Marginal Maximum Likelihood Estimation of Item Parameters: Application of an EM Algorithm

1981/12/01 by R. Darrell Bock, Murray Aitkin · 2,350 citations
Computer Science · Decision Sciences · Mathematics · Psychology · #Advanced Statistical Modeling Techniques #Algorithm #Applied mathematics #Cognitive Abilities and Testing #Computer science #Dimension (graph theory) #Estimation #Estimation theory #Expectation–maximization algorithm #Item response theory #Marginal distribution #Marginal likelihood #Mathematics #Maximum likelihood #Maximum likelihood sequence estimation #Psychometric Methodologies and Testing #Psychometrics #Random variable #Simple (philosophy) #Statistics

paper · doi:10.1007/bf02293801

published in Psychometrika 46(4), 443-459 (Springer Science+Business Media)

openalex publication_date 1981/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

Abstract

Maximum likelihood estimation of item parameters in the marginal distribution, integrating over the distribution of ability, becomes practical when computing procedures based on an EM algorithm are used. By characterizing the ability distribution empirically, arbitrary assumptions about its form are avoided. The Em procedure is shown to apply to general item-response models lacking simple sufficient statistics for ability. This includes models with more than one latent dimension.

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