is not used in practice. The current topic is quite urgent due to the growing popularity of the logistic regression models application in social sciences. The aim of the study is a theoretical and empirical comparison of quality indicators (classification table and pseudo-R2) of multinomial and binary logistic regressions built on the same data and recommendations on the adequacy of these indicators application. The object is measures of the predictive power of logistic regression (classification table and pseudo-R2), the subject is the differences in the application, interpretation and evaluation of pseudo-R2 measures as indicators of the logistic regression quality. The theoretical framework provides an analysis of econometric and statistical publications on all known and most frequently used pseudo-R2 measures: Allison P., Kvalseth T., Menard S., Nagelkerke N., Tjur T., etc. The main result is a comparative description of the analyzed pseudo-R2 measures and an empirically supported rationale for choosing one of them as the most adequate statistic. The results obtained allow comparing the predictive power of binary and multinomial logistic regression models in the case of factors which determine the type of alcohol consumption among students.