We discuss “Linear mixed models with endogenous covariates: modeling sequential treatment effects with application to a mobile health study” by Qian, Klasnja and Murphy. In this discussion, we study when the linear mixed effects models with endogenous covariates are feasible to use by providing examples and diagnostic tools as well as discussing potential extensions. This includes evaluating feasibility of partial likelihood-based inference, checking the conditional independence assumption, estimation of marginal effects, and kernel extensions of the model.
"Comment: Diagnostics and Kernel-based Extensions for Linear Mixed Effects Models with Endogenous Covariates." Statist. Sci. 35 (3) 396 - 399, August 2020. https://doi.org/10.1214/20-STS782