, Volume 53, Issue 3, pp 383–392 | Cite as

Two-group classification in latent trait theory: Scores with monotone likelihood ratio

  • D. A. Grayson


This paper deals with two-group classification when a unidimensional latent trait,ϑ, is appropriate for explaining the data,X. It is shown that ifX has monotone likelihood ratio then optimal allocation rules can be based on its magnitude when allocation must be made to one of two groups related toϑ. These groups may relate toϑ probabilistically via a non-decreasing functionp(ϑ), or may be defined by all subjects above or below a selected value onϑ.

In the case where the data arise from dichotomous items, then only the assumption that the items have nondecreasing item characteristic functions is enough to ensure that the unweighted sum of responses (the number-right score or raw score) possesses this fundamental monotone likelihood ratio property.

Key words

monotone likelihood ratio latent trait two-group classification number-right score 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. Birnbaum, A. (1968). Some latent trait models and their use in inferring an examinee's ability. In F. M. Lord & M. R. Novick (Ed.),Statistical theories of mental test scores (pp. 397–479). Reading, MA: Addison-Wesley.Google Scholar
  2. Duncan-Jones, P., Grayson, D. A., & Moran, P. A. P. (1986). The utility of latent trait models in psychiatric epidemiology.Psychological Medicine, 16, 391–405.Google Scholar
  3. Ferguson, J. S. (1967).Mathematical statistics: A decision theoretic approach. New York: Academic Press.Google Scholar
  4. Huynh, H. (1975). Statistical consideration of mastery score.Psychometrika,41, 65–78.Google Scholar
  5. Lehmann, E. L. (1959).Testing statistical hypotheses. New York: John Wiley and Sons.Google Scholar
  6. Lord, F. M. (1980).Applications of item response theory to practical testing problems. Hillsdale, NJ: Lawrence Erlbaum.Google Scholar
  7. Minc, H. (1978).Permanents. Reading, MA: Addison-Wesley.Google Scholar
  8. Rasch, G. (1960).Probabilistic models for some intelligence and attainment tests. Copenhagen: Denmarks Paedagogiske Institut.Google Scholar

Copyright information

© The Psychometric Society 1988

Authors and Affiliations

  • D. A. Grayson
    • 1
  1. 1.NH&MRC Social Psychiatry Research UnitAustralian National UniversityCanberraAustralia

Personalised recommendations