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An Additional Measure of Overall Effect Size for Logistic Regression Models

Jef f Allen & Huy Le

Journal of Educational and Behavioral Statistics, 33(416). 416441.

DOI: http://dx.doi.org/10.3102/1076998607306081
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Journal Article

In this article, we propose an overall effect size measure for multiple logistic regression (MLOGR) models. We first discuss common measures of overall effect size: classical R 2 applied to multiple linear regression (MLR) and R 2 analogs applied to other generalized linear models (GLMs). We then discuss how the population variance of the model's multiple linear predictor (MLP) represents overall effect size for GLMs and for MLOGR how the population overall odds ratio is a simple function of the variance of the MLP. Next, we show how to estimate the variance of the MLP (and overall odds ratio) using the sample variance of the MLP. Because this variance estimator (and overall odds ratio estimator) is generally biased, we propose a method to correct the overestimation problem. Then through a simulation study, we explore the properties of the overall odds ratio estimator. An example is presented where the overall Under ...

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