Maximum Likelihood Estimation of Non-Normal Random Effects and Random Errors in Nonlinear Random Effects Models

Abstract

Nonlinear random effects models (NREMs) are particularly useful for modeling longitudinal data that follow intrinsically nonlinear trends. However, NREMs assume both random effects and random errors to be normally distributed, which is likely violated when the outcome variable does not appear normal. No existing software under the frequentist framework provides researchers the flexibility to specify non-normal random effects to date. To address this significant gap in the application and research of NREMs, we developed an R routine NEfit.R that allows the specification of non-normal random effects and random errors using Gauss-Hermite Quadrature approximation and Newton-Raphson iteration. This study includes a motivating real-data application and a comprehensive Monte Carlo simulation study that supports the robustness of the performance of NEfit.R.