We address the issue of non-ignorable nonresponses in the self-initiated assessments in Ecological Momentary Assessments (EMA) or other mobile health (mHealth) studies, where subjects are instructed to self-initiate reports on their mood and the environment when experiencing events, e.g., smoking. In this case, existing methods for missing data can be insufficient because the occurrences of nonresponses in self-initiated event reports are unknown and the missingness may not be at random. Certain EMA studies provided some information about the extent of missingness. But still, the nonresponses can be associated with mood, the primary longitudinal outcome, in terms of mood level (location) and stability (scale). Specifically, we propose a shared-parameter location-scale growth model to link the primary outcome model for mood to a model for subjects’ responsivity by shared latent effects regarding subject’s mood level, mood change pattern as well as mood variability. Via simulations and real data analysis, our proposed model is shown to be more informative and has better coverage of parameters and provides better fit to the data than conventional models.