, Volume 55, Issue 4, pp 577–601 | Cite as

On the sampling theory roundations of item response theory models

  • Paul W. Holland


Item response theory (IT) models are now in common use for the analysis of dichotomous item responses. This paper examines the sampling theory foundations for statistical inference in these models. The discussion includes: some history on the “stochastic subject” versus the random sampling interpretations of the probability in IRT models; the relationship between three versions of maximum likelihood estimation for IRT models; estimating θ versus estimating θ-predictors; IRT models and loglinear models; the identifiability of IRT models; and the role of robustness and Bayesian statistics from the sampling theory perspective.

Key words

stochastic subjects marginal maximum likelihood (MML) conditional maximum likelihood (CML) unconditional maximum likelihood (UML) joint maximum likelihood (JML) probability simplex loglinear models robustness 


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Copyright information

© The Psychometric Society 1990

Authors and Affiliations

  • Paul W. Holland
    • 1
  1. 1.Educational Testing ServicePrinceton

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