An essential set-up set in REML analyses is to find a permutation of the rows and columns in the coefficient matrix of the mixed model equations that makes the ‘fill-in’ arising during factorisation small and thus minimises the computational efforts per likelihood evaluation and REML iterate. This needs to be done only once per analysis (WOMBAT saves the results from this step for re-use in any subsequent steps). As it can have a dramatic impact on the time and memory required per analysis, it is well worth considerable effort to find the ‘best’ order. Especially for analyses involving large data sets or multiple random effects, the time spend trying several, or even numerous alternatives is readily recouped within the first few iterates . WOMBAT selects a default ordering strategy based on the number of equations in the analysis.
Three different stratgies are implemented :