Estimation for the Rasch Model When Both Ability and Difficulty Parameters are Random.
Technical rept. 1 Jan 85-31 Dec 86,
MISSOURI UNIV-COLUMBIA DEPT OF STATISTICS
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Estimation of the parameters of the Rasch model, a one parameters item response model, is considered when both the item parameters and the ability parameters are considered random quantities. It is assumed that the item parameters are drawn from a Ngamma tau to the 2nd power distribution, and the abilities are drawn from a Nomicron, sigma to the 2nd power distribution. A variation of the EM algorithm is used to find approximate maximum likelihood estimates of gamma, tack and sigma. A second approach assumes that the difficulty parameters are drawn from a uniform distribution over part of the real line. Real and simulated data sets are discussed for illustration. Keywords Statistical data TablesData.
- Statistics and Probability