Examination of Nonlinear and Functional Mixed-Effects Models with Nonparametrically Generated Data

Previous research has shown functional mixed-effects models and traditional mixed-effects models perform similarly when recovering individual trajectories when data were generated following a parametric structure. We extend this previous work and compare nonlinear mixed-effects (NMEM) and functional mixed-effects models' (FMEM) ability to recover underlying trajectories when generated from an inherently nonparametric process. Nonlinear trajectories were generated using B-splines, NMEMs and FMEMs were estimated, and the accuracy of the estimated curves was examined. Sample size, number of time points per curve, and measurement design were varied across simulation conditions. Results showed the FMEMs recovered the underlying mean curve more accurately than the NMEMs, and that, the FMEMs tended to recover the underlying individual curves more accurately than the NMEMs. Progesterone cycle data were then analyzed to demonstrate the utility of both approaches, and models performed similarly when analyzing these data.