A 3-level mixed-effects location scale model with an application in ecological momentary assessment data

In longitudinal studies, the homogeneous variance assumption, both within- and between-subjects, can be violated, and the random subject effects can further be correlated with the error terms. The existing methodology for variance modeling is only available for 2-level models. For this, in this dissertation, 3-level mixed-effects location scale models that allow for heterogeneous variance modeling were developed. The proposed 3-level random-location random-scale (RL-RS) model is based on a conventional 3-level mixed-effects regression model with a random intercept at each level, but allows covariates to additionally influence the variances at each level using a log-linear representation throughout. The error variance is further allowed to vary across subjects, above and beyond the contribution of covariates, through a normally distributed subject-level random scale effect (in the log-linear model). The error variance then has a log-normal distribution at the subject level. The random scale effect is also allowed to be correlated with the subject-level random location effects. A simpler 3-level random-location fixed-scale (RL-FS) model that is similar to the 3-level RL-RS model in every aspect, but without the random scale effect in the error variance, was also developed. For parameter estimation, the maximum marginal likelihood (MML) estimation method was proposed. Fisher's scoring optimization algorithm was derived to achieve the MML solution in the RL-FS model, while an iterative Newton-Raphson optimization algorithm using multidimensional Gauss-Hermite quadrature was derived for the RL-RS model. A SAS program using PROC NLMIXED was also developed to fit the 3-level mixed-effects location scale models with/without the random scale effects. The accuracy of the parameter estimation of the proposed 3-level RL-RS model was investigated using a series of simulations via SAS PROC NLMIXED.;Data from an Adolescent Smoking Study using Ecological Momentary Assessment (EMA) was used to illustrate the application of the 3-level mixed-effects location scale models. The parameter estimates, standard errors and deviances from the 3-level random intercept model, RL-FS model and RL-RS model were then compared.