Title: MM Algorithms for Variance Component Estimation and Selection in Logistic Linear Mixed Model,
Abstract: Logistic linear mixed model is widely used in experimental designs and
genetic analysis with binary traits. Motivated by modern applications, we
consider the case with many groups of random effects and each group corresponds
to a variance component. When the number of variance components is large,
fitting the logistic linear mixed model is challenging. We develop two
efficient and stable minorization-maximization (MM) algorithms for the
estimation of variance components based on the Laplace approximation of the
logistic model. One of them leads to a simple iterative soft-thresholding
algorithm for variance component selection using maximum penalized approximated
likelihood. We demonstrate the variance component estimation and selection
performance of our algorithms by simulation studies and a real data analysis.