Comparing Logit and Probit Coefficients From Same-Sample Nested Models: Adapting the (Revised) KHB Method to an SEM Framework

Karlson et al. (2012) suggested an estimation strategy for logistic and probit regression models, the so-called KHB method, which allows differences between regression coefficients in same-sample nested regression models to be interpreted. We introduce the pseudo mediation model (PMM), which implements the KHB method in a structural equation modeling (SEM) framework. The PMM has several advantages over the “standard” KHB method: First, missing data can be handled under less restrictive assumptions. Second, predictors can be included as latent variables to avoid bias due to measurement error. Finally, nested data structures and survey weights can be accounted for. We illustrate the method with empirical examples.