Relatively little research has been conducted with the noncompensatory class of multidimensional item response theory (MIRT) models. A Monte Carlo simulation study was conducted exploring the estimation of a two-parameter noncompensatory item response theory (IRT) model. The estimation method used was a Metropolis-Hastings within Gibbs algorithm that accepted or rejected new parameters in a bivariate fashion. Results showed that acceptable estimation of the noncompensatory model required a sample size of 4,000 people, six unidimensional items per dimension, and latent traits that are not highly correlated. Although the data requirements to estimate this model are a bit daunting, future advances in methodology could make this model valuable for modeling multidimensional data where the latent traits are not expected to be highly correlated.
Ackerman, T. ( 1996). Graphical representation of multidimensional item response theory analyses. Applied Psychological Measurement, 20, 311-329.
2.
Ackerman, T.A. ( 1994). Using multidimensional item response theory to understand what items and tests are measuring. Applied Measurement in Education, 7, 255-278.
3.
Babcock, B. ( 2008). Item parameter recovery in the case of a peaked test: Marginal maximum likelihood vs. Gibbs sampling (Unpublished master’s thesis). University of Minnesota, Minneapolis.
4.
Béguin, A.A., & Glas, C.A.W. ( 2001). MCMC estimation and some model-fit analysis of multidimensional IRT models. Psychometrika, 66, 541-562.
5.
Bolt, D.M., & Lall, V.F. ( 2003). Estimation of compensatory and noncompensatory multidimensional item response models using Markov chain Monte Carlo. Applied Psychological Measurement, 27, 395-414.
6.
Brooks, S.P., & Gelman, A. ( 1998). General methods for monitoring convergence of iterative simulations. Journal of Computational and Graphical Statistics , 7, 434-455.
7.
Chib, S., & Greenberg, E. ( 1995). Understanding the Metropolis-Hastings algorithm. The American Statistician, 19, 327-335.
8.
Drasgow, F. ( 1989). An evaluation of marginal maximum likelihood estimation for the two-parameter logistic model. Applied Psychological Measurement, 13, 77-90.
9.
Embretson, S.E., & Reise, S.P. ( 2000). Item response theory for psychologists. Mahwah, NJ: Erlbaum.
10.
Hulin, C.L., Lissak, R.I., & Drasgow, F. ( 1982). Recovery of two- and three-parameter logistic item characteristic curves: A Monte Carlo study. Applied Psychological Measurement , 6, 349-260.
11.
McDonald, R. ( 2000). A basis for multidimensional item response theory. Applied Psychological Measurement, 24, 99-114.
12.
Mulaik, S.A. ( 1972). Orthogonal analytic rotation. In The foundations of factor analysis (pp. 249-271). New York, NY: McGraw-Hill.
13.
Patz, R.J., & Junker, B.W. ( 1999). A straightforward approach to Markov chain Monte Carlo methods for item response models. Journal of Educational and Behavioral Statistics, 24, 146-178.
14.
R Development Core Team. (2008). R: A language and environment for statistical computing. R Foundation for Statistical Computing, Vienna, Austria. Retrieved from http://www.R-project.org
15.
Reckase, M.D. ( 1997a). A linear logistic multidimensional model for dichotomous item response data. In W. J. van der Linden & R. K. Hambelton (Eds.), Handbook of modern item response theory (pp. 271-286). New York, NY : Springer.
16.
Reckase, M.D. ( 1997b). The past and future of multidimensional item response theory. Applied Psychological Measurement, 21, 25-36.
17.
Reckase, M.D., & McKinley, R.L. (1991). The discriminating power of items that measure more than one dimension. Applied Psychological Measurement, 15, 361-373.
18.
Roussos, L.A., Templin, J.L., & Henson, R.A. ( 2007). Skills diagnosis using IRT-based latent class models . Journal of Educational Measurement, 44, 293-311.
19.
Sijtsma, K., & Junker, B.W. ( 2006). Item response theory: Past performance, present developments, and future expectations. Behaviormetrika, 33, 75-102.
20.
Spray, J.A., Davey, T.C., Reckase, M.D., Ackerman, T.A., & Carlson, J.E. ( 1990). Comparison of two logistic multidimensional item response theory models (Research Report No. ACT-RR-90-8). Iowa City: ACT Research Report Series .
21.
Sympson, J.B. ( 1977, July). A model for testing with multidimensional items . Paper presented at the 1977 Computerized Adaptive Testing Conference, Minneapolis, MN. Retrieved from http://www.psych.umn.edu/psylabs/catcentral/
Weiss, D.J., & Yoes, M.E. ( 1991). Item response theory. In R. K. Hambleton & J. N. Zaal (Eds.), Advances in educational and psychological testing: Theory and applications (pp. 69-95). Boston, MA: Kluwer Academic.
