A class of multidimensional IRT models for testing unidimensionality and clustering items

Akaike, H. (1973). Information theory and an extension of the maximum likelihood principle. In B.N. Petrov & F. Csaki (eds.), Second international symposium on information theory (pp. 267–281). Budapest: Akademiai Kiado.

Andersen, E.B. (1973). Conditional inference and models for measuring. Copenhagen: Mentalhygiejnisk Forlag.

Bartolucci, F., & Forcina, A. (2001). Analysis of capture-recapture data with a Rasch-type model allowing for conditional dependence and multidimensionality. Biometrics, 57, 714–719.

Bartolucci, F., & Forcina, A. (2005). Likelihood inference on the underlying structure of IRT models. Psychometrika, 70, 31–43.

Birnbaum, A. (1968). Some latent trait models and their use in inferring an examinee’s ability. In F.M. Lord & M.R. Novick (eds.), Statistical theories of mental test scores (pp. 395–379). Reading, MA: Addison-Wesley.

Burnham, K.P., & Anderson, D.R. (2002), Model selection and multi-model inference: A practical information-theoretic approach (2nd ed.), New York: Springer-Verlag.

Carstensen, C.H., and Rost, J. (2001). MULTIRA (version 1.63) [Computer software and manual]. Retrived from http://www.multira.de.

Christensen, K.B., & Bjorner, J. B. (2003). SAS macros for Rasch based latent variable modelling (Research Report No. 03/13). Department of Biostatistics, University of Copenhagen.

Christensen, K.B., Bjorner, J.B., Kreiner, S., & Petersen, J.H. (2002). Testing unidimensionality in polytomous Rasch models. Psychometrika, 67, 563–574.

de Leeuw, J., & Verhelst, N. (1986). Maximum likelihood estimation in generalized Rasch models. Journal of Educational Statistics, 11, 183–196.

Dempster, A.P., Laird, N.M., & Rubin, D.B. (1977). Maximum likelihood from incomplete data via the EM algorithm (with discussion). Journal of the Royal Statistical Society, Series B, 39, 1–18.

Embretson, S.E. (1996). Item response theory models and spurious interaction effects in factorial ANOVA designs. Applied Psychological Measurement, 20, 201–212.

Forcina, A., & Bartolucci, F. (2004). Modelling quality of life variables with non-parametric mixtures. Environmetrics, 15, 519–528.

Formann, A.K. (1995). Linear logistic latent class analysis and the Rasch model. In G.H. Fischer, & I.W. Molenaar (Eds.), Rasch models: Foundations, recent developments, and applications (pp. 239–255). New York: Springer-Verlag.

Glas, C.A.W. (1989). Contributions to estimating and testing Rasch models. Doctoral thesis. Enschede: University of Twente.

Glas, C.A.W., & Verhelst, N.D. (1995). Testing the Rasch model. In G.H. Fischer, & I.W. Molenaar (Eds.), Rasch models: Foundations, recent developments, and applications (pp. 69–75). New York: Springer-Verlag.

Goodman, L.A. (1974). Exploratory latent structure analysis using both identifiable and unidentifiable models. Biometrika, 61, 215–231.

Hardouin, J.B., & Mesbah, M. (2004). Clustering binary variables in subscales using an extended Rasch model and Akaike information criterion. Communications in Statistics. Theory and Methods, 33, 1277–1294.

Hoijtink, H., & Vollema, M. (2003). Contemporary extensions of the Rasch model. Quality & Quantity, 37, 263–276.

Kelderman, H. (1984). Loglinear Rasch model tests. Psychometrika, 49, 223–245.

Kelderman, H., & Rijkes, C.P.M. (1994). Loglinear multidimensional IRT models for polytomously scored items. Psychometrika, 59, 147–176.

Kiefer, J., & Wolfowitz, J. (1956). Consistency of the maximum likelihood estimator in the presence of infinitely many nuisance parameters. Annals of Mathematical Statistics, 27, 887–906.

Kreiner, S., & Christensen, K.B. (2004). Analysis of local dependence and multidimensionality in graphical loglinear Rasch models, Communications in Statistics: Theory and Methods, 33, 1239–1276.

Lazarsfeld, P.F., & Henry, N.W. (1968). Latent structure analysis. Boston: Houghton Mifflin.

Lindsay, B., Clogg, C., & Grego, J. (1991). Semiparametric estimation in the Rasch model and related exponential response models, including a simple latent class model for item analysis. Journal of the American Statistical Association, 86, 96–107.

Magidson, J., & Vermunt, J.K. (2001). Latent class factor and cluster models, bi-plots, and related graphical displays. Sociological Methodology, 31, 223–264.

Martin-Löf, P. (1973). Statistiska modeller. Anteckningar fr{å}n seminarier las{å}ret 1969–1970, utarbetade av Rolf Sundberg. Obetydligt ändrat nytryck, October 1973. Stockholm: Institütet för Försäkringsmatemetik och Matematisk Statistisk vid Stockholms Universitet.

McKinley, R.L., & Reckase, M.D. (1982). The use of the general Rasch model with multidimensional item response data. Iowa City, IA: American College Testing.

Molenaar, I.W. (1983). Some improved diagnostics for failure of the Rasch model. Psychometrika, 48, 49–72.

Rasch, G. (1961). On general laws and the meaning of measurement in psychology. Proceedings of the IV Berkeley Symposium on Mathematical Statistics and Probability, 4, 321–333.

Samejima, F. (1996). Evaluation of mathematical models for ordered polychotomous responses. Behaviormetrika, 23, 17–35.

Stegelmann, W. (1983). Expanding the Rasch model to a general model having more than one dimension. Psychometrika, 48, 259–267.

Thissen, D. (1982). Marginal maximum likelihood estimation for the one-parameter logistic model. Psychometrika, 47, 175–186.

Tjur, T. (1982). A connection between Rasch’s item analysis model and a multiplicative Poisson model. Scandinavian Journal of Statistics, 9, 23–30.

van Abswoude, A.A.H., van der Ark, L.A., & Sijtsma, K. (2004). A comparative study of test data dimensionality procedures under nonparametric IRT models. Applied Psychological Measurement, 28, 3–24.

van den Wollenberg, A.L. (1979). The Rasch model and time limit tests. Doctoral thesis. Nijmegen: University of Nijmegen.

van den Wollenberg, A.L. (1982). Two new test statistics for the Rasch model. Psychometrika, 47, 123–140.

Verhelst, N.D. (2001). Testing the unidimensionality assumption of the Rasch model. Methods of Psychological Research Online, 6, 231–271.

Vermunt, J.K. (2001). The use of restricted latent class models for defining and testing nonparametric and parametric item response theory models. Applied Psychological Measurement, 25, 283–294.