ERMs, simple tools for complicated data

While the term "extended regression model" (ERM) may be new, the method is not. ERMs are regression models with continuous outcomes (including censored and tobit outcomes), binary outcomes, and ordered outcomes that are fit via maximum likelihood and that also account for endogenous covariates, sample selection, and nonrandom treatment assignment. These models can be used when you are worried about bias due to unmeasured confounding, trials with informative dropout, outcomes that are missing not at random, selection on unobservables, and more. ERMs provide a unifying framework for handling these complications individually or in combination. I will briefly review the types of complications that ERMs can address. I will work through examples that demonstrate several of these complications and show some inferences we can make despite those complications.