Two-part mixed-effects location scale models

Longitudinal time use data afford the opportunity to study within- and between-individual differences, but can present challenges in data analysis. Often the response set includes a large number of zeros representing those who did not engage in the target behavior. Coupled with this is a continuous measure of time use for those who did engage. The latter is strictly positive and skewed to the right if relatively few individuals engage in the behavior to a greater extent. Data analysis is further complicated for repeated measures, because within-individual responses are typically correlated, and some respondents may have missing data. This combination of zeros and positive responses is characteristic of a type of semicontinuous data in which the response is equal to a discrete value and is otherwise continuous. Two-part models have been successfully applied to cross-sectional time use data when the research goals distinguish between a respondent's likelihood to engage in a behavior and the time spent conditional on any time being spent, as these models allow different covariates to relate to each distinct aspect of a behavior. Two-part mixed-effects models extend two-part models for analysis of longitudinal semicontinuous data to simultaneously address longitudinal decisions to engage in a behavior and time spent conditional on any time spent. Heterogeneity between and within individuals can be studied in unique ways. This paper presents applications of these models to daily diary data to study individual differences in time spent relaxing or engaged in leisure activities for an adult sample.