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Rasch Models for Item Bundles

Published online by Cambridge University Press:  01 January 2025

Mark Wilson and
Raymond J. Adams
Mark Wilson*
Affiliation:
University of California, Berkeley
Raymond J. Adams
Affiliation:
Australian Council for Educational Research
*
Requests for reprints should be sent to Mark Wilson, Graduate School of Education, University of California, Berkeley, CA 94720.
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Abstract

This paper discusses the application of a class of Rasch models to situations where test items are grouped into subsets and the common attributes of items within these subsets brings into question the usual assumption of conditional independence. The models are all expressed as particular cases of the random coefficients multinomial logit model developed by Adams and Wilson. This formulation allows a very flexible approach to the specification of alternative models, and makes model testing particularly straightforward. The use of the models is illustrated using item bundles constructed in the framework of the SOLO taxonomy of Biggs and Collis.

Keywords

item bundlesRasch modelpartial credit modelconditional independence

Information

Type
Original Paper
Information
Psychometrika , Volume 60 , Issue 2 , June 1995, pp. 181 - 198
Copyright
Copyright © 1995 The Psychometric Society

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Footnotes

The work of both authors was supported by fellowships from the National Academy of Education Spencer Fellowship.

References

Adams, R. A., & Wilson, M. (1992). A random coefficients multinomial logit: Generalising Rasch models. Paper presented at the annual meeting of the American Educational Research Association, San Francisco.Google Scholar
Adams, R. A., & Wilson, M. (in press). Formulating the Rasch model as a mixed coefficients multinomial logit. In Engelhard, G. & Wilson, M. (Eds.), Objective measurement: Theory into practice Volume III. Norwood, NJ: Ablex.Google Scholar
Akaike, H. (1973). Information theory and an extension of the maximum likelihood principle. In Petrov, B. N., Csáki, F. (Eds.), 2nd International Symposium on Information Theory (pp. 267–281). Budapest: Akadémiai Kiadó.Google Scholar
Andersen, E. B. (1973). Conditional inference for multiple choice questionnaires. British Journal of Mathematical and Statistical Psychology, 26, 31–44.CrossRefGoogle Scholar
Andersen, E. B. (1983). A general latent structure model for contingency table data. In Wainer, H., Messick, S. (Eds.), Principals of modern psychological measurement (pp. 117–138). Hillsdale, NJ: Lawrence Erlbaum.Google Scholar
Andrich, D. A. (1978). A rating formulation for ordered response categories. Psychometrika, 43, 561–573.CrossRefGoogle Scholar
Andrich, D. A. (1985). A latent trait model for items with response dependencies: Implications for test construction and analysis. In Embretson, S. E. (Eds.), Test design (pp. 245–275). New York: Academic Press.CrossRefGoogle Scholar
Biggs, J. B., Collis, K. F. (1982). Evaluating the quality of learning: The SOLO taxonomy, New York: Academic Press.Google Scholar
Birnbaum, A. (1968). Some latent trait models and their use in inferring an examinees' ability. In Lord, F. M., Novick, M. R. (Eds.), Statistical theories of mental test scores, Reading, MA: Addison-Wesley.Google Scholar
Collis, K. F. (1983). Development of a group test of mathematical understanding using superitems SOLO technique. Journal of Science and Mathematics Education in South East Asia, 6, 5–14.Google Scholar
Collis, K. F., Davey, H. A. (1986). A technique for evaluating skills in high school science. Journal of Research in Science Teaching, 23, 651–663.CrossRefGoogle Scholar
Cureton, E. E. (1965). Reliability and validity: Basic assumptions and experimental designs. Educational and Psychological Measurement, 25, 326–346.CrossRefGoogle Scholar
Fischer, G. H., Parzer, P. (1991). An extension of the rating scale model with an application to the measurement of change. Psychometrika, 56, 637–652.CrossRefGoogle Scholar
Glas, C. A. W. (1989). Contributions to estimating and testing Rasch models, Twente, The Netherlands: Twente University.Google Scholar
Glas, C. A. W. (1991). Testing Rasch models for polytomous items with an example concerning detection of item bias. Paper presented at the annual meeting of the American Educational Association, Chicago.Google Scholar
Kelderman, H. (1984). Loglinear Rasch model tests. Psychometrika, 49, 223–245.CrossRefGoogle Scholar
Kelderman, H. (1989). Loglinear multidimensional IRT models for polytomously scored items. Paper presented at the Fifth International Objective Measurement Workshop, Berkeley, CA.Google Scholar
Kelderman, H., Steen, R. (1988). LOGIMO: A program for loglinear IRT modeling, Enschede, The Netherlands: University of Twente, Department of Education.Google Scholar
Linacre, J. M. (1989). Many faceted Rasch measurement. Unpublished doctoral dissertation, University of Chicago.Google Scholar
Masters, G. N. (1982). A Rasch model for partial credit scoring. Psychometrika, 47, 149–174.CrossRefGoogle Scholar
Rasch, G. (1960). Probabilistic models for some intelligence and attainment tests, Copenhagen: Denmark's Paedagogistic Institut.Google Scholar
Romberg, T. A., Collis, K. F., Donovan, B. F., Buchanan, A. E., Romberg, M. N. (1982). The development of mathematical problem solving superitems (Report of NIE/EC Item Development Project), Madison, WI: Wisconsin Center for Education Research.Google Scholar
Romberg, T. A., Jurdak, M. E., Collis, K. F., Buchanan, A. E. (1982). Construct validity of a set of mathematical superitems (Report of NIE/ECS Item Development Project), Madison, WI: Wisconsin Center for Education Research.Google Scholar
Rosenbaum, P. R. (1984). Testing the conditional independence and monotonicity assumptions of item response theory. Psychometrika, 49, 425–435.CrossRefGoogle Scholar
Rosenbaum, P. R. (1988). Item bundles. Psychometrika, 53, 349–359.CrossRefGoogle Scholar
Samejima, F. (1969). Estimation of latent ability using a response pattern of graded scores. Psychometrika Monograph No. 17, 34 (4, Pt. 2).Google Scholar
Siegler, R. S. (1981). Developmental sequences within and between concepts. Monograph of the Society for Research in Child Development, 46.CrossRefGoogle Scholar
Siegler, R. S. (1987). The perils of averaging data over strategies: An example from children's addition. Journal of Experimental Psychology: General, 116, 250–264.CrossRefGoogle Scholar
van Hiele, P. M. (1986). Structure and insight: A theory of mathematics education, Orlando, FL: Academic Press.Google Scholar
Wainer, H., Kiely, G. L. (1987). Item clusters and computerized adaptive testing: A case for testlets. Journal of Educational Measurement, 24, 185–201.CrossRefGoogle Scholar
Wilson, M. (1988). Detecting breakdowns in local independence using a family of Rasch models. Applied Psychological Measurement, 12, 353–364.CrossRefGoogle Scholar
Wilson, M. (1989). The partial order model, Berkeley: University of California.Google Scholar
Wilson, M. (1992). The ordered partition model: An extension of the partial credit model. Applied Psychological Measurement, 16(3), 309–325.CrossRefGoogle Scholar
Wilson, M., Adams, R. J. (1993). Marginal maximum likelihood estimation for the ordered partition model. Journal of Educational Statistics, 18(1), 69–90.CrossRefGoogle Scholar
Wilson, M., Iventosch, L. (1988). Using the Partial Credit model to investigate responses to structured subtests. Applied Measurement in Education, 1(4), 319–334.CrossRefGoogle Scholar