A Monte Carlo-based pseudo-coefficient of determination for generalized linear models with binary outcome

In this article, we focus on a pseudo-coefficient of determination for generalized linear models with binary outcome. Although there are numerous coefficients of determination proposed in the literature, none of them is identified as the best in terms of estimation accuracy, or incorporates all desired characteristics of a precise coefficient of determination. Considering this, we propose a new coefficient of determination by using a computational Monte Carlo approach, and exhibit main characteristics of the proposed coefficient of determination both analytically and numerically. We evaluate and compare performances of the proposed and nine existing coefficients of determination by a comprehensive Monte Carlo simulation study. The proposed measure is found superior to the existent measures when dependent variable is balanced or moderately unbalanced for probit, logit, and complementary log-log link functions and a wide range of sample sizes. Due to the extensive design space of our simulation study, we identify new conditions in which previously recommended coefficients of determination should be used carefully.