A multidimensional Rasch model is presented here, which is a multidimensional extension of item component models. Relations to existing multidimensional item response theory models are discussed. Apart from other applications, it is also suitable for analyzing tests and questionnaires, which are designed according to two or more facets. An application to a 77-item questionnaire on students’ interest in physics with a two-facet structure demonstrates that the model parameters can even be estimated when 17 latent dimensions are to be measured simultaneously (by means of joint maximum likelihood methods).
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References
1.
Adams, R. , Wilson, M., & Wang, W. C. (1997). The multidimensional random coefficients multinomial logit model. Applied Psychological Measurement, 21(1), 1-23.
2.
Albanese, M. T. , & Knott, M. (1992). TWOMISS: A computer program for fitting a oneor two-factor logit-probit latent variable model to binary data when observations may be missing. Technical report. London: London School of Economics and Political Science, Statistics Department.
3.
Andrich, D. (1978). Application of a psychometric rating model to ordered categories which are scored with successive integers. Applied Psychological Measurement, 2, 581-594.
4.
Andrich, D. (1982). An extension of the Rasch model for ratings providing both location and dispersion parameters. Psychometrika, 47(1), 105-113.
5.
Bartholomew, D. J. (1987). Latent variable models and factor analysis. London: Charles Griffin.
6.
Carstensen, C. H. , & Rost, J. (1998). MULTIRA [Computer program]. Kiel, Germany: IPN— Institute for Science Education. Available from http://www.ppm.ipn.uni-kiel.de/multira/
7.
Embretson, S. E. (1997). Multicomponent response models. In W. Linden & R. K. van der Hambleton (Eds.), Handbook of modern item response theory (pp. 305-322). New York: Springer.
8.
Fischer, G. H. (1972). A measurement model for the effect of mass-media. Acta Psychologica, 36, 207-220.
9.
Fischer, G. H. (1973). The linear logistic test model as an instrument in educational research. Acta Psychologica, 37, 359-374.
10.
Fischer, G. H. (1974). Einführung in die Theorie psychologischer Tests. Bern, Germany: Huber.
11.
Fischer, G. H. (1977). Linear logistic trait models: Theory and application. In H. Spada & W. Kempf (Eds.), Structural models of thinking and learning (pp. 203-225). Bern, Germany: Huber.
12.
Fischer, G. H. (1983). Logistic latent trait models with linear constraints. Psychometrika, 48, 3-26.
13.
Fischer, G. H. (1987). Applying the principles of specific objectivity and generalizability to the measurement of change. Psychometrika, 52, 565-587.
14.
Fischer, G. H. (1997). Unidimensional linear logistic Rasch models. In W. Linden & R. K. van der Hambleton (Eds.), Handbook of modern item response theory (pp. 225-244). New York: Springer.
15.
Fischer, G. H. , & Parzer, P. (1991). An extension of the rating scale model with an application to the measurement of treatment effects. Psychometrika, 56, 637-651.
16.
Fischer, G. H. , & Ponocny, I. (1994). An extension of the partial credit model with an application to the measurement of change. Psychometrika, 59, 177-192.
17.
Haberman, S. J. (1977). Maximum likelihood estimates in exponential response models. The Annals of Statistics, 5(5), 815-841.
18.
Häußler, P. , Hoffmann, L., Langeheine, R., Rost, J., & Sievers, K. (1998). A typology of student’s interest in physics and the distribution of gender and age within each type. International Journal of Science Education, 20(2), 223-238.
19.
Hicks, L. E. (1970). Some properties of ipsative, normative, and forced-choice normative measures. Psychological Bulletin, 74, 167-184.
20.
Hoffmann, L., Häußler, P., Lehrke, M., & Todt, E. (1984). Schülerfragebogen zur Veränderung von Schülerinteressen an Physik und Technik vom 5. Bis 10. Schuljahr (polyscript). Kiel, Germany: IPN.
21.
Kelderman, H. , & Rijkes, C.P.M. (1994). Loglinear multidimensional IRT models for polytomously scored items. Psychometrika, 59, 149-176.
22.
Knott, M. , & Tzamourani, P. (1997). Fitting a latent trait model for missing observations to racial prejudice data. In J. Rost & R. Langeheine (Eds.), Applications of latent trait and latent class models in the social sciences. Münster, Germany: Waxmann.
23.
Linacre, J. M. (1989). Many-faceted Rasch Measurement. Chicago: MESA.
24.
Lunz, M. , & Wright, B. D. (1997). Latent trait models for performance examinations. In J. Rost & R. Langeheine (Eds.), Applications of latent trait and latent class models in the social sciences. Münster, Germany: Waxmann.
25.
Masters, G. N. (1982). A Rasch model for partial credit scoring. Psychometrika, 47, 149-174.
26.
Meiser, T. (1996). Loglinear Rasch models for the analysis of stability and change. Psychometrika, 61(4), 629-645.
27.
Muraki, E. , & Carlson, J. E. (1995). Full-information factor analysis for polytomous item responses. Applied Psychological Measurement, 19(1), 73-90.
28.
Neyman, J. , & Scott, E. L. (1948). Consistent estimates based on partially consistent observations. Econometrica, 16(1), 1-32.
29.
Rasch, G. (1961). On general laws and the meaning of measurement in psychology. Berkeley: University of California Press.
30.
Reckase, M. D. (1997). The past and future of multidimensional item response theory. Applied Psychological Measurement, 21(1), 25-36.
31.
Stegelmann, W. (1983). Expanding the Rasch model to a general model having more than one dimension. Psychometrika, 48(2), 259-267.
32.
Volodin, N. , & Adams, R. J. (1995). Identifying and estimating a d-dimensional Rasch model. Camberwell: Australian Council for Educational Research.
33.
Warm, T. A. (1989). Weighted likelihood estimation of ability in item response models. Psychometrika, 54, 427-450.
34.
Wu, M. , Adams, R. J., & Wilson, M. (1997). ConQuest—Generalised item response modelling software, draft release 2. Camberwell: Australian Council for Educational Research.
