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Conjunctive Item Response Theory Kernels

Published online by Cambridge University Press:  01 January 2025

Robert J. Jannarone
Robert J. Jannarone*
Affiliation:
University of South Carolina
*
Requests for reprints should be sent to Robert J. Jannarone, Psychology Department, University of South Carolina, Columbia, SC 29208.
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Abstract

Conjunctive item response models are introduced such that (a) sufficient statistics for latent traits are not necessarily additive in item scores; (b) items are not necessarily locally independent; and (c) existing compensatory (additive) item response models including the binomial, Rasch, logistic, and general locally independent model are special cases. Simple estimates and hypothesis tests for conjunctive models are introduced and evaluated as well. Conjunctive models are also identified with cognitive models that assume the existence of several individually necessary component processes for a global ability. It is concluded that conjunctive models and methods may show promise for constructing improved tests and uncovering conjunctive cognitive structure. It is also concluded that conjunctive item response theory may help to clarify the relationships between local dependence, multidimensionality, and item response function form.

Keywords

configural scoringconjunctivitylocal dependencenonadditive itemsRasch model

Information

Type
Original Paper
Information
Psychometrika , Volume 51 , Issue 3 , September 1986, pp. 357 - 373
Copyright
Copyright © 1986 The Psychometric Society

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Footnotes

I appreciate the many helpful suggestions that were given by the reviewers and Ivo Molenaar.

References

Andersen, E. B. (1980). Discrete statistical models with social science applications, Amsterdam: North Holland.Google Scholar
Andersen, E. B. (1982). Latent trait models and ability parameter estimation. Applied Psychological Measurement, 6, 445–461.CrossRefGoogle Scholar
Anderson, N. H. (1981). Foundations of information integration theory, New York: Academic Press.Google Scholar
Andrich, D. (1984, April). The attenuation paradox of traditionalist test theory as a breakdown of local independence in person item response theory. Paper presented at the National Conference of Measurement in Education, New Orleans.Google Scholar
Andrich, D. (1985). A latent-trait model for items with response dependencies: Implications for test construction and analysis. In Embretson, S. E. (Eds.), Test design, Orlando, FL: Academic Press.Google Scholar
Birnbaum, A. (1968). Some latent trait models and their use in inferring an examinee's ability. In Lord, F. M., Novick, M. R. (Eds.), Statistical theories of mental test scores, Reading, MA: Addison-Wesley.Google Scholar
Bussmeyer, J. R., Jones, L. E. (1983). Analysis of multiplicative combination rules when the causal variables are measured with error. Psychological Bulletin, 93, 549–552.CrossRefGoogle Scholar
Embretson (Whitely), S. (1984). A general latent trait model for response processes. Psychometrika, 49, 175–186.CrossRefGoogle Scholar
Embretson, S. (1985, June). Component latent trait models: A remedy for local dependence? Paper presented at the 50th Annual Meeting of the Psychometric Society, Nashville.Google Scholar
Fischer, G. (1973). The linear logistic test model as an instrument in educational research. Acta Psychologica, 37, 359–374.CrossRefGoogle Scholar
Fischer, G. (1981). On the existence and uniqueness of maximum-likelihood estimates in the Rasch model. Psychometrika, 46, 59–77.CrossRefGoogle Scholar
Fischer, G., Formann, A. K. (1982). Some applications of logistic latent trait models with linear constraints on the parameters. Applied Psychological Measurement, 6, 397–416.CrossRefGoogle Scholar
Gaier, E. L., Lee, M. C. (1953). Pattern analysis. The configural approach to predictive measurement. Psychological Bulletin, 50, 140–148.CrossRefGoogle ScholarPubMed
Goldstein, H. (1980). Dimensionality, bias, independence and measurement scale problems in latent trait test score models. British Journal of Mathematical and Statistical Psychology, 33, 234–246.CrossRefGoogle Scholar
Hambleton, R. K., Swaminathan, H., Cook, L. L., Eignor, D. E., Gifford, J. A. (1978). Developments in latent trait theory: Models, technical issues, and applications. Review of Educational Research, 48, 467–510.CrossRefGoogle Scholar
Harper, D. (1972). Local dependence latent structure models. Psychomerika, 37, 53–57.CrossRefGoogle Scholar
Holland, P. W. (1981). When are item response models consistent with observed data?. Psychometrika, 46, 79–92.CrossRefGoogle Scholar
Horst, P. (1954). Pattern analysis and configural scoring. Journal of Clinical Psychology, 10, 3–11.3.0.CO;2-7>CrossRefGoogle ScholarPubMed
Huynh, H. (1977). Two simple cases of mastery scores based on the beta-binomial mode. Psychometrika, 42, 601–608.CrossRefGoogle Scholar
Jannarone, R. J., Roberts, J. S. (1984). Reflecting item interactions in scale construction: Meehl's paradox revisited. Journal of Personality and Social Psychology, 47, 631–637.CrossRefGoogle Scholar
Kelderman, H. (1984). Loglinear Rasch model tests. Psychometrika, 49, 223–245.CrossRefGoogle Scholar
Kempf, W. F. (1977). A dynamic test model and its use in the microevaluation of instructional material. In Spada, H., Kempf, W. F. (Eds.), Structural models of thinking and learning, Vienna: Hans Huber.Google Scholar
Koch, G. G., Landis, J. R. (1977). A general methodology for the analysis of experiments with repeated measurements of categorical data. Biometrics, 33, 133–158.CrossRefGoogle ScholarPubMed
Lord, F. M., Novick, M. R. (1968). Statistical theories of mental test scores, Reading, MA: Addison-Wesley.Google Scholar
McDonald, R. P. (1967). Nonlinear factor analysis. Psychometric Monograph, Number 15, 32(4, Pt 2).Google Scholar
McKinley, R. L., Reckase, M. D. (1983). An extension of the two-parameter logistic model to the multidimensional latent space, Iowa City: American College Testing Program.Google Scholar
Megargee, E. I. (1972). The California Psychological Inventory Handbook, London: Josey-Bass.Google Scholar
Molenaar, I. W. (1983). Some improved diagnostics for failure of the Rasch model. Psychometrika, 48, 49–72.CrossRefGoogle Scholar
Rao, C. R. (1965). Linear statistical inference and its applications 2nd ed.,, New York: Wiley.Google Scholar
Rasch, G. (1980). Probabilistic models for some intelligence and attainment tests, Chicago: University of Chicago Press.Google Scholar
Rosenbaum, P. R. (1984). Testing the conditional independence and monoticity assumptions of item response theory. Psychometrika, 49, 425–436.CrossRefGoogle Scholar
Stegelmann, W. (1983). Extending the Rasch model to a general model having more than one dimension. Psychometrika, 48, 259–268.CrossRefGoogle Scholar
Sternberg, R. S. (1977). Intelligence, information processing and analogical reasoning, Hillsdale, NJ: Erlbaum.Google Scholar
Sympson, J. B. (1977, July). A model for testing with multidimensional items. Paper presented at the University of Minnesota, Computerized Adaptive Testing Conference, Minneapolis.Google Scholar
Wainwright, G. (1965). Configural information in item responses. Unpublished doctoral dissertation, University of Washington.Google Scholar
Whitely, S. E. (1980). Multi-component latent trait models for ability tests. Psychometrika, 45, 479–494.CrossRefGoogle Scholar
Yellot, J. I. Jr. (1977). The relationship between Luce's choice axiom, Thurstone's theory of comparative judgement and the double exponential distribution. Journal of Mathematical Psychology, 15, 109–144.CrossRefGoogle Scholar
Yen, W. M. (1981). Using simulation results to test a latent trait model. Applied Psychological Measurement, 5, 245–262.CrossRefGoogle Scholar