Three-Level Mixed-Effects Location Scale Model With Modeling Random Scale Variance

In this dissertation, we propose a three-level mixed-effects random location scale model with modeling random scale variance (RL-RSS model). This model allows covariates to influence both error variance and random scale variance through a log-linear representation. The error variance varies across subjects through a subject-level normally distributed random scale effect, above and beyond the contribution of covariates on error variance. The subject-level random scale effect and random location effect are allowed to correlate with each other. Parameter estimation was based on the combination of maximum marginal likelihood (MML) method and Empirical Bayes (EB) method. An iterative Newton-Raphson solution was used to maximize the log likelihood, and multi-dimensional Gauss-Hermite quadrature is used to numerically approximate integral values. An SAS program via PROC NLMIXED using adaptive quadrature was developed to fit the proposed model. The data from Ecological Momentary Assessment (EMA) Adolescent Smoking Study are used to illustrate the application of the proposed model. In this study, a three-level clustering data structure, level-1 smoking events/occasions nested within level-2 waves nested within level-3 subjects, was used in the data analysis. The proposed RL-RSS model was fit to the data. Simulation process was carried out to validate the accuracy and reliability of the proposed three-level RL-RSS model. The simulation results show that RL-RSS resolves the intercept over-estimation of random scale variance occurring in the simple mixed-effect random location scale model.