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Abstract
A multidimensional Rasch-type item response model, the multidimensional random coefficients multinomial logit model, is presented as an extension to the Adams & Wilson (1996) random coefficients multinomial logit model. The model is developed in a form that permits generalization to the multidimensional case of a wide class of Rasch models, including the simple logistic model, Masters' partial credit model, Wilson's ordered partition model, and Fischer's linear logistic model. Moreover, the model includes several existing multidimensional models as special cases, including Whitely's multicomponent latent trait model, Andersen's multidimensional Rasch model for repeated testing, and Embretson's multidimensional Rasch model for learning and change. Marginal maximum likelihood estimators for the model are derived and the estimation is examined using a simulation study. Implications and applications of the model are discussed and an example is given.
|
Ackerman, T. A. (1992). A didactic explanation of item bias, item impact, and item validity from a multidimensional perspective. Journal of Educational Measurement, 29, 67-91. Google Scholar | Crossref | ISI | |
|
Adams, R. J. , & Wilson, M. R. (1996). Formulating the Rasch model as a mixed coefficients multinomial logit. In G. Engelhard & M. Wilson (Eds.), Objective measurement: Theory into practice (Vol III; pp. 143-166). Norwood NJ: Ablex. Google Scholar | |
|
Adams, R. J. , Wilson, M. R. , & Wu, M. L. (in press). Multilevel item response modelling: An approach to errors in variables regression. Journal of Educational and Behavioral Statistics. Google Scholar | |
|
Akaike, H. (1977). On entropy maximisation principle. In P. R. Krischnaiah (Ed.), Applications of statistics (pp. 27-41). New York: North Holland. Google Scholar | |
|
Andersen, E. B. (1970). Asymptotic properties of conditional maximum likelihood estimators. Journal of the Royal Statistical Society, 32 (Series B), 283-301. Google Scholar | |
|
Andersen, E. B. (1985). Estimating latent correlations between repeated testings. Psychometrika, 50, 3-16. Google Scholar | Crossref | ISI | |
|
Andersen, E. B. , & Madsen, M. (1977). Estimating the parameters of the latent population distribution. Psychometrika, 42, 357-374. Google Scholar | Crossref | ISI | |
|
Andrich, D. (1978). A rating formulation for ordered response categories. Psychometrika, 43, 561-573. Google Scholar | Crossref | ISI | |
|
Ansley, T. N. , & Forsyth, R. A. (1985). An examination of the characteristics of unidimensional IRT parameter estimates derived from twodimensional data. Applied Psychological Measurement, 9, 37-48. Google Scholar | SAGE Journals | ISI | |
|
Beaton, A. E. (1987). Implementing the new design: The NAEP 1983-84 technical report (Research Rep. No. 15-TR-20). Princeton NJ: Educational Testing Service. Google Scholar | |
|
Biggs, J. B. , & Collis, K. F. (1982). Evaluating the quality of learning: The SOLO taxonomy. New York: Academic Press. Google Scholar | |
|
Bock, R. D. , & Aitkin, M. (1981). Marginal maximum likelihood estimation of item parameters: An application of the EM algorithm. Psychometrika, 46, 443-459. Google Scholar | Crossref | ISI | |
|
Camilli, G. (1992). A conceptual analysis of differential item functioning in terms of a multidimensional item response model. Applied Psychological Measurement, 16, 129-147. Google Scholar | SAGE Journals | ISI | |
|
Davey, T. , & Hirsch, T. M. (1991, May). Concurrent and consecutive estimates of examinee ability profiles. Paper presented at the Annual Meeting of the Psychometric Society, New Brunswick NJ. Google Scholar | |
|
de Leeuw, J. , & Verhelst, N. (1986). Maximum likelihood estimation in generalized Rasch models. Journal of Educational Statistics, 11, 183-196. Google Scholar | Crossref | |
|
Dempster, A. P. , Laird, N. M. , & Rubin, D. B. (1977). Maximum likelihood from incomplete data via the EM algorithm. Journal of the Royal Statistical Society, 39, (Series B), 1-38. Google Scholar | |
|
Donlon, T. F (Ed.). (1984). The College Board technical handbook for the Scholastic Aptitude Tests and achievement tests. New York: College Entrance Examination Board. Google Scholar | |
|
Embretson, S. E. (1991). A multidimensional latent trait model for measuring learning and change. Psychometrika, 56, 495-515. Google Scholar | Crossref | ISI | |
|
Fischer, G. H. (1973). The linear logistic model as an instrument in educational research. Acta Psychologica, 37, 359-374. Google Scholar | Crossref | ISI | |
|
Fischer, G. H. , & Pononcy, I. (1994). An extension of the partial credit model with an application to the measurement of change. Psychometrika, 59, 177-192. Google Scholar | Crossref | ISI | |
|
Folk, V. G. , & Green, B. F. (1989). Adaptive estimation when the unidimensionality assumption of IRT is violated. Applied Psychological Measurement, 13, 373-389. Google Scholar | SAGE Journals | ISI | |
| Glas, C. A. W. (1989). Contributions to estimating and testing Rasch models. Unpublished doctoral dissertation. University of Twente, The Netherlands. Google Scholar | |
|
Glas, C. A. W. (1992). A Rasch model with a multivariate distNbution of ability. In M. Wilson (Ed.), Objective measurement: Theory into practice (Vol. 1; pp. 236-258). Norwood NJ: Ablex. Google Scholar | |
|
Glas, C. A. W. , & Verhelst, N. D. (1989). Extensions of the partial credit model. Psychometrika, 54, 635-659. Google Scholar | Crossref | ISI | |
|
Hambleton, R. K. , & Murray, L. N. (1983). Some goodness of fit investigations for item response models. In R. K. Hambleton (Ed.), Applications of item response theory (pp. 71-94). Vancouver BC: Educational Research Institute of British Columbia. Google Scholar | |
|
Hoijtink, H. (1995). Linear and repeated measures models for the person parameters. In G. H. Fischer & I. W. Molenaar (Eds.), Rasch models: Foundations, recent developments, and applications(pp. 203-214). NewYork: Springer-Verlag. Google Scholar | Crossref | |
|
Kelderman, H. , & Rijkes, C. P. M. (1994). Loglinear multidimensional IRT models for polytomously scored items. Psychometrika, 59, 149-176. Google Scholar | Crossref | ISI | |
|
Linacre, J. M. (1989). Many-faceted Rasch measurement. Chicago: MESA Press. Google Scholar | |
|
Lord, F. M. (1980). Applications of item response theory to practical testing problems. Hillsdale NJ: Erlbaum. Google Scholar | |
|
Luecht, R. M. , & Miller, R. (1992). Unidimensional calibrations and interpretations of composite traits for multidimensional tests. Applied Psychological Measurement, 16, 279-293. Google Scholar | SAGE Journals | ISI | |
|
Masters, G. N. (1982). A Rasch model for partial credit scoring. Psychometrika, 47, 149-174. Google Scholar | Crossref | ISI | |
|
Masters, G. N. (1988). Measurement models for ordered response categories. In R. Langeheine & J. Rost (Eds.), Latent trait and latent class models (pp. 11-50). Plenum: New York. Google Scholar | Crossref | |
|
Mislevy, R. J. , & Bock, R. D. (1983). BILOG II: Item analysis and test scoring with binary logistic models. Mooresville IN: Scientific Software. Google Scholar | |
|
Muraki, E. (1992). A generalized partial credit model: Application of an EM algorithm. Applied Psychological Measurement, 16, 159-176. Google Scholar | SAGE Journals | ISI | |
|
Oshima, T. C. , & Miller, M. D. (1992). Multidimensionality and item bias in item response theory. Applied Psychological Measurement, 16, 237-248. Google Scholar | SAGE Journals | ISI | |
|
Pfanzagl, J. (1994). On item parameter estimation in certain latent trait models. In G. H. Fischer & D. Laming, Contributions to mathematical psychology, psychometrics, and methodology (pp. 249-263). New York: Springer-Verlag. Google Scholar | Crossref | |
|
Rasch, G. (1960/80). Probabilistic models for some intelligence and attainment tests. (Copenhagen, Danish Institute for Educational Research). Expanded edition (1980), with foreword and afterword by B. D. Wright. Chicago, The University of Chicago Press. Google Scholar | |
|
Rasch, G. (1961). On general laws and the meaning of measurement in psychology. Proceedings of the Fourth Berkeley Symposium on Mathematical Statistics and Probability, 4, 321-334. Google Scholar | |
|
Reckase, M. D. (1985). The difficulty of test items that measure more than one ability. Applied Psychological Measurement, 9, 401-412. Google Scholar | SAGE Journals | ISI | |
|
Reckase, M. D. , & McKinley, R. L. (1991). The discriminating power of items that measure more than one dimension. Applied Psychological Measurement, 15, 361-373. Google Scholar | SAGE Journals | ISI | |
| Volodin, N., & Adams, R. J. (1995). Identifying and estimating a D-dimensional Rasch model. Unpublished manuscript, Australian Council for Educational Research, Camberwell, Victoria, Australia. Google Scholar | |
| Wang, W. C. (1994). Implementation and application of the multidimensional random coefficients multinomial logit. Unpublished doctoral dissertation, University of California, Berkeley. Google Scholar | |
| Wang, W. C., Wilson, M. R., & Adams, R. J. (1996). Implications and applications of the multidimensional random coefficients multinomial logit model. Unpublished manuscript, Australian Council for Educational Research, Camberwell, Victoria, Australia. Google Scholar | |
|
Way, W. D. , Ansley, T. N. , & Forsyth, R. A. (1988). The comparative effects of compensatory and noncompensatory two-dimensional data on unidimensional IRT estimation. Applied Psychological Measurement, 12, 239-252. Google Scholar | SAGE Journals | ISI | |
|
Whitely, S. E. (1980). Multicomponent latent trait models for ability tests. Psychometrika, 45, 479-494. Google Scholar | Crossref | ISI | |
|
Whitely, S. E. (1984). A general latent trait model for response processes. Psychometrika, 49, 175-186. Google Scholar | Crossref | ISI | |
|
Wilson, D. T. , Wood, R. , & Gibbons, R. (1991). TESTFACT: Test scoring, item statistics, and item factor analysis. Mooresville IN: Scientific Software. Google Scholar | |
|
Wilson, M. (1988). Detecting breakdowns in local independence using a family of Rasch models. Applied Psychological Measurement, 12, 353-364. Google Scholar | SAGE Journals | ISI | |
|
Wilson, M. R. (1992). The partial order model: An extension of the partial credit model. Applied Psychological Measurement, 16, 309-325. Google Scholar | SAGE Journals | ISI | |
|
Wilson, M. R. , & Adams, R. J. (1993). Marginal maximum likelihood estimation for the ordered partition model. Journal of Educational Statistics, 18, 69-90. Google Scholar | Crossref | |
|
Wilson, M. R. , & Adams, R. J. (1995). Rasch models for item bundles. Psychometrika, 60, 181-198. Google Scholar | Crossref | ISI | |
|
Wilson, M. R. , & Wang, W. C. (in press). Complex composites: Issues that arise in combining different models of assessment. Applied Psychological Measurement, 19, 51-72. Google Scholar | SAGE Journals | ISI | |
|
Wright, B. D. , & Masters, G. N. (1982). Rating scale analysis. Chicago: MESA Press. Google Scholar | |
|
Wu, M. L. , & Adams, R. J. (1993, April). Simulating parameter recovery for the random coefficients multinomial logit. Paper presented at the Sixth International Objective Measurement Workshop, Atlanta. Google Scholar | |
|
Wu, M. L. , Adams, R. J. , & Wilson, M. R. (1995). MATS: Multi-aspect test software. Melbourne, Australia: Australian Council for Educational Research. Google Scholar | |
|
Zwinderman, A. H. (1991). A generalized Rasch model for manifest predictors. Psychometrika, 56, 589-600. Google Scholar | Crossref | ISI |
