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Testing random effects in the linear mixed model using approximate bayes factors.

ABSTRACT: Deciding which predictor effects may vary across subjects is a difficult issue. Standard model selection criteria and test procedures are often inappropriate for comparing models with different numbers of random effects due to constraints on the parameter space of the variance components. Testing on the boundary of the parameter space changes the asymptotic distribution of some classical test statistics and causes problems in approximating Bayes factors. We propose a simple approach for testing random effects in the linear mixed model using Bayes factors. We scale each random effect to the residual variance and introduce a parameter that controls the relative contribution of each random effect free of the scale of the data. We integrate out the random effects and the variance components using closed-form solutions. The resulting integrals needed to calculate the Bayes factor are low-dimensional integrals lacking variance components and can be efficiently approximated with Laplace's method. We propose a default prior distribution on the parameter controlling the contribution of each random effect and conduct simulations to show that our method has good properties for model selection problems. Finally, we illustrate our methods on data from a clinical trial of patients with bipolar disorder and on data from an environmental study of water disinfection by-products and male reproductive outcomes.

SUBMITTER: Saville BR

PROVIDER: S-EPMC3136354 | biostudies-other | 2009 Jun

REPOSITORIES: biostudies-other

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Testing random effects in the linear mixed model using approximate bayes factors.

Saville Benjamin R BR Herring Amy H AH

Biometrics 20090601 2

<h4>Summary</h4>Deciding which predictor effects may vary across subjects is a difficult issue. Standard model selection criteria and test procedures are often inappropriate for comparing models with different numbers of random effects due to constraints on the parameter space of the variance components. Testing on the boundary of the parameter space changes the asymptotic distribution of some classical test statistics and causes problems in approximating Bayes factors. We propose a simple appro ...[more]

PMID: 18759835

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Project description:BACKGROUND: Different high-dimensional regression methodologies exist for the selection of variables to predict a continuous variable. To improve the variable selection in case clustered observations are present in the training data, an extension towards mixed-effects modeling (MM) is requested, but may not always be straightforward to implement.In this article, we developed such a MM extension (GA-MM-MMI) for the automated variable selection by a linear regression based genetic algorithm (GA) using multi-model inference (MMI). We exemplify our approach by training a linear regression model for prediction of resistance to the integrase inhibitor Raltegravir (RAL) on a genotype-phenotype database, with many integrase mutations as candidate covariates. The genotype-phenotype pairs in this database were derived from a limited number of subjects, with presence of multiple data points from the same subject, and with an intra-class correlation of 0.92. RESULTS: In generation of the RAL model, we took computational efficiency into account by optimizing the GA parameters one by one, and by using tournament selection. To derive the main GA parameters we used 3 times 5-fold cross-validation. The number of integrase mutations to be used as covariates in the mixed effects models was 25 (chrom.size). A GA solution was found when R2MM > 0.95 (goal.fitness). We tested three different MMI approaches to combine the results of 100 GA solutions into one GA-MM-MMI model. When evaluating the GA-MM-MMI performance on two unseen data sets, a more parsimonious and interpretable model was found (GA-MM-MMI TOP18: mixed-effects model containing the 18 most prevalent mutations in the GA solutions, refitted on the training data) with better predictive accuracy (R2) in comparison to GA-ordinary least squares (GA-OLS) and Least Absolute Shrinkage and Selection Operator (LASSO). CONCLUSIONS: We have demonstrated improved performance when using GA-MM-MMI for selection of mutations on a genotype-phenotype data set. As we largely automated setting the GA parameters, the method should be applicable on similar datasets with clustered observations.

Dataset Information

Testing random effects in the linear mixed model using approximate bayes factors.

Publications

Testing random effects in the linear mixed model using approximate bayes factors.

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