Goodness-of-fit measures of R2 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 (R2) as goodness-of-fit measures for LMEM with repeated measures longitudinal data. Theorems are presented describing the properties of R2 and relationships between the R2 statistics. A simulation study was conducted to evaluate and compare the R2 along with other criteria from literature. Finally, we applied the proposed R2 to a real virologic response data of an HIV-patient cohort. We conclude that our proposed R2 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.