Bayes Factor for Linear Mixed Model in Genetic Association Studies

Motivation Bayes factor has advantages over p-value as test statistics for association, particularly when comparing multiple alternative models. A software package to compute Bayes factor for linear mixed model is lacking. Results We transformed the standard linear mixed model as Bayesian linear regression, substituting the random effect by fixed effects with eigenvectors as covariates whose prior effect sizes are proportional to their corresponding eigenvalues. Using conjugate normal inverse gamma priors on regression parameters, Bayes factors can be computed in a closed form. We then showed that the transformed Bayesian linear regression produced identical estimates to those of the best linear unbiased prediction (BLUP), providing a new derivation to a known connection between BLUP and Bayesian estimates. Availability and implementation Methods described in this note are implemented in the software IDUL as two new functionalities: computing Bayes factors and residuals for the linear mixed model. IDUL and its source code are freely available at . ### Competing Interest Statement The authors have declared no competing interest.