College of Educational and Behavioral Sciences, Department of Applied Statistics and Research Methods
University of Northern Colorado
Type of Resources
Place of Publication
University of Northern Colorado
In classical statistical problems, variability is often considered a nuisance parameter in both the technical and the practical sense. However, emerging evidence suggests that in certain settings, the underlying variability of subject measures may play an equally important role as other covariates in predicting future outcomes of interest. Intensive longitudinal data has become increasingly popular in many scientific applications, providing opportunities to explore the variability of predictors within subjects to address a wide range of research questions. Despite its potential, there remains a dearth of research on models that incorporate variation as a predictor in the mean model. Furthermore, there has been a recent surge of interest in jointly modeling outcomes for intensive longitudinal data, as it offers a powerful framework for exploring the complex relationships between outcomes. Ignoring the inherent association between the outcomes by conducting separate analyses can lead to biased results. Joint modeling has been extensively studied for normal outcomes to better understand between- and within-subject dynamic changes in modeling multiple outcomes. However, there is a significant need for more studies on multivariate longitudinal models that jointly model mean and dispersion for non-normal data. This dissertation presents a novel multivariate hierarchical generalized linear model for intensive longitudinal data from exponential families to evaluate the association among the outcomes. A unique focus of this study is on the role of outcome variability as a predictor in mean models, which enables the detection of associations between within-subject variation and outcomes of interest. The proposed model is applied to analyze the marijuana data from the Motivation Research Lab at the University of Northern Colorado. To validate the effectiveness of the presented model with dispersion, it is compared with the same model without dispersion as a predictor. The simulation results showed that the model with dispersion performed better in terms of standard error, bias, and prediction mean square error for a wide range of sample sizes and parameter schemes. Applying the model to the marijuana data set demonstrated that the dispersion factor included in the model was a significant factor in predicting the outcome of interest. Specifically, the study addressed the collaborator’s research question regarding the relationship between craving variability and frequency of marijuana use. The results indicated that individuals with higher variability around their craving means tend to have a higher frequency of marijuana use. Overall, the findings highlight the importance of considering variability as a predictor in mean models and demonstrate the utility of the proposed multivariate hierarchical generalized linear model for analyzing intensive longitudinal data.
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