Implementation of Marginal Bayesian Estimation with Four-Parameter Beta Prior Distributions

Abstract

Item parameter estimation for the threeparameter logistic model (3PLM) is sometimes problematic. The estimation algorithm of the 3PLM maximum likelihood estimation procedure often fails, which results in invalid parameter estimates. A procedure based on the marginal Bayesian estimation method introduced by Bock & Aitkin (1981), Swaminathan & Gifford (1985, 1986), and Mislevy & Bock (1990) is proposed here to improve the item parameter estimates for the 3PLM. Four-parameter beta distributions are used as prior distributions for estimating item parameters. A computer simulation study suggested that implementing the marginal Bayesian estimation algorithm with four-parameter beta prior distributions and then updating the priors with empirical means of the updated intermediate estimates can improve item parameter estimation when accurate prior information about the unknown parameters is not available.