Ecological Momentary Assessment (EMA) studies aim to explore how subjects’ psychological states or behaviors interact with the real environment. Hand-held devices such as smartphones enable the participants in EMA studies to respond to the prompted assessments or self-initiate the assessments in real time. Besides conventional hand-held devices, wearable devices, e.g., actigraphy, have enabled more accurate and intensive tracking of subject's behaviors such as physical activities (PA). Relevant statistical methods for intensive longitudinal data analysis are continuing to be developed, however challenges remain such as modeling of the complex multilevel serial correlation in the data, informative nonresponses in self-initiated assessments, and identical data entries and also the irregularly distributed PA data. In this thesis, extended methods specifically for deal with the above mentioned issues were proposed. First, during EMA studies, subjects can receive prompted assessments intensively across days and within each day, which results in three-level longitudinal data, e.g., subject-level (level-3), day-level nested in subject (level-2) and assessment-level nested in each day (level-1). Given the three-level EMA data, we proposed a linear mixed effects model with autocorrelated random effects at day-level and assessment-level. And with real time stamps of the assessments, we also provided a useful extension of this proposed model to deal with irregularly-spaced EMA assessments. Second, we addressed the issue of non-responsivity of self-initiated assessments in EMA studies, where subjects are instructed to self-initiate reports when experiencing defined events, e.g., smoking. The frequency and determinants of non-responses in these event reports is usually unknown and these non-responses can even be associated with the primary longitudinal EMA outcome (e.g., mood) in which case a joint modeling of the non-responsitivity and the mood outcome is possible. In certain EMA studies, random prompts, distinct from the self-initiated reports, may be converted to event reports, which provide some information about the subject's non-responsivity of event reporting. Using such data, we proposed a shared-parameter location-scale model to link the primary outcome model for mood and a model for subjects’ non-responsivity by shared random effects which characterize a subject’s mood change pattern and mood variability. Third, for application of the MELS model, a problem that occurs is when subjects provide identical responses and therefore exhibit almost zero variance in their responses. It is assumed that certain latent clustering may exist to distinguish those who displayed different variance patterns. To deal with this, we assumed a mixture of normal distributions for scale random effects. For estimation, we incorporated Maximize-A-Posteriori (MAP) algorithm into the Expectation-Maximization (EM) algorithm framework so that we can estimate the posterior probability of clustering membership for each subject. Lastly, to model the intensive irregularly distributed PA counts, we proposed a negative binomial mixed effects location-scale model (NBLS) to model these intensive longitudinal PA counts and to account for the heterogeneity in both the mean and dispersion level across subjects. Further, to handle the issue of inflated numbers of zeros in the PA data, we also proposed a hurdle/zero-inflated version which additionally includes the modeling of the probability of having non-zero PA levels.



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