Thinking Through Logit and a Way Forward

• In Event: Methodology Section Open Call Paper Session

Abstract

Logit models have long occupied a central place in sociological research on binary outcomes. Prior methodological literature argues that they suffer from three problems: coefficients cannot be compared across nested models, coefficients are biased when there is unmodeled variation in the outcome, and coefficients cannot be compared across groups. This paper offers a new pedagogical perspective on logit and re-evaluates these three claims.

Departing from prior work, I avoid the latent outcome formulation and instead emphasize the distinction between estimand and estimation. I argue that much confusion arises from conflating properties of the log odds ratio as an estimand with properties of logit as a parametric estimator. As an estimand, the log odds ratio exhibits noncollapsibility without confounding, meaning that marginal and conditional effects need not align even absent confounding. As an estimator, logit relies on functional form assumptions that are generally incompatible across nested models, which is an important issue that has been overlooked.

From this perspective, I revisit the three purported problems. I show that difficulties with nested model comparisons stem from both noncollapsibility and functional form incompatibility. In contrast to existing works, I argue that estimating logit in the presence of unmodeled outcome variation is not problematic. Likewise, cross-group comparisons do not introduce bias as long as the functional form assumption holds in each group.

Finally, I outline a way forward. At the estimand level, I advocate for more interpretable alternatives such as risk differences and average marginal effects. At the estimation level, I recommend flexible nonparametric approaches such as double/debiased machine learning and targeted maximum likelihood estimation.

Author

• Ang Yu, Hong Kong University of Science and Technology