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

Abstract

Marginal maximum likelihood (MML) estimation of the logistic response model assumes a structure for the distribution of ability (θ). If this assumption is incorrect, the statistical properties of MML estimates may not hold. Monte carlo methods were used to evaluate MML estimation of item parameters and maximum likelihood (ML) estimates of θ in the two-parameter logistic model for varying test lengths, sample sizes, and assumed θ distribution. 100 datasets were generated for each of the combinations of factors, allowing for item-level analyses based on means across replications. MML estimates of item difficulty were generally precise and stable in small samples, short tests, and under varying distributional assumptions of θ. When the true distribution of θ was normal, MML estimates of item discrimination were also generally precise and stable. ML estimates of θ were generally precise and stable, although the distribution of θ estimates was platykurtic and truncated at the high and low ends of the score range. Index terms: marginal maximum likelihood, monte carlo, MULTILOG, two-parameter logistic response model.