Abstract
Chang and Stout (1993) presented a derivation of the asymptotic posterior normality of the latent trait given examinee responses under nonrestrictive nonparametric assumptions for dichotomous IRT models. This paper presents an extention of their results to polytomous IRT models in a fairly straightforward manner. In addition, a global information function is defined, and the relationship between the global information function and the currently used information functions is discussed. An information index that combines both the global and local information is proposed for adaptive testing applications.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Andrich, D. (1978). A rating formulation for ordered response categories.Psychometrika, 43, 516–573.
Bock, R. D. (1972). Estimating item parameters and latent ability when the responses are scored in two or more nominal categories.Psychometrika, 37, 29–51.
Chang, H.-H. (1994).Some asymptotic results of polytomous IRT models. Unpublished manuscript, Educational Testing Service, Princeton, NJ.
Chang, H.-H., & Stout, W. F. (1991).The asymptotic posterior normality of the latent trait in an IRT model (ONR Research Report 91-4). Urbana-Champaign: University of Illinois, Department of Statistics. (ERIC Document Reproduction Service No. ED 336-397 or TM 017-040).
Chang, H.-H., & Stout, W. F. (1993). The asymptotic posterior normality of the latent trait in an IRT model.Psychometrika, 58, 37–52.
Chang, H.-H., & Ying, Z. (in press). A global information approach to computerized adaptive testing.Applied Psychological Measurement.
Cover, T. M., & Thomas, J. A. (1991).Elements of information theory. New York: John Wiley & Sons.
Holland, P. W. (1990). On the sampling theory foundations of item response theory models.Psychometrika, 55, 577–601.
Johnson, E. G., & Carlson, J. E. (1994)The NAEP 1992 technical report. Washington, DC: National Center of Education Statistics.
Junker, B. W. (1991). Essential independence and likelihood based ability estimation for polytomous items.Psychometrika, 56, 255–278.
Lehmann, E. L. (1983).Theory of point estimation. New York: John Wiley & Sons.
Lord, M. F. (1971). Robbins-Monro procedures for tailored testing.Educational and Psychological Measurement, 31, 3–31.
Masters, G. N. (1982). A Rasch model for partial credit scoring.Psychometrika, 47, 149–174.
Muraki, E. (1992). A generalized partial credit model: application of an EM algorithm.Applied Psychological Measurement, 16, 159–176.
Samejima, F. (1969). Estimation of latent ability using a response pattern of graded scores.Psychometrika Monograph Supplement No. 17, 34 (4, Pt. 2).
Samejima, F. (1972). A general model for free-response data.Psychometrika Monograph No. 18, 37 (4, Pt. 2).
Serfling, R. J. (1980).Approximation theorems in mathematical statistics. New York: John-Wiley & Sons.
Thissen, D., & Steinberg, L. (1984). A response model for multiple choice items.Psychometrika, 49, 501–519.
Thissen, D., & Steinberg, L. (1986). A taxonomy of item response models.Psychometrika, 51, 567–577.
Wald, A. (1949). Note on the consistency of the maximum likelihood estimate.Annals of Mathematical Statistics, 20, 595–601.
Walker, A. M. (1969). On the asymptotic behavior of posterior distributions.Journal of the Royal Statistical Society, Series B, 31, 80–88.
Weiss, D. J. (1982). Improving measurement equality and efficiency with adaptive testing.Applied Psychological Measurement, 6, 379–396.
Wilson, M., & Masters, G. N. (1993). The partial credit model and null categories.Psychometrika, 58, 87–99.
Wright, B., & Masters, G. N. (1982).Rating scale analysis. Chicago: MESA Press.
Author information
Authors and Affiliations
Additional information
This research was partially supported by Educational Testing Service Allocation Project No. 79424. The author wishes to thank Charles Davis, Xuming He, Frank Jenkins, Spence Swinton, William Stout, Ming-Mai Wang, and Zhiliang Ying for their helpful comments and discussions. The author particularly wishes to thank the Editor, Shizuhiko Nishisato, the Associate Editor, and three anonymous reviewers for their thoroughness and thoughtful suggestions.
Rights and permissions
About this article
Cite this article
Chang, HH. The asymptotic posterior normality of the latent trait for polytomous IRT models. Psychometrika 61, 445–463 (1996). https://doi.org/10.1007/BF02294549
Received:
Revised:
Issue Date:
DOI: https://doi.org/10.1007/BF02294549