Recovery of marginal maximum likelihood estimates in the two-parameter logistic response model: An evaluation of MULTILOG

Marginal maximum likelihood (MML) estimationof the logistic response model assumes a structurefor the distribution of ability (θ). If this assumptionis incorrect, the statistical properties of MMLestimates may not hold. Monte carlo methods wereused to evaluate MML estimation of item parametersand maximum likelihood (ML) estimates of θin the two-parameter logistic model for varyingtest lengths, sample sizes, and assumed θ distribution.100 datasets were generated for each ofthe combinations of factors, allowing for item-levelanalyses based on means across replications.MML estimates of item difficulty were generallyprecise and stable in small samples, short tests,and under varying distributional assumptions of θ.When the true distribution of θ was normal, MMLestimates of item discrimination were also generallyprecise and stable. ML estimates of θ weregenerally precise and stable, although the distributionof θ estimates was platykurtic and truncatedat the high and low ends of the scorerange. Index terms: marginal maximum likelihood,monte carlo, MULTILOG, two-parameter logisticresponse model.