Testing random effects in linear mixed‐effects models with serially correlated errors

Drikvandi, Reza and Noorian, Sajad (2019) Testing random effects in linear mixed‐effects models with serially correlated errors. Biometrical Journal, 61 (4). pp. 802-812. ISSN 0323-3847

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Abstract

In linear mixed-effects models, random effects are used to capture the heterogeneityand variability between individuals due to unmeasured covariates or unknown bio-logical differences. Testing for the need of random effects is a nonstandard problembecause it requires testing on the boundary of parameter space where the asymptoticchi-squared distribution of the classical tests such as likelihood ratio and score testsis incorrect. In the literature several tests have been proposed to overcome this diffi-culty, however all of these tests rely on the restrictive assumption of i.i.d. measurementerrors. The presence of correlated errors, which often happens in practice, makes test-ing random effects much more difficult. In this paper, we propose a permutation testfor random effects in the presence of serially correlated errors. The proposed test notonly avoids issues with the boundary of parameter space, but also can be used fortesting multiple random effects and any subset of them. Our permutation procedureincludes the permutation procedure in Drikvandi, Verbeke, Khodadadi, and PartoviNia (2013) as a special case when errors are i.i.d., though the test statistics are dif-ferent. We use simulations and a real data analysis to evaluate the performance of theproposed permutation test. We have found that random slopes for linear and quadratictime effects may not be significant when measurement errors are serially correlated.