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 by-products of the methodology.
Select Help > Sample Data Library and open
Select Analyze > Fit Model.
Select Batting and click Y, Response.
Select Player and click X, Factor.
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 at-bats, is shrunken more towards the grand mean than estimates for other players with more at-bats.