Comparing effects within and across models using marginal effects

Comparing effects is a common task for the applied data analyst. For example, tests of interaction involve comparing the effects of one variable at multiple levels of another variable. Comparisons of effect sizes within models involve quantifying each focal variable's effect and testing their equality. Cross-model comparisons are also common, for example when comparing processes across different groups. Tests of attenuation like mediation similarly involve comparisons across multiple models. Despite their ubiquity, such tests have challenges: coefficients that do not quantify effects in the metric of interest, rescaling of coefficients in nonlinear and categorical models, and predictors on differing metrics. In this presentation, I detail the statistical underpinnings of within- and across-model comparisons, present a marginal effects framework that allows for comparisons across most any regression model or predictor type, and show how to automate these tests using the new suest2, mecompare, meinequality, and totalme commands. Compared with existing software, the new commands can be used for single or multiple models; single-level, multilevel, and longitudinal models; any amount of change for continuous predictors; summary measures for nominal and ordinal variables; comparisons across variables on different metrics; comparisons across different model types; and custom and nonstandard tests of effects. I demonstrate the utility of the approach and the new commands using publicly available social science data.