Coordinate Descent for Variance-Component Models

Variance-component models are an indispensable tool for statisticians wanting to capture both random and fixed model effects. They have applications in a wide range of scientific disciplines. While maximum likelihood estimation (MLE) is the most popular method estimating variance-component parameters, it numerically challenging large data sets. In this article, we consider class coordinate descent (CD) algorithms computing MLE. We show that basic implementation costly implement does not easily satisfy standard theoretical conditions convergence. instead propose two parameter-expanded versions CD, called PX-CD PXI-CD. These novel only converge faster than existing competitors (MM EM algorithms) but also more amenable convergence analysis. PXI-CD particularly well-suited sets—namely, as scale increases, performance gap between CD current competitor methods increases.