ASCAL: A Microcomputer Program for Estimating Logistic IRT (Item Response Theory) Item Parameters.
Technical rept. 1 Sep 83-11 Nov 85,
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ASCAL is a microcomputer-based program for calibrating items according to the three-parameter logistic model of item response theory. ASCAL employs Lords 1974 modified likelihood equations for items that are omitted or not reached and Bayesian prior distributions on the discrimination, guessing, and ability parameters to arrive at final estimates to the item parameters. No ability parameters are produced. ASCAL uses a modified multivariate Newton-Raphson procedure for estimating item parameters. The estimation process begins by specifying starting points for the ability and item parameters. In this procedure, abilities are first estimated using the preliminary estimates of the item parameters. After ability estimates have been obtained for all examinees, they are sorted and grouped into 20 fractiles with approximately equal numbers of examinees in each. The item parameters are then estimated by assuming that the 20 fractile means are representative of the entire ability distribution. The sequence of ability estimation, ability grouping, and parameter estimation is repeated until the item parameters converge on stable values or fail to improve. This procedure was evaluated using Monte Carlo simulation techniques.
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