Log-likelihood-based Pseudo-R2 in Logistic Regression

Giselmar A. J. Hemmert, Laura M. Schons, Jan Wieseke and Heiko Schimmelpfennig

Sociological Methods & Research, 2018, vol. 47, issue 3, 507-531

Abstract: The literature proposes numerous so-called pseudo- R 2 measures for evaluating “goodness of fit†in regression models with categorical dependent variables. Unlike ordinary least square- R 2 , log-likelihood-based pseudo- R 2 s do not represent the proportion of explained variance but rather the improvement in model likelihood over a null model. The multitude of available pseudo- R 2 measures and the absence of benchmarks often lead to confusing interpretations and unclear reporting. Drawing on a meta-analysis of 274 published logistic regression models as well as simulated data, this study investigates fundamental differences of distinct pseudo- R 2 measures, focusing on their dependence on basic study design characteristics. Results indicate that almost all pseudo- R 2 s are influenced to some extent by sample size, number of predictor variables, and number of categories of the dependent variable and its distribution asymmetry. Hence, an interpretation by goodness-of-fit benchmark values must explicitly consider these characteristics. The authors derive a set of goodness-of-fit benchmark values with respect to ranges of sample size and distribution of observations for this measure. This study raises awareness of fundamental differences in characteristics of pseudo- R 2 s and the need for greater precision in reporting these measures.

Keywords: pseudo-R2; logistic regression; goodness-of-fit; benchmarks; reporting (search for similar items in EconPapers)
Date: 2018
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Persistent link: https://EconPapers.repec.org/RePEc:sae:somere:v:47:y:2018:i:3:p:507-531

DOI: 10.1177/0049124116638107

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