A1562
Title: On testing random effects in linear and non-linear mixed effects models
Authors: Germaine Uwimpuhwe - Durham University (United Kingdom) [presenting]
Reza Drikvandi - Durham University (United Kingdom)
Abstract: Linear and non-linear mixed models (LMMs and NLMMs) are frequently used to analyse longitudinal data with nested structures. Unlike LMMs, testing the necessity of random effects in NLMMs remains challenging due to the limitations of traditional likelihood-based methods, which are constrained by assumptions of boundary issues and normality, as well as convergence issues and difficulties with correlated random effects. To address those issues, a permutation-based test is developed and extended, originally designed for linear models, to the non-linear context. The approach uses non-parametric estimation techniques, including variance least squares (VLS) and method of moments (MM) based on two-stage and first-order approximation. Through extensive empirical analyses, these tests are compared with the traditional mixture of chi-square tests (MLRT) based on empirical power, Type I error rate, and bias. Results show that permutation-based tests outperform the traditional methods. For example, a test based on VLS achieves power between 92\% and 100\%, while MM-based methods range from 88\% to 100\%, with a controlled Type I error rate. Tests have stable convergence rates across scenarios, in contrast to the MLRT method, which suffers from convergence issues. The R package TestREnlme is developed for the implementation of these methods, facilitating non-parametric estimation and permutation tests for random effects.
