Effects of dichotomizing continuous outcome on efficiencies of measures of explained variation in logistic regression: Simulation study and application

Abstract

Dichotomizing continuous outcome variables is a common procedure in medical sciences. When analyzing these variables using binary logistic regression, great attention should be paid to the choice of the measure of explained variation ( $R^2)$. Since there are many different R² in logistic regression, in order to make correct inferences about models, evaluating their performances has become more important. The purpose of this paper is to reveal asymptotically more efficient and reliable R² measure when analyzing the models with dichotomized outcome. The eight most recommended R² statistics and ordinary least squares R² associated with the underlying continuous outcome have been included. Their asymptotic distributions have been studied. They have also been compared under varying correlational conditions between outcome and covariate. Extensive simulations using the bootstrap method have been conducted under two modeling scenarios. A real data example is also presented. The findings provide support and important basis for making efficient decisions.

KEYWORDS:

• Asymptotic relative efficiency
• dichotomizing
• explained variation
• logistic regression

Acknowledgments

I am grateful to Mustafa Dundar for his valuable helps on programming.