The Use of Permutation Tests for Variance Components in Linear Mixed Models

Samuh, Monjed H.; Grilli, Leonardo; Rampichini, Carla; Salmaso, Luigi; Lunardon, Nicola

doi:10.1080/03610926.2011.587933

Cited by 20 publications

(17 citation statements)

References 14 publications

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“…Here we implicitly assume that no correlation between X and Z exists. If we only generate the new response variable y (say y *) from the fitted null model (i.e., the fixed effects logistic model with only covariates X ) while letting both X and Z unchanged, then we are performing the parametric bootstrap test [ 15 , 16 , 25 , 36 , 37 ]. The permutation and bootstrap algorithms are almost the same except the production of the new resampling dataset in the second step.…”

Section: Methodsmentioning

confidence: 99%

“…Usually, the number of replicates B in the permutation test is set to 1000 ~ 2000 for a relatively large significance level, say α = 0.05. Whereas some authors [ 14 , 16 ] empirically found that much smaller values of B (e.g., 200 or 500) could also behave satisfactorily.…”

Section: Methodsmentioning

confidence: 99%

“…On the other hand, when encountering complex hypothesis testing scenarios in practical data analyses, resorting to resampling-based methods is a very natural and effective strategy. Faraway [ 15 ] and Samuh, et al [ 16 ] applied the parametric bootstrap approach for testing the variance component. Lee and Braun [ 17 ] and Samuh, et al [ 16 ] used the permutation procedure to resolve this problem.…”

Section: Introductionmentioning

confidence: 99%

“…Faraway [ 15 ] and Samuh, et al [ 16 ] applied the parametric bootstrap approach for testing the variance component. Lee and Braun [ 17 ] and Samuh, et al [ 16 ] used the permutation procedure to resolve this problem. Their results demonstrated that the bootstrap and permutation tests can control the type I error rate correctly and are more powerful compared to the tests that are based on the usual asymptotic mixture.…”

Section: Introductionmentioning

confidence: 99%

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Permutation-based variance component test in generalized linear mixed model with application to multilocus genetic association study

Zeng

Zhao

Li³

et al. 2015

BMC Med Res Methodol

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BackgroundIn many medical studies the likelihood ratio test (LRT) has been widely applied to examine whether the random effects variance component is zero within the mixed effects models framework; whereas little work about likelihood-ratio based variance component test has been done in the generalized linear mixed models (GLMM), where the response is discrete and the log-likelihood cannot be computed exactly. Before applying the LRT for variance component in GLMM, several difficulties need to be overcome, including the computation of the log-likelihood, the parameter estimation and the derivation of the null distribution for the LRT statistic.MethodsTo overcome these problems, in this paper we make use of the penalized quasi-likelihood algorithm and calculate the LRT statistic based on the resulting working response and the quasi-likelihood. The permutation procedure is used to obtain the null distribution of the LRT statistic. We evaluate the permutation-based LRT via simulations and compare it with the score-based variance component test and the tests based on the mixture of chi-square distributions. Finally we apply the permutation-based LRT to multilocus association analysis in the case–control study, where the problem can be investigated under the framework of logistic mixed effects model.ResultsThe simulations show that the permutation-based LRT can effectively control the type I error rate, while the score test is sometimes slightly conservative and the tests based on mixtures cannot maintain the type I error rate. Our studies also show that the permutation-based LRT has higher power than these existing tests and still maintains a reasonably high power even when the random effects do not follow a normal distribution. The application to GAW17 data also demonstrates that the proposed LRT has a higher probability to identify the association signals than the score test and the tests based on mixtures.ConclusionsIn the present paper the permutation-based LRT was developed for variance component in GLMM. The LRT outperforms existing tests and has a reasonably higher power under various scenarios; additionally, it is conceptually simple and easy to implement.

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Section: Methodsmentioning

confidence: 99%

Section: Methodsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Permutation-based variance component test in generalized linear mixed model with application to multilocus genetic association study

Zeng

Zhao

Li³

et al. 2015

BMC Med Res Methodol

View full text Add to dashboard Cite

show abstract

“…In the literature under complex hypothesis-testing scenarios a natural way to resolve the problem is to resort to the bootstrap technique because of its generality and conceptual simplicity [ 23 - 25 ]. Faraway [ 26 ] and Samuh et al [ 27 ] adopted parametric bootstrap methods for the likelihood ratio variance component test in linear mixed models. To examine the variance component in generalized linear mixed models, Sinha [ 28 ] proposed a score test and conducted it by a means of parametric bootstrap.…”

Section: Introductionmentioning

confidence: 99%

Bootstrap Restricted Likelihood Ratio Test for the Detection of Rare Variants

Zeng¹,

Wang

2015

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In this paper the detection of rare variants association with continuous phenotypes of interest is investigated via the likelihood-ratio based variance component test under the framework of linear mixed models. The hypothesis testing is challenging and nonstandard, since under the null the variance component is located on the boundary of its parameter space. In this situation the usual asymptotic chisquare distribution of the likelihood ratio statistic does not necessarily hold. To circumvent the derivation of the null distribution we resort to the bootstrap method due to its generic applicability and being easy to implement. Both parametric and nonparametric bootstrap likelihood ratio tests are studied. Numerical studies are implemented to evaluate the performance of the proposed bootstrap likelihood ratio test and compare to some existing methods for the identification of rare variants. To reduce the computational time of the bootstrap likelihood ratio test we propose an effective approximation mixture for the bootstrap null distribution. The GAW17 data is used to illustrate the proposed test.

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Synergized Bootstrapping: The Whole is Faster than the Sum of Its Parts

Loossens

Verdonck

Tuerlinckx

2020

Springer Proceedings in Mathematics &Amp; Statistics

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Re-sampling methods are popular for assessing uncertainty, testing hypotheses or for cross-validation because of their simplicity. They all rely on a similar scheme: generating replicated datasets by sampling data points from an original dataset, fitting a model or conducting a statistical test on each of these, and aggregating the results. However, when fitting the model or conducting the statistical test becomes time-consuming, re-sampling methods become impractical because of the many replications. Many methods have been proposed to alleviate the computational burden, but they generally do not incorporate two key features of re-sampled datasets. One, re-sampled datasets all stem form the same origin and therefore have similar characteristics. Two, there is a large class of cost functions for which the cost of a parameter set given data can be computed by summing its costs across the individual data points. As a consequence, once the costs of the individual data points are known, the parameter set's cost can be obtained for any of the cost functions related to one of the replicated datasets. The synergized bootstrap method put forward in this paper exploits these two features to accelerate the optimization procedures for re-sampling methods. It is applied to the non-parametric bootstrapping of the parameters of a univariate mixture model, of which the min-log-likelihood function can be shown to have multiple local minima, using the Differential Evolution heuristic as global optimizer. It is demonstrated that the synergized method can lead to incredible accelerations (up to 100-500 times faster) while being more accurate than the standard DE method.

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The Use of Permutation Tests for Variance Components in Linear Mixed Models

Cited by 20 publications

References 14 publications

Permutation-based variance component test in generalized linear mixed model with application to multilocus genetic association study

Permutation-based variance component test in generalized linear mixed model with application to multilocus genetic association study

Bootstrap Restricted Likelihood Ratio Test for the Detection of Rare Variants

Synergized Bootstrapping: The Whole is Faster than the Sum of Its Parts

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