Some observations on the metric of PC-BILOG results

Abstract

The computer program PC-BILOG uses the estimated posterior θ distribution to establish the location and metric of the θ scale. This approach to solving the identification problem has not been examined extensively. Consequently, this study investigated the equating of PC-BILOG results to an underlying metric when a two-parameter IRT model was used. The simulation results showed that the means of the estimated item and θ parameters generally were insensitive to characteristics of the prior distribution on the item discriminations. The finding of greatest interest was that the PC-BILOG procedures preserved the variability of true θ distributions having small variances while standardizing the variability of those having large variances. However, in both cases the results could be equated to the true metric using existing techniques. Index terms: ability metric, Bayesian estimation, BILOG, equating, item response theory, prior distributions.