A shared parameter location scale mixed effect model for EMA data subject to informative missing

In this paper, we address the problem of accounting for informative missing in the context of ecological momentary assessment studies (sometimes referred to as intensive longitudinal studies), where each study unit gets measured intensively over time and intermittent missing is usually present. We present a shared parameter modeling approach that links the primary longitudinal outcome with potentially informative missingness by a common set of random effects that summarize a subjects’ specific traits in terms of their mean (location) and variability (scale). The primary outcome, conditional on the random effects, are allowed to exhibit heterogeneity in terms of both the mean and within subject variance. Unlike previous methods which largely rely on numerical integration or approximation, we estimate the model by a full Bayesian approach using Markov Chain Monte Carlo. An adolescent mood study example is illustrated together with a series of simulation studies. Results in comparison to more conventional approaches suggest that accounting for the common but unobserved random subject mean and variance effects, shared between the primary outcome and missingness models, can significantly improve the model fit, and also provide the benefit of understanding how missingness can affect the inference for the primary outcome.