Abstract
Item response theory (IRT) models have been widely used for various educational and psychological testing purposes such as detecting differential item functioning (DIF), test construction, ability estimation, equating, and computer adaptive testing. The main assumption underlying these models is that local independence holds with respect to the latent ability being modeled (Lord and Novick 1968).
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References
Ackerman, T. A. (1989). Unidimensional IRT calibration of compensatory and noncompensatory multidimensional items. Applied Psychological Measurement, 13, 113–127.
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.
Ackerman, T. A., Gierl, M. J., & Walker, C. M. (2003). Using multidimensional item response theory to evaluate educational and psychological tests. Educational Measurement: Issues and Practice, 22(3), 37–51.
Bock, R. D., Gibbons, R., & Muraki, E. (1988). Full-Information item factor analysis. Applied Psychological Measurement, 12, 261–280.
Browne, M. W., & Cudeck, R. (1993). Alternative ways of assessing model fit. In K. A. Bollen & J. S. Long (Eds.), Testing structural equation models (pp. 136–162). Newbury Park, CA: Sage.
Christoffersson, A. (1975). Factor analysis of dichotomized variables. Psychometrika, 40, 5–32.
Cudeck, R. (2000). Exploratory factor analysis. In H. E. A. Tinsley & S. D. Brown (Eds.), Handbook of applied multivariate statistics and mathematical modeling (pp. 265–296). San Diego, CA: Academic.
Fraser, C., & McDonald, R. P. (1988). NOHARM: Least squares item factor analysis. Multivariate Behavioral Research, 23, 267–269.
Han, K. T. (2006). WinGen: Windows software that generates IRT parameters and item responses. Applied Psychological Measurement, 31, 457–459.
Hattie, J. (1984). An empirical study of various indices for determining unidimensionality. Multivariate Behavioral Research, 19, 49–78.
Hu, L.-T., & Bentler, P. M. (1999). Cutoff criteria for fit indexes in covariance structure analysis: Conventional criteria versus new alternatives. Structural Equation Modeling, 6, 1–55.
Hulin, C. L., Drasgow, F., & Parsons, L. K. (1983). Item response theory. Homewood, IL: Dow-Jones-Irwin.
Kaiser, H. F. (1960). The application of electronic computers to factor analysis. Educational and Psychological Measurement, 20, 141–151.
Kim, H. R. (1994). New techniques for the dimensionality assessment of standardized test data (Unpublished doctoral dissertation). University of Illinois, Urbana–Champaign.
Knol, D. L., & Berger, M. P. F. (1991). Empirical comparison between factor analysis and multidimensional item response models. Multivariate Behavioral Research, 26, 457–477.
Lord, F. M. (1980). Application of item response theory to practical testing problems. Hillsdale, NJ: Lawrence Erlbaum.
Lord, F. M., & Novick, M. R. (1968). Statistical theories of mentaltest scores. Reading, MA: Addison-Wesley.
McDonald, R. P. (1981). The dimensionality of tests and items. British Journal of Mathematical and Statistical Psychology, 34, 100–117.
McDonald, R. P. (1982). Linear versus nonlinear models in item response theory. Applied Psychological Measurement, 6, 379–396.
McLeod, L. D., Swygert, K. A., & Thissen, D. (2001). Factor analysis for items scored in two categories. In D. Thissen & H. Wainer (Eds.), Test scoring (pp. 189–216). Mahwah, NJ: Erlbaum.
Mislevy, R. J., & Bock, R. D. (1990). BILOG-MG 3: Item analysis and test scoring with binary logistic models [Computer software]. Chicago, IL: Scientific Software International.
Mulaik, S. A. (2009). The foundations of factor analysis. New York: CRC.
Muthén, B. (1977). Statistical methodology for structural equation models involving latent variables with dichotomous indicators (Unpublished doctoral dissertation). Department of Statistics, University of Uppsala, Uppsala.
Muthén, B. (1978). Contributions to factor analysis of dichotomous variables. Psychometrika, 43, 551–560.
Muthén, L. K., & Muthén, B. O. (2010). Mplus user’s guide. Los Angeles, CA: Author.
Nandakumar, R. (1994). Assessing the dimensionality of a set of item responses: Comparison of different approaches. Journal of Educational Measurement, 31, 17–35.
Nandakumar, R., & Stout, W. (1993). Refinements of Stout’s procedure for assessing latent trait unidimensionality. Journal of Educational Statistics, 18, 41–68.
Nandakumar, R., & Yu, F. (1996). Empirical validation of DIMTEST on nonnormal ability distributions. Journal of Educational Measurement, 33, 355–368.
Parry, C. D., & McArdle, J. J. (1991). An applied comparison of methods for least-squares factor analysis of dichotomous variables. Applied Psychological Measurement, 15, 35–46.
Reckase, M. D. (1979). Unifactor latent trait models applied to multifactor tests: Results and implications. Journal of Educational Statistics, 4, 207–230.
Stone, C. A., & Yeh, C.-C. (2006). Assessing the dimensionality and factor structure of multiple-choice exams: An empirical comparison of methods using the multistate bar examination. Educational and Psychological Measurement, 66, 193–214.
Stout, W. (1987). A nonparametric approach for assessing latent trait unidimensionality. Psychometrika, 52, 589–617.
Stout, W. (1990). A new item response theory modeling approach with applications to unidimensionality assessment and ability estimation. Psychometrika, 55, 293–325.
Tate, R. (2003). A comparison of selected empirical methods for assessing the structure of responses to test items. Applied Psychological Measurement, 27, 159–203.
Thissen, D., & Wainer, H. (2001). Test scoring. Mahwah, NJ: Lawrence Erlbaum Associates.
Wilson, D. T., Wood, R., & Gibbons, R. (2003). TESTFACT: Test scoring, item statistics, and item factor analysis [Computer program]. Chicago, IL: Scientific Software International.
Yeh, C.-C. (2007). The effect of guessing on assessing dimensionality in multiple-choice tests: A Monte Carlo study with application. Unpublished dissertation. University of Pittsburg.
Zhang, J., & Stout, W. (1999a). Conditional covariance structure of generalized compensatory multidimensional items. Psychometrika, 64, 129–152.
Zhang, J., & Stout, W. (1999b). The theoretical DETECT index of dimensionality and its application to approximate simple structure. Psychometrika, 64, 213–249.
Zimowski, M. F., Muraki, E., Mislevy, R. J., & Bock, R. D. (2002). BILOG-MG for windows [Computer software]. Lincolnwood, IL: Scientific Software International.
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Sen, S., Cohen, A.S., Kim, SH. (2013). A Comparison of Algorithms for Dimensionality Analysis. In: Millsap, R.E., van der Ark, L.A., Bolt, D.M., Woods, C.M. (eds) New Developments in Quantitative Psychology. Springer Proceedings in Mathematics & Statistics, vol 66. Springer, New York, NY. https://doi.org/10.1007/978-1-4614-9348-8_14
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DOI: https://doi.org/10.1007/978-1-4614-9348-8_14
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