There is no way to conduct this BRR method in a mixed effects model in SAS. You can manually achieve this BRR method by following these instructions from the PATH user guide: "Although software packages do not universally accommodate replicate weights for all analytic methods, the replication method can be applied by repetition to any analytic routine. That is, the desired analysis would first be run using the full-sample weight. Then, it would be repeated replacing the full-sample weight by each replicate weight, in turn (i.e., 100 times for PATH). The formula for BRR variance estimates (provided in equation 5.2.1) would then be used to estimate the variance of any parameter (e.g., regression coefficient) of interest."
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