Testing multiple variance components in linear mixed-effects models

Drikvandi, Reza; Verbeke, Geert; Khodadadi, Ahmad; Nia, Vahid Partovi

doi:10.1093/biostatistics/kxs028

Cited by 52 publications

(95 citation statements)

References 25 publications

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“…First, there are linear mixed effects models not of form (3), for example, those including both random intercepts and random slopes (Drikvandi et al, 2013). First, there are linear mixed effects models not of form (3), for example, those including both random intercepts and random slopes (Drikvandi et al, 2013).…”

Section: Analysis Of Longitudinal Pulmonary Microbiome Datamentioning

confidence: 99%

“…Let m be the total number of phenotypic variance components except the error variance component. Later Drikvandi, Verbeke, Khodadadi, and PartoviNia (2013) proposed a permutation test that does not depend on the distribution of the random effects and errors except for their mean and variance and can be applied to the m > 1 situation. Greven, Crainiceanu, Küchenhoff, and Peters (2008) provided a pseudolikelihood-heuristic extension of this method to the m > 1 situation.…”

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Exact variance component tests for longitudinal microbiome studies

Zhai

Knox

Twigg

et al. 2019

Genetic Epidemiology

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In metagenomic studies, testing the association between microbiome composition and clinical outcomes translates to testing the nullity of variance components. Motivated by a lung human immunodeficiency virus (HIV) microbiome project, we study longitudinal microbiome data by using variance component models with more than two variance components. Current testing strategies only apply to models with exactly two variance components and when sample sizes are large. Therefore, they are not applicable to longitudinal microbiome studies. In this paper, we propose exact tests (score test, likelihood ratio test, and restricted likelihood ratio test) to (a) test the association of the overall microbiome composition in a longitudinal design and (b) detect the association of one specific microbiome cluster while adjusting for the effects from related clusters. Our approach combines the exact tests for null hypothesis with a single variance component with a strategy of reducing multiple variance components to a single one. Simulation studies demonstrate that our method has a correct type I error rate and superior power compared to existing methods at small sample sizes and weak signals. Finally, we apply our method to a longitudinal pulmonary microbiome study of HIV‐infected patients and reveal two interesting genera Prevotella and Veillonella associated with forced vital capacity. Our findings shed light on the impact of the lung microbiome on HIV complexities. The method is implemented in the open‐source, high‐performance computing language Julia and is freely available at https://github.com/JingZhai63/VCmicrobiome.

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Section: Analysis Of Longitudinal Pulmonary Microbiome Datamentioning

confidence: 99%

mentioning

confidence: 99%

Exact variance component tests for longitudinal microbiome studies

Zhai

Knox

Twigg

et al. 2019

Genetic Epidemiology

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“…Our permutation procedure includes the permutation procedure in Drikvandi et al. () as a special case when errors are i.i.d., though the test statistics are different.…”

Section: Introductionmentioning

confidence: 99%

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

Drikvandi

Noorian

2019

Biometrical J

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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.

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“…When the number of fixed effects are given with no need to select, the examples include Stram and Lee [17] that considered variance components testing in longitudinal mixed effects models under the normality assumption and Greven et al [6] that proposed a restricted likelihood ratio test for the existence of random effects in linear mixed models. Drikvandi et al [3] introduced a test that only assumes the existence of second order moments of random effects and errors. Moreover, some tests for variance components were also constructed for generalized linear mixed models [10,16], semiparametric mixed models [18,9], nonlinear mixed-effects elliptical models [14], and ANOVA models [8], among others.…”

Section: Introductionmentioning

confidence: 99%

Inference for mixed models of ANOVA type with high-dimensional data

Chen

Shi

et al. 2015

Journal of Multivariate Analysis

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a b s t r a c tInference for variance components in linear mixed models of ANOVA type, including estimation and testing, has been investigated when the number of fixed effects is fixed. However, for high-dimensional data, this number is large and would be regarded as a divergent value as the sample size goes to infinity. In this paper, existing tests are extended to handle this problem with a sparse model structure. To avoid the impact from insignificant fixed effects, the proposed tests are post-selection-based with an orthogonality-based selection of SCAD type applied to selecting significant fixed effects into working model. The selection and estimation of fixed effects are under the assumption on the existence of second order moments for errors. Two types of tests for random effects are considered and some new insights are obtained. The proposed tests are distribution-free, though they request the existence of the fourth moments of random effects and errors. The proposed methods are illustrated by simulation studies and a real data analysis.

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Testing multiple variance components in linear mixed-effects models

Cited by 52 publications

References 25 publications

Exact variance component tests for longitudinal microbiome studies

Exact variance component tests for longitudinal microbiome studies

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

Inference for mixed models of ANOVA type with high-dimensional data

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