Log Odds and the Interpretation of Logit Models

Abstract

Objective: We discuss how to interpret coefficients from logit models, focusing on the importance of the standard deviation (σ) of the error term to that interpretation. Study Design: We show how odds ratios are computed, how they depend on the standard deviation (σ) of the error term, and their sensitivity to different model specifications. We also discuss alternatives to odds ratios. Principal Findings: There is no single odds ratio; instead, any estimated odds ratio is conditional on the data and the model specification. Odds ratios should not be compared across different studies using different samples from different populations. Nor should they be compared across models with different sets of explanatory variables. Conclusions: To communicate information regarding the effect of explanatory variables on binary {0,1} dependent variables, average marginal effects are generally preferable to odds ratios, unless the data are from a case–control study.