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34A Integration of Models

Elsevier Science & Technology
DOI: 10.1016/s0169-7161(06)26034-6
  • Linguistics
  • Logic
  • Mathematics


Publisher Summary When considering relationships among models, it is important to attend to both mathematical and conceptual issues. Mathematics can address syntactical similarities, but semantics and inference require attention towards conceptual issues. Both conceptually and mathematically, it can be argued that classical test theory is largely a special case of generalizability theory. The classical test theory and generalizability theory employ an expected-value notion of true score. By contrast, when item response theory (IRT) is used with dichotomously-scored items, some of the arguments among the proponents of the one-parameter logistic (1PL) and two parameter logistic (2PL) models vis-à-vis the three-parameter logistic (3PL) model are essentially arguments about what shall be considered as true score. The 3PL model with its non-zero lower asymptote is reasonably consistent with defining true score as an expected value because it acknowledges that a low-ability examinee has a positive probability of a correct response. By contrast, the 1PL and 2PL models require that low ability examinees have a probability-of-correct response approaching zero. In this sense, it appears that these latter models are based on defining true score in the more platonic sense of “knowing” the answer to an item, as opposed to getting it correct.

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