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

The accuracy of marginal maximum likelihood estimatesof the item parameters of the two-parameter logisticmodel was investigated. Estimates were obtainedfor four sample sizes and four test lengths; joint maximumlikelihood estimates were also computed for thetwo longer test lengths. Each condition was replicated10 times, which allowed evaluation of the accuracy ofestimated item characteristic curves, item parameterestimates, and estimated standard errors of item parameterestimates for individual items. Items that aretypical of a widely used job satisfaction scale andmoderately easy tests had satisfactory marginal estimatesfor all sample sizes and test lengths. Largersamples were required for items with extreme difficultyor discrimination parameters. Marginal estimationwas substantially better than joint maximum likelihoodestimation. Index terms: Fletcher-Powellalgorithm, item parameter estimation, item responsetheory, joint maximum likelihood estimation, marginalmaximum likelihood estimation, two-parameter logisticmodel.