Mixed-Effects Location-Scale Models for Conditionally Normally Distributed Repeated-Measures Data

Hypotheses about psychological processes are most frequently dedicated to individual mean differences, but individual differences in variability are likely to be important as well. The mixed-effects location-scale model estimates individual differences in both mean level and variability in a single model, and represents an important advance in testing variability-related hypotheses. However, the mixed-effects location-scale model remains relatively novel to empirical scientists as statistical software is often handicapped by more complex models and a paucity of methodological studies exist examining the statistical properties of this model. This dissertation investigates the mixed-effects location-scale model through the development of open-source software for its estimation and through simulation and empirical studies. First, the theoretical framework for the mixed-effects location-scale model is presented followed by a description of the Metropolis-Hastings algorithm developed to estimate this model. Then, two simulation studies are presented evaluating the power to detect and predict individual differences in variability as well as identify the consequences of model misspecification. Finally, results of an empirical analysis examining individual differences in mean level and variability of unstructured movements from a sample of older adults with and without probable mild Alzheimer’s disease is presented. Results of the power investigation simulation study indicated that the power to detect the scale-model random intercept variance and the effect of an individual-level predictor of residual variability increased with greater numbers of individuals and occasions, and that failing to detect the scale-model random intercept variance essentially precluded the detection of systematically varying fixed effects for an individual-level predictor of residual heterogeneity. Results of the misspecification simulation study indicated that misspecifying the location model and/or scale model for the residual variance had consequences only for fixed and random effects on the same side of the model. Finally, results of the empirical data analysis indicated individuals with probable mild Alzheimer’s disease averaged less movement compared to healthy individuals, but did not differ in the variability of their unstructured movements. In sum, this dissertation provides information useful to empirical scientists as they progress from study design through analysis, interpretation, and reporting for publication. Advisors: Lesa Hoffman & Jonathan Templi