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The Best Linear Predictor for True Score From a Direct Estimate and Several Derived Estimates NAEP

Haberman, Shelby J.; Qian, Jiahe
Publication Year:
Report Number:
ETS Research Report
Document Type:
Page Count:
Subject/Key Words:
CGROUP, National Assessment of Educational Progress (NAEP), Importance Sampling Method, Stochastic Integration, Best Linear Predictors


Statistical prediction problems often involve both a direct estimate of a true score and covariates of this true score. Given the criterion of mean squared error, this study determines the best linear predictor of the true score given the direct estimate and the covariates. Results yield an extension of Kelley's formula for estimation of the true score to cases in which covariates are present. The best linear predictor is a weighted average of the direct estimate and of the linear regression of the direct estimate onto the covariates. The weights depends on the reliability of the direct estimate and on the multiple correlation of the true score with the covariates. One application of the best linear predictor is to approximate the human true score from the observed holistic score of an essay and from essay features derived from a computer analysis.

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