Multilevel Analysis of Educational Data by R. Darrell Bock

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It should be recalled that, even under the best of circumstances, care must be taken to obtain valid estimates of the uncertainty surrounding EB estimates. This point is addressed well by Morris (1983). The connection between Bayes and EB methods are also discussed by Deeley & Lindley (1981). However, they are concerned with the formulation Empirical Bayes Methods 49 of the EB problem proposed by Robbins (1955), which differs from that discussed here. 2 Robustness One issue that has received comparatively Uttle attention is that of robust­ ness of EB procedures.

42 Braun where Σ,· is the variance-covariance matrix of the predictors among students in department i and is the EB estimate of the residual variance about the regression plane. The plot of against Vi (Figure 5) shows that f,tends to be substantially smaller than v,. 58. What accounts for this difference? My interpretation is that ϋ{ represents an "adjusted" estimate of crossvalidated predictive validity while Vi represents an "adjusted" estimate of calibrated predictive vaUdity. That is, suppose we were able to generate a second set of data for each department, independently of the first, and having the same Σ^· as before.

B. (1982). Comparing effect sizes of indepen­ dent studies. Psychological Bulletin, 92, 500-504. Rubin, D . B. (1980). Using empirical Bayes techniques in the law school vaUdity studies. Journal of the American Statistical Association, 75, 801-816. Rubin, D. B. (1981). Estimation in parallel randomized experiments. nal of Educational Statistics, 6(4), 377-400. Jour­ Schmidt, F. L. (1988). VaUdity generalization and the future of criterionrelated validity. In Test validity (Ed. by H. Wainer, & H.

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