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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.


In linear mixed‐effects models, random effects are used to capture the heterogeneity and variability between individuals due to unmeasured covariates or unknown biological differences. Testing for the need of random effects is a nonstandard problem because it requires testing on the boundary of parameter space where the asymptotic chi‐squared distribution of the classical tests such as likelihood ratio and score tests is incorrect. In the literature several tests have been proposed to overcome this difficulty, however all of these tests rely on the restrictive assumption of i.i.d. measurement errors. The presence of correlated errors, which often happens in practice, makes testing random effects much more difficult. In this paper, we propose a permutation test for random effects in the presence of serially correlated errors. The proposed test not only avoids issues with the boundary of parameter space, but also can be used for testing multiple random effects and any subset of them. Our permutation procedure includes the permutation procedure in Drikvandi, Verbeke, Khodadadi, and Partovi Nia (2013) as a special case when errors are i.i.d., though the test statistics are different. We use simulations and a real data analysis to evaluate the performance of the proposed permutation test. We have found that random slopes for linear and quadratic time effects may not be significant when measurement errors are serially correlated.

Item Type:Article
Full text:(AM) Accepted Manuscript
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Publisher statement:This is the peer reviewed version of the following article: Drikvandi, Reza & Noorian, Sajad (2019). Testing random effects in linear mixed-effects models with serially correlated errors. Biometrical Journal 61(4): 802-812., which has been published in final form at This article may be used for non-commercial purposes in accordance with Wiley Terms and Conditions for Use of Self-Archived Versions.
Date accepted:19 December 2018
Date deposited:22 October 2021
Date of first online publication:05 February 2019
Date first made open access:22 October 2021

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