The parameter estimates associated with random effects are called BLUPs (Best Linear Unbiased Predictors). Some researchers consider these BLUPs as parameters of interest, and others consider them uninteresting byproducts of the methodology.
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Select Analyze > Fit Model.

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Select Player in the Construct Model Effects box, and select Random Effect from the Attributes list.

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Click Run.

Comparison of Estimates between Method of Moments and REML shows the Least Squares Means from the Player report for a REML (Recommended) fit. Also shown are the Method of Moment estimates, obtained using the EMS Method. The Method of Moment estimates are the ordinary Player means. Note that the REML estimate for Suarez, who has only three atbats, is shrunken more towards the grand mean than estimates for other players with more atbats.