Arbitrarily Normalized Coefficients, Information Sets, and False Reports of "Biases" in Binary Outcome Models

Abstract

Empirical researchers sometimes misinterpret how additional regressors, heterogeneity corrections, and multilevel factors impact the interpretation of the estimated parameters in binary outcome models such as logit and probit. This can result in incorrect inferences about the importance of incorporating such features in these nonlinear statistical models. Some reports of biases in binary outcome models appear related to the arbitrary variance normalization required in binary outcome models. A focus on readily interpretable numerical quantities, rather than conveniently chosen "effects" as measured by arbitrarily scaled coefficients, would eliminate nearly all of the interpretation problems we highlight in this paper. Copyright by the President and Fellows of Harvard College and the Massachusetts Institute of Technology.