  Hierarchical models allow for heterogeneous behaviours in a population while
simultaneously borrowing estimation strength across all subpopulations.
Unfortunately, existing likelihood-based methods for fitting hierarchical
models have high computational demands, and these demands have limited their
adoption in large-scale prediction and inference problems. This paper proposes
a moment-based procedure for estimating the parameters of a hierarchical model
which has its roots in a method originally introduced by Cochran in 1937. The
method trades statistical efficiency for computational efficiency. It gives
consistent parameter estimates, competitive prediction error performance, and
substantial computational improvements. When applied to a large-scale
recommender system application and compared to a standard maximum likelihood
procedure, the method delivers competitive prediction performance while
reducing the sequential computation time from hours to minutes.
