A bivariate mixed-effects location-scale model with application to ecological momentary assessment (EMA) data

A bivariate mixed-effects location-scale model is proposed for estimation of means, variances, and covariances of two continuous outcomes measured concurrently in time and repeatedly over subjects. Modeling the two outcomes jointly allows examination of BS and WS association between the outcomes and whether the associations are related to covariates. The variance–covariance matrices of the BS and WS effects are modeled in terms of covariates, explaining BS and WS heterogeneity. The proposed model relaxes assumptions on the homogeneity of the within-subject (WS) and between-subject (BS) variances. Furthermore, the WS variance models are extended by including random scale effects. Data from a natural history study on adolescent smoking are used for illustration. 461 students, from 9th and 10th grades, reported on their mood at random prompts during seven consecutive days. This resulted in 14,105 prompts with an average of 30 responses per student. The two outcomes considered were a subject’s positive affect and a measure of how tired and bored they were feeling. Results showed that the WS association of the outcomes was negative and significantly associated with several covariates. The BS and WS variances were heterogeneous for both outcomes, and the variance of the random scale effects were significantly different from zero.