Once focused on fields like biology and psychology, usage of mixed models now includes "New Statistics" applications such as recommender systems (Gao and Owen, 2015; Perry, 2015). Powerful, highly versatile packages such as R's lme4 are now available to meet the needs of both the new and old applications.
But today's applications often involve very large datasets and/or very complex models, and this applies especially to mixed effects modeling. There are major challenges in terms of long computational run times, and even worse, many applications simply won't fit into available memory (Pennel and Dunson, 2007). Using the method of Software Alchemy (Matloff, 2015), this paper will show that major speedups for mixed model computation can be attained, both for MLE and Method of Moments estimation approaches, while also solving the memory-constraint problems.
In these complex models, though, Method of Moments estimates can be very difficult to compute algebraically. Thus the paper will present methodology which will greatly simplify Method of Moments computation.