Bayesian Estimation in the One-Parameter Latent Trait Model

摘要

When several parameters are to be estimated simultaneously, and when both structural and incidental parameters have to be estimated, a Bayesian solution to the estimation problem may be appropriate. This is the case in latent trait models, where the 'structural' parameters are item parameters, while the 'incidental parameters' are ability parameters since these increase without bound as the numbers of examinees is increased to provide stable estimates of the item parameters. Bayesian estimates for the parameters in the one-parameter latent trait model were obtained for two cases: (1) conditional estimation of ability (for those situations when items are previously calibrated), and (2) joint estimation of item and ability parameters. For each of the two cases, a simulation study was carried out to study the efficacy of the two Bayesian procedures described and to compare the Bayesian estimates with the comparable maximum likelihood estimates.