Estimating adjusted associations between random effects from multilevel models

We describe a method to estimate associations between random effects from multilevel models. We provide two new postestimation commands, reffadjustsim and reffadjust4nlcom, which are distributed as the reffadjust package. These commands produce the estimates and their associated confidence intervals. The commands are used after official Stata multilevel model estimation commands mixed, meqrlogit, and meqrpoisson (formerly named xtmixed, xtmelogit, and xtmepoisson, respectively, before Stata 13) and with models fit in the MLwiN statistical software package via the runmlwin command. We demonstrate our commands with several simulated datasets and for a bivariate outcome model investigating the relationship between weight and mean arterial pressure in pregnant women using data from the Avon Longitudinal Study of Parents and Children. Our method and commands help to improve the interpretability of estimated random-effects variance components from multilevel models.