On Holland's Dutch identity conjecture

Jinming Zhang, William Stout

Research output: Contribution to journalArticlepeer-review


The manifest probabilities of observed examinee response patterns resulting from marginalization with respect to the latent ability distribution produce the marginal likelihood function in item response theory. Under the conditions that the posterior distribution of examinee ability given some test response pattern is normal and the item logit functions are linear, Holland (1990a) gives a quadratic form for the log-manifest probabilities by using the Dutch Identity. Further, Holland conjectures that this special quadratic form is a limiting one for all "smooth" unidimensional item response models as test length tends to infinity. The purpose of this paper is to give three counterexamples to demonstrate that Holland's Dutch Identity conjecture does not hold in general. The counterexamples suggest that only under strong assumptions can it be true that the limits of log-manifest probabilities are quadratic. Three propositions giving sets of such strong conditions are given.

Original languageEnglish (US)
Pages (from-to)375-392
Number of pages18
Issue number3
StatePublished - Sep 1997
Externally publishedYes


  • Dutch identity
  • IRT
  • Item response theory
  • Manifest probabilities
  • Posterior distribution

ASJC Scopus subject areas

  • Mathematics (miscellaneous)
  • Psychology(all)
  • Psychology (miscellaneous)
  • Social Sciences (miscellaneous)


Dive into the research topics of 'On Holland's Dutch identity conjecture'. Together they form a unique fingerprint.

Cite this