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Psychometric Latent Response Models

Published online by Cambridge University Press:  01 January 2025

Eric Maris
Eric Maris*
Affiliation:
University of Nijmegen
*
Requests for reprints should be sent to Eric Marls, Nijmegen Institute for Cognition and Information (NICI), Department of Mathematical Psychology, University of Nijmegen, PO Box 9104, 6500 HE Nijmegen, THE NETHERLANDS. E-mall: [email protected]
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Abstract

In this paper, some psychometric models will be presented that belong to the larger class of latent response models (LRMs). First, LRMs are introduced by means of an application in the field of componential item response theory (Embretson, 1980, 1984). Second, a general definition of LRMs (not specific for the psychometric subclass) is given. Third, some more psychometric LRMs, and examples of how they can be applied, are presented. Fourth, a method for obtaining maximum likelihood (ML) and some maximum a posteriori (MAP) estimates of the parameters of LRMs is presented. This method is then applied to the conjunctive Rasch model. Fifth and last, an application of the conjunctive Rasch model is presented. This model was applied to responses to typical verbal ability items (open synonym items).

Keywords

latent response modelscomponential IRTconjunctive Rasch modelincomplete dataEM algorithmverbal abilityopen synonym items
Type
Original Paper
Information
Psychometrika , Volume 60 , Issue 4 , December 1995 , pp. 523 - 547
Copyright
Copyright © 1995 The Psychometric Society

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Footnotes

This paper presents theoretical and empirical results of a research project supported by the Research Council [Onderzoeksraad] of the University of Leuven (grant number 89-9) to Paul De Boeck and Luc Delbeke.

The author wishes to thank Paul De Boeck, Jan van Leeuwe, and Norman Verhelst for their helpful comments, and Rianne Janssen and Machteld Hoskens for the use of their data.

References

Albert, A., Anderson, J. A. (1984). On the existence of maximum likelihood estimates in logistic regression models. Biometrika, 71, 1–10.CrossRefGoogle Scholar
Bock, R. D., Aitkin, M. (1981). Marginal maximum likelihood estimation of item parameters: Application of an EM-algorithm. Psychometrika, 46, 443–459.CrossRefGoogle Scholar
Billingsley, P. (1986). Probability and measure, New York: Wiley.Google Scholar
Carpenter, P. A., Just, M. A. (1986). Spatial ability: An information processing approach to psychometrics. In Sternberg, R. J. (Eds.), Advances in the psychology of human intelligence (pp. 221–253). Hillsdale, NJ: Lawrence Erlbaum.Google Scholar
De Boeck, P. (1988). A psychometric study of cognitive components in verbal intelligence tasks, Leuven: University of Leuven, Research Group on Quantitative Methods.Google Scholar
Dempster, A. P., Laird, N. M., Rubin, D. B. (1977). Maximum likelihood estimation from incomplete data via the EM Algorithm (with discussion). Journal of the Royal Statistical Society, Series B, 39, 1–38.CrossRefGoogle Scholar
Embretson, S. (1980). Multicomponent latent trait models for ability tests. Psychometrika, 45, 479–494.Google Scholar
Embretson, S. (1984). A general latent trait model for response processes. Psychometrika, 49, 175–186.CrossRefGoogle Scholar
Embretson, S. (in press). Working memory versus general control processes in intelligence. Intelligence.Google Scholar
Fischer, G. H. (1974). Einfuhrung in die Theorie psychologischer Tests [Introduction to the theory of psychological tests], Bern: Huber.Google Scholar
Fischer, G. H. (1981). On the existence and uniqueness of maximum likelihood estimates in the Rasch model. Psychometrika, 46, 59–77.CrossRefGoogle Scholar
Gill, P. E., Murray, W., Wright, M. H. (1981). Practical optimization, New York: Academic Press.Google Scholar
Glas, C. A. W. (1988). The derivation of some tests for the Rasch model from the multinomial distribution. Psychometrika, 53, 525–546.CrossRefGoogle Scholar
Glas, C. A. W. (1990). Rasch incomplete design analysis [Computer program], Arnhem, The Netherlands: National Institute for Educational Measurement (CITO).Google Scholar
Goldman, S. R., Pellegrino, J. W. (1984). Deductions about induction: Analyses of developmental and individual differences. In Sternberg, R. J. (Eds.), Advances in the psychology of human intelligence (pp. 149–198). Hillsdale, NJ: Lawrence Erlbaum.Google Scholar
Jannarone, R. J., Yu, K. F., Laughlin, J. E. (1990). Easy Bayes estimates for Rasch-type models. Psychometrika, 55, 449–460.CrossRefGoogle Scholar
Janssen, R., Hoskens, M., De Boeck, P. (1993). An application of Embretson's multicomponent latent trait model to synonym tests. In Steyer, R., Wender, K. F., Widaman, K. F. (Eds.), Proceedings of the 7th European Meeting of the Psychometric Society (pp. 187–190). Stuttgart and New York: Gustav Fischer Verlag.Google Scholar
Kiefer, J., Wolfowitz, J. (1956). Consistency of the maximum likelihood estimator in the presence of infinitely many incidental parameters. Annals of Mathematical Statistics, 27, 887–903.CrossRefGoogle Scholar
Luce, R. D. (1986). Response times: Their role in inferring elementary mental organization, New York: Oxford University Press.Google Scholar
Maris, E. (1992). Psychometric models for psychological processes and structures, Belgium: University of Leuven.Google Scholar
Mayer, R. E., Larkin, J. H., Kadane, J. B. (1984). A cognitive analysis of mathematical problem-solving ability. In Sternberg, R. J. (Eds.), Advances in the psychology of human intelligence (pp. 231–273). Hillsdale, NJ: Lawrence Erlbaum.Google Scholar
McClelland, J. L., Rumelhart, D. E. (1981). An interactive activation model of context effects in letter perception: Part 1. An account of basic findings. Psychological Review, 88, 375–407.CrossRefGoogle Scholar
Mood, A. M., Graybill, F. A., Boes, D. C. (1974). Introduction to the theory of statistics, London: McGraw-Hill.Google Scholar
Muthén, B. (1978). Contributions to factor analysis of dichotomized variables. Psychometrika, 43, 551–560.CrossRefGoogle Scholar
Novick, M. R., Jackson, P. H. (1974). Statistical methods for educational and psychological research, New York: Mc-Graw-Hill.Google Scholar
Pellegrino, J. W., Kail, R. (1982). Process analysis of spatial aptitude. In Sternberg, R. J. (Eds.), Advances in the psychology of human intelligence (pp. 311–366). Hillsdale, NJ: Lawrence Erlbaum.Google Scholar
Rasch, G. (1980). Probabilistic models for some intelligence and attainment tests, Chicago: The University of Chicago Press.Google Scholar
Rubin, D. B., Thayer, D. T. (1982). EM algorithms for factor analysis. Psychometrika, 47, 69–76.CrossRefGoogle Scholar
Sternberg, R. J. (1977). Intelligence, information processing, and analogical reasoning: The componential analysis of human abilities, Hillsdale, NJ: Lawrence Erlbaum.Google Scholar
Thurstone, L. L. (1927). A law of comparative judgment. Psychological Review, 34, 273–286.CrossRefGoogle Scholar
Verhelst, N. D., Verstralen, H. H. F. M. (1993). A stochastic unfolding model derived from the partial credit model. Kwantitatieve Methoden, 42, 73–92.Google Scholar
Wu, C. F. J. (1983). On the convergence properties of the EM-algorithm. The Annals of Statistics, 11, 95–103.CrossRefGoogle Scholar