Rasch models for item bundles
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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.
- 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.
- Adams, R. A., & Wilson, M. (in press). Formulating the Rasch model as a mixed coefficients multinomial logit. In G. Engelhard & M. Wilson (Eds.),Objective measurement: Theory into practice Volume III. Norwood, NJ: Ablex.
- Akaike, H. (1973). Information theory and an extension of the maximum likelihood principle. In B. N. Petrov & F. Csáki (Eds.),2nd International Symposium on Information Theory (pp. 267–281). Budapest: Akadémiai Kiadó.
- Andersen, E. B. (1973). Conditional inference for multiple choice questionnaires.British Journal of Mathematical and Statistical Psychology, 26, 31–44.
- Andersen, E. B. (1983). A general latent structure model for contingency table data. In H. Wainer & S. Messick (Eds.),Principals of modern psychological measurement (pp. 117–138). Hillsdale, NJ: Lawrence Erlbaum.
- Andrich, D. A. (1978). A rating formulation for ordered response categories.Psychometrika, 43, 561–573. CrossRef
- Andrich, D. A. (1985). A latent trait model for items with response dependencies: Implications for test construction and analysis. In S. E. Embretson (Ed.),Test design (pp. 245–275). New York: Academic Press.
- Biggs, J. B., & Collis, K. F. (1982).Evaluating the quality of learning: The SOLO taxonomy. New York: Academic Press.
- Birnbaum, A. (1968). Some latent trait models and their use in inferring an examinees' ability. In F. M. Lord & M. R. Novick (Ed.),Statistical theories of mental test scores. Reading, MA: Addison-Wesley.
- 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.
- 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.
- Cureton, E. E. (1965). Reliability and validity: Basic assumptions and experimental designs.Educational and Psychological Measurement, 25, 326–346.
- 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. CrossRef
- Glas, C. A. W. (1989).Contributions to estimating and testing Rasch models. Unpublished doctoral disssertation, Twente University, Twente, The Netherlands.
- 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.
- Kelderman, H. (1984). Loglinear Rasch model tests.Psychometrika, 49, 223–245. CrossRef
- Kelderman, H. (1989).Loglinear multidimensional IRT models for polytomously scored items. Paper presented at the Fifth International Objective Measurement Workshop, Berkeley, CA.
- Kelderman, H., & Steen, R. (1988).LOGIMO: A program for loglinear IRT modeling. Enschede, The Netherlands: University of Twente, Department of Education.
- Linacre, J. M. (1989).Many faceted Rasch measurement. Unpublished doctoral dissertation, University of Chicago.
- Masters, G. N. (1982). A Rasch model for partial credit scoring.Psychometrika, 47, 149–174. CrossRef
- Rasch, G. (1960).Probabilistic models for some intelligence and attainment tests. Copenhagen: Denmark's Paedagogistic Institut.
- 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.
- 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.
- Rosenbaum, P. R. (1984). Testing the conditional independence and monotonicity assumptions of item response theory.Psychometrika, 49, 425–435.
- Rosenbaum, P. R. (1988). Item bundles.Psychometrika, 53, 349–359. CrossRef
- Samejima, F. (1969). Estimation of latent ability using a response pattern of graded scores.Psychometrika Monograph No. 17, 34 (4, Pt. 2).
- Siegler, R. S. (1981). Developmental sequences within and between concepts.Monograph of the Society for Research in Child Development, 46.
- 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. CrossRef
- van Hiele, P. M. (1986).Structure and insight: A theory of mathematics education. Orlando, FL: Academic Press.
- Wainer, H., & Kiely, G. L. (1987). Item clusters and computerized adaptive testing: A case for testlets.Journal of Educational Measurement, 24, 185–201. CrossRef
- Wilson, M. (1988). Detecting breakdowns in local independence using a family of Rasch models.Applied Psychological Measurement, 12, 353–364.
- Wilson, M. (1989).The partial order model. Paper presented at the Fifth International Objective Measurement Workshop, University of California, Berkeley.
- Wilson, M. (1992). The ordered partition model: An extension of the partial credit model.Applied Psychological Measurement, 16(3), 309–325.
- Wilson, M., & Adams, R. J. (1993). Marginal maximum likelihood estimation for the ordered partition model.Journal of Educational Statistics, 18(1), 69–90.
- Wilson, M., & Iventosch, L. (1988). Using the Partial Credit model to investigate responses to structured subtests.Applied Measurement in Education, 1(4), 319–334. CrossRef
- Rasch models for item bundles
Volume 60, Issue 2 , pp 181-198
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