Approximation for Bayesian Ability Estimation.
Technical rept. 1 Jan 85-31 Dec 86,
MISSOURI UNIV-COLUMBIA DEPT OF STATISTICS
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An approximation is proposed for the posterior mean and standard deviation of the ability parameter in an item response model. The procedure assumes that approximations to the posterior mean and covariance matrix of item parameters are available. It is based on the posterior mean of a Taylor series approximation to the posterior mean conditional on the item parameters. The method is illustrated for the two-parameter logistic model using data from an ACT math test with 39 items. A numerical comparison with the empirical Bayes method shows that the point estimates are very similar but the standard deviations under empirical Bayes are about two percent smaller than those under Bayes. The effect of sample size is demonstrated by illustrating the increase in the standard deviations for a smaller data set. Author
- Statistics and Probability