PX x AI: Algorithmics for better convergence in restricted maximum likelihood estimation

Abstract

Features of algorithms to locate the maximum of the likelihood function in restricted maximum likelihood (REML) estimation are briefly reviewed. Differences between average information (AI) and expectation maximisation (EM) algorithms, in particular the 'parameter expanded' variant of EM (PX-EM), are highlighted. Convergence rates of AI, EM and PX-EM algorithms are contrasted for several 'difficult' practical examples of analyses of beef cattle data, involving numerous traits or multiple random effects, and thus many parameters to be estimated. Results suggest that more reliable - and often faster - convergence of REML analyses can be achieved by combining algorithms: Exploit the stability and good performance of the PX-EM algorithm in the first few iterates, then switch to the AI algorithm with rapid convergence close to the maximum of the likelihood function.