Examination of mixed-effects models with nonparametrically generated data

Previous research has shown functional mixed-effects models and traditional mixed-effects models perform similarly when recovering mean and individual trajectories (Fine, Suk, & Grimm, 2019). However, Fine et al. (2019) showed traditional mixed-effects models were able to more accurately recover the underlying mean curves compared to functional mixed-effects models. That project generated data following a parametric structure. This paper extended previous work and aimed to compare nonlinear mixed-effects models and functional mixed-effects models on their ability to recover underlying trajectories which were generated from an inherently nonparametric process. This paper introduces readers to nonlinear mixed-effects models and functional mixed-effects models. A simulation study is then presented where the mean and random effects structure of the simulated data were generated using B-splines. The accuracy of recovered curves was examined under various conditions including sample size, number of time points per curve, and measurement design. Results showed the functional mixed-effects models recovered the underlying mean curve more accurately than the nonlinear mixed-effects models. In general, the functional mixed-effects models recovered the underlying individual curves more accurately than the nonlinear mixed-effects models. Progesterone cycle data from Brumback and Rice (1998) were then analyzed to demonstrate the utility of both models. Both models were shown to perform similarly when analyzing the progesterone data.