Goodness-of-fit measures of R 2 for repeated measures mixed effect models

Linear mixed effects model (LMEM) is efficient in modeling repeated measures longitudinal data. However, little research has been done in developing goodness-of-fit measures that can evaluate the models, particularly those that can be interpreted in an absolute sense without referencing a null model. This paper proposes three coefficient of determination (R 2) as goodness-of-fit measures for LMEM with repeated measures longitudinal data. Theorems are presented describing the properties of R 2 and relationships between the R 2 statistics. A simulation study was conducted to evaluate and compare the R 2 along with other criteria from literature. Finally, we applied the proposed R 2 to a real virologic response data of an HIV-patient cohort. We conclude that our proposed R 2 statistics have more advantages than other goodness-of-fit measures in the literature, in terms of robustness to sample size, intuitive interpretation, well-defined range, and unnecessary to determine a null model.