This paper illustrates how graphical analyses can en hance the interpretation and understanding of multidi mensional item response theory (IRT) analyses. Many unidimensional IRT concepts, such as item response functions and information functions, can be extended to multiple dimensions; however, as dimensionality in creases, new problems and issues arise, most notably how to represent these features within a multidimen sional framework. Examples are provided of several dif ferent graphical representations, including item response surfaces, information vectors, and centroid plots of con ditional two-dimensional trait distributions. All graphs are intended to supplement quantitative and substantive analyses and thereby assist the test practitioner in deter mining more precisely such information as the construct validity of a test, the degree of measurement precision, and the consistency of interpretation of the number- correct score scale.
Ackerman, T.A. (1989). Unidimensional IRT calibration of compensatory and noncompensatory items. Applied Psychological Measurement , 13, 113-127.
2.
Ackerman, T.A. (1992). An explanation of differential item functioning from a multidimensional perspective. Journal of Educational Measurement, 24, 67-91.
3.
Ackerman, T.A. (1994a). Creating a test information profile in a two-dimensional latent space. Applied Psychological Measurement, 18, 257-275.
4.
Ackerman, T.A. (1994b). Using multidimensional item response theory to understand what items and tests are measuring. Applied Measurement in Education, 7, 255-278.
5.
American College Testing Program. (1989). ACT assessment. Iowa City IA: Author .
6.
Computer Associates International, Inc. (1989 ). DISSPLA 10.0 [Computer software]. Garden City NY: Author.
7.
Davey, T., & 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 .
8.
Drasgow, F., & Lissak, R.I. (1983). Modified parallel analysis: A procedure for examining the latent dimensionality of dichotomously scored item responses. Journal of Applied Psychology, 68, 363-373.
9.
Fraser, C., & McDonald, R.P. (1988). NOHARM II: A FORTRANprogram forfitting both unidimensional and multidimensional normal ogive models of latent trait theory [Computer software]. Armidale, Australia: University of New England, Centre for Behavioral Studies .
10.
Hambleton, R.K., & Swaminathan, H. (1985). Item response theory: Principles and applications. Boston MA: Kluwer Nijhoff.
11.
Horn, J.L. (1965). A rationale and test for the number of factors in factor analysis. Psychometrika, 30, 179-185.
12.
Hsu, Y. ( 1995). Item parameter estimation of a two-dimensional generalized MIRT model (Doctoral dissertation, University of Illinois , 1995). Dissertation Abstracts International , 57, 1584.
13.
Kim, H.R., & Stout, W.F. (1994, April). A new index for assessing the amount of multidimensionality and/or simple structure present in test data. Paper presented at the annual meeting of the American Educational Research Association, New Orleans.
14.
Lim, C. ( 1993). An application of the joint maximum likelihood estimation procedure to a two-dimensional case of Sympson's noncompensatory IRT model (Doctoral dissertation, University of Iowa, 1993). Dissertation Abstracts International, 54, 2549.
15.
McDonald, R.P. (1981). The dimensionality of tests and items. British Journal of Mathematical and Statistical Psychology, 34, 100-117.
16.
Reckase, M.D. (1979). Unifactor latent trait models applied to multi-factor tests: Results and implications. Journal of Educational Statistics , 4, 207-230.
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., & Stout, W. (1996). A multidimensionality-based DIF analysis paradigm . Applied Psychological Measurement, 20, 355-371.
19.
Roznowski, M., Tucker, L.R., & Humphreys, L.G. (1991). Three approaches to determining the dimensionality of binary items. Applied Psychological Measurement, 15, 109-127.
20.
Samejima, F. (1977). Weakly parallel tests in latent trait theory with some criticisms of classical test theory. Psychometrika, 42, 193-198.
21.
Stocking, M., & Lord, F.M. (1983). Developing a common metric in item response theory . Applied Psychological Measurement, 7, 201-210.
22.
Stout, W.F. (1987). A nonparametric approach to assessing latent trait unidimensionality. Psychometrika, 52, 589-617.
23.
Sympson, J.B. (1978). A model for testing 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.
24.
Wilson, D., Wood, R., & Gibbons, R. (1987). TESTFACT [Computer program]. Mooresville IN: Scientific Software.
