Multidimensional item response theory (MIRT) is a relatively new methodology for modeling the relationships in a matrix of responses to a set of test items. MIRT has been used to help understand the skills required to successfully respond to test items, the extraneous examinee characteristics that affect the probability of response to items (DIF), and the complexities behind equating test forms, among other applications. This paper provides a short introduction to the historical antecedents of MIRT, the initial development of MIRT procedures, the similarities of MIRT procedures to other analysis techniques, and potential future directions for MIRT.
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References
1.
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.
2.
Bejar, I. I. (1977). An application of the continuous response level model to personality measurement. Applied Psychological Measurement, 1509-521.
3.
Bock, R. D. , & Aitkin, M. (1981). Marginal maximum likelihood estimation of item parameters: Application of an EM algorithm. Psychometrika, 46, 443-459.
4.
Bock, R. D. , Gibbons, R., & Muraki, E. (1988). Full information item factor analysis. Applied Psychological Measurement, 12, 261-280.
5.
Camilli, G. , Wang, M., & Fesq, J. (1995). The effects of dimensionality on equating the Law School Admission Test. Journal of Educational Measurement, 32, 79-96.
6.
Carroll, J. B. (1945). The effect of difficulty and chance success on correlations between items or between tests. Psychometrika, 10, 1-19.
7.
Christoffersson, A. (1975). Factor analysis of dichotomized variables. Psychometrika, 40, 5-32.
8.
Davey, T. C. , & Oshima, T. C. (1994, April). Linking multidimensional item calibrations. Paper presented at the annual meeting of the National Council on Measurement in Education, New Orleans.
9.
Drasgow, F. , Levine, M. V., & McLaughlin, M. E. (1991). Appropriateness measurement for some multidimensional test batteries. Applied Psychological Measurement, 15, 171-191.
10.
Fraser, C. (1988). NOHARM II: A Fortran program forfitting unidimensional and multidimensional normal ogive models of latent trait theory. Armidale, Australia: The University of New England.
11.
Glas, C. A. W. (1992). A Rasch model with a multivariate distribution of ability. In M. Wilson (Ed.), Objective measurement: Theory into practice (Vol. 1, pp. 236-258). Norwood NJ: Ablex.
12.
Harman, H. H. (1976). Modern factor analysis (3rd ed., revised). Chicago: University of Chicago Press.
13.
Horst, P. (1965). Factor analysis of data matrices. New York: Holt, Rinehart and Winston.
14.
Kelderman, H. (1994). Objective measurement with multidimensional polytomous latent trait models. In M. Wilson (Ed.), Objective measurement: Theory into practice (Vol. 2, pp. 235-243). Norwood NJ: Ablex.
15.
Lazarsfeld, P. F. (1950). The logical and mathematical foundation of latent structure analysis. In S. A. Stouffer (Ed.), Measurement and prediction (pp. 362-412). Princeton NJ: Princeton University Press.
16.
Liou, M. , & Chang, C. (1992). Constructing the exact significance level for a person fit statistic. Psychometrika, 57, 169-181.
17.
Lord, F. M. (1980). Applications of item response theory to practical testing problems. Hillsdale NJ: Erlbaum.
18.
Lord, F. M. , & Novick, M. R. (1968). Statistical theories of mental test scores. Reading MA: Addison-Wesley.
19.
McDonald, R. P. (1967). Nonlinear factor analysis. Psychometric Monographs, No. 15, 1-167.
20.
McDonald, R. P. (1985). Factor analysis and related methods. Hillsdale NJ: Erlbaum.
21.
McKinley, R. L. (1989). Confirmatory analysis of test structure using multidimensional item response theory (RR-99-3 1). Princeton NJ: Educational Testing Service.
22.
McKinley, R. L. , & Reckase, M. D. (1982). The use of the general Rasch model with multidimensional item response data (Research Report ONR 82-1). Iowa City IA: American College Testing.
23.
Miller, T. R. (1991). Empirical estimation of standard errors of compensatory MIRT model parameters obtainedfrom the NOHARM estimation program (Research Report ONR 91-2). Iowa City IA: American College Testing.
24.
Miller, T. R. , & Hirsch, T. M. (1992). Cluster analysis of angular data in applications of multidimensional item response theory. Applied Measurement in Education, 5, 193-211.
25.
Mulaik, S. A. (1972, March). A mathematical investigation of some multidimensional Rasch models for psychological tests. Paper presented at the annual meeting of the Psychometric Society, Princeton NJ.
26.
Muraki, E. , & Bejar, I. I. (1995, July). Full information factor analysis of polytomous item responses of NCARB exams. Paper presented at the European meeting of the Psychometric Society, Leiden, The Netherlands.
27.
Muthen, B. (1978). Contributions to factor analysis of dichotomous variables. Psychometrika, 43, 551-560.
28.
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.
29.
Rasch, G. (1962). On general laws and the meaning of measurement in psychology. Proceedings of the Fourth Berkeley Symposium on Mathematical Statistics and Probability, 4, 321-334.
30.
Reckase, M. D. (1972). Development and application of a multivariate logistic latent trait model. Unpublished doctoral dissertation, Syracuse University, Syracuse NY.
31.
Reckase, M. D. (1985). The difficulty of test items that measure more than one ability. Applied Psychological Measurement, 9, 401-412.
32.
Reckase, M. D. (1989, August). Controlling the psychometric snake: Or, how I learned to love multidimensionality. Invited address at the meeting of the American Psychological Association, New Orleans.
33.
Reckase, M. D. , Ackerman, T. A., & Carlson, J. E. (1988). Building a unidimensional test using multidimensional items. Journal of Educational Measurement, 25, 193-204.
34.
Reckase, M. D. , & Hirsch, T. M. (1991, April). Interpretation of number-correct scores when the true numbers of dimensions assessed by a test is greater than two. Paper presented at the annual meeting of the National Council on Measurement in Education, Chicago.
35.
Reckase, M. D. , & McKinley, R. L. (1991). The discriminating power of items that measure more than one dimension. Applied Psychological Measurement, 15361-373.
36.
Reise, S. P. , Widaman, K. F., & Pugh, R. H. (1993). Confirmatory factor analysis and item response theory: Two approaches for exploring measurement invariance. Psychological Bulletin, 114, 552-566.
37.
Samejima, F. (1974). Normal ogive model on the continuous response level in the multidimensional latent space. Psychometrika, 39, 111-121.
38.
Spearman, C. (1927). The abilities of man. New York: Macmillan.
39.
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 ONR 90-8). Iowa City IA: American College Testing.
40.
Sympson, J. B. (1978). A model for testing with multidimensional items. In D. J. Weiss (Ed.), Proceedings of the 1977 Computerized Adaptive Testing Conference (pp. 82-98). Minneapolis: University of Minnesota, Department of Psychology, Psychometric Methods Program.
41.
Thurstone, L. L. (1947). Multiple factor analysis. Chicago: University of Chicago Press.
42.
Whitely, S. E. (1980). Measuring aptitude processes with multicomponent latent trait models (Technical Report No. NIE-80-5). Lawrence: University of Kansas.
43.
Wilson, D. , Wood, R., & Gibbons, R. D. (1987). TESTFACT: Test scoring, item statistics, and item factor analysis. Mooresville IN: Scientific Software.
