A Two-Stage Approach to a Latent Variable Mixed-Effects Location-Scale Model

Understanding within- and between-subject variation in repeated measures is central to longitudinal behavioral investigations. Mixed-effects location-scale models include distinct variance models to permit study of heterogeneity of within- and between-subject variation. Recent developments have extended the model to address measurement error in the longitudinal response. Accounting for variation in the response that is due to measurement error is especially important in studies that focus efforts to understand the within-subject variation. Relative to a mixed-effects location-scale model for a variable assumed to be measured without error, the latent variable version of the model is more complicated, and this complexity can be carried over to increased computational demands. One approach to the estimation of the latent variable version of the model simplifies the calculation by analytically removing the random scale effect from the marginal response distribution, resulting in a substantial reduction in the computational burden using maximum likelihood estimation. This paper proposes a two-stage approach in which factor scores and their corresponding standard errors of measurement are estimated and then incorporated into a mixed-effects location-scale model. This paper considers the two approaches in the context of daily diary data from a large sample of adults in the United States.