An Evaluation of Marginal Maximum Likelihood Estimation for the Two-Parameter Logistic Model

Abstract

The accuracy of marginal maximum likelihood esti mates of the item parameters of the two-parameter lo gistic model was investigated. Estimates were obtained for four sample sizes and four test lengths; joint maxi mum likelihood estimates were also computed for the two longer test lengths. Each condition was replicated 10 times, which allowed evaluation of the accuracy of estimated item characteristic curves, item parameter estimates, and estimated standard errors of item pa rameter estimates for individual items. Items that are typical of a widely used job satisfaction scale and moderately easy tests had satisfactory marginal esti mates for all sample sizes and test lengths. Larger samples were required for items with extreme diffi culty or discrimination parameters. Marginal estima tion was substantially better than joint maximum like lihood estimation. Index terms: Fletcher-Powell algorithm, item parameter estimation, item response theory, joint maximum likelihood estimation, marginal maximum likelihood estimation, two-parameter logistic model.