The Answer is in the Question: A Guide for Describing and Investigating the Conceptual Foundations and Statistical Properties of Cognitive Psychometric Models

One of the most revolutionary advances in psychometric research during the last decades has been the systematic development of statistical models that allow for cognitive psychometric research (CPR) to be conducted. Many of the models currently available for such purposes are extensions of basic latent variable models in item response theory (IRT). While the requirements of basic IRT models in terms of data collection designs, measurement scales of variables, and sample sizes for learners and items are relatively well understood, the added requirements that the cognitive components of modeling processes for CPR bring along with them are understood to a much lesser degree. Therefore, this article contains a guide in the form of a series of questions, which support measurement and substantive specialists in describing and investigating the conceptual foundations and statistical properties of models for CPR. An application of the guide to the rule-space methodology (e.g., Tatsuoka, 1983 Tatsuoka, K. K. 1983. Rule-space: An approach for dealing with misconceptions based on item response theory.. Journal of Educational Measurement, 20: 345–354. [Crossref], [Web of Science ®] , [Google Scholar], 1985 Tatsuoka, K. K. 1985. A probabilistic model for diagnosing misconceptions by the pattern classification approach.. Journal of Educational Statistics, 10: 55–73. [Crossref] , [Google Scholar], 1995 Tatsuoka, K. K. 1995. “Architecture of knowledge structures and cognitive diagnosis: A statistical pattern recognition and classification approach.”. In Cognitively diagnostic assessment, Edited by: Nichols, P. D., Chipman, S. F. and Brennan, R. L. 327–360. Hillsdale, NJ: Lawrence Erlbaum Associates, Inc.. [Google Scholar]) is presented, which extends the conceptual-logical discussion of Gierl, Leighton, and Hunka (2000) by focusing more heavily on cognitive and statistical considerations.