A Bivariate Location -Scale Mixed-Effects Model

In longitudinal and clustered data, homogeneous between-subject (BS) and within-subject (WS) variance assumptions are often not supported by data. Also, in social, behavioral, and medical studies multiple outcomes are measured per subject. Often, these outcomes are modeled separately. In this dissertation a bivariate model with heterogeneous between- and within-subject variance for continuous outcomes were developed. The proposed model specified BS and WS covariance as dependent on a set of covariates. This allowed researchers to investigate how association of two outcomes differed for various subject subpopulations. The WS variance also included random scale effect that explained variation in WS variance above and beyond contribution of covariates. The error variance had log-normal distribution at the subject level. Conditional subject measurement errors are independent from the random location and scale effects, whereas the random location and scale effect are allowed to be correlated. For the parameter estimation, maximum marginal likelihood estimation method was proposed. The model was implemented in SAS PROC NLMIXED. Frequent recording of mood, feelings, and thoughts using handheld devices is referred to as Ecological Momentary Assessment (EMA). This method of data collection produces data with many observations per subject. Proposed model was used to analyze EMA data on adolescent smoking. Two continuous measures of mood, Positive Affect (PA) and Tired/Bored (TB), were modeled jointly. Covariates collected at the baseline wave and used in the analysis included grade in high school (9th or 10th grade), gender, day of the week, negative mood regulation, novelty seeking, depression, and smoking status. Results of the final model showed that the BS and WS variances were heterogeneous for both outcomes, and the variance of the random scale effects were significantly different from zero. Also the WS covariance differed between subject groups with the estimated reference WS covariance being -0.6269 (estimated correlation -0.25).