An evaluation of marginal maximum likelihood estimation for the two-parameter logistic model

Abstract

The accuracy of marginal maximum likelihood estimates of the item parameters of the two-parameter logistic model was investigated. Estimates were obtained for four sample sizes and four test lengths; joint maximum 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 parameter estimates for individual items. Items that are typical of a widely used job satisfaction scale and moderately easy tests had satisfactory marginal estimates for all sample sizes and test lengths. Larger samples were required for items with extreme difficulty or discrimination parameters. Marginal estimation was substantially better than joint maximum likelihood estimation. Index terms: Fletcher-Powell algorithm, item parameter estimation, item response theory, joint maximum likelihood estimation, marginal maximum likelihood estimation, two-parameter logistic model.