  Mobile health is a rapidly developing field in which behavioral treatments
are delivered to individuals via wearables or smartphones to facilitate
health-related behavior change. Micro-randomized trials (MRT) are an
experimental design for developing mobile health interventions. In an MRT the
treatments are randomized numerous times for each individual over course of the
trial. Along with assessing treatment effects, behavioral scientists aim to
understand between-person heterogeneity in the treatment effect. A natural
approach is the familiar linear mixed model. However, directly applying linear
mixed models is problematic because potential moderators of the treatment
effect are frequently endogenous---that is, may depend on prior treatment. We
discuss model interpretation and biases that arise in the absence of additional
assumptions when endogenous covariates are included in a linear mixed model. In
particular, when there are endogenous covariates, the coefficients no longer
have the customary marginal interpretation. However, these coefficients still
have a conditional-on-the-random-effect interpretation. We provide an
additional assumption that, if true, allows scientists to use standard software
to fit linear mixed model with endogenous covariates, and person-specific
predictions of effects can be provided. As an illustration, we assess the
effect of activity suggestion in the HeartSteps MRT and analyze the
between-person treatment effect heterogeneity.
