In a Mixed model, the random effects are SAMPLED from a potentially large population and may not be replicated. In the general case, you can only do marginal prediction, integrating out random effects, if the levels of random subjects in scoring data set is different from what you used in modeling. What you can do is conducting a monte carlo based approach. On the other hand if the levels in the scoring data set ARE REPLICATES of those in training data, then what you can do is simply transpose the random effects solution dataset and combined with the fixed effect data set to be the scoring coefficient data set, then apply the design matrices with the scoring coefficient data set in PROC SCORE, just like how you would score in GLM.
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