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Abstract
According to the weak local independence approach to defining dimensionality, the fundamental quantities for determining a test's dimensional structure are the co variances of item-pair responses conditioned on exam inee trait level. This paper describes three dimensionality assessment procedures-HCA/CCPROX, DIMTEST, and DETECT—that use estimates of these con ditional covariances. All three procedures are nonpara metric ; that is, they do not depend on the functional form of the item response functions. These procedures are applied to a dimensionality study of the LSAT, which illustrates the capacity of the approaches to assess the lack of unidimensionality, identify groups of items manifesting approximate simple structure, determine the number of dominant dimensions, and measure the amount of multidimensionality.
|
Ackerman, T. (1994, April). Graphical representation of multidimensional IRT analysis. Paper presented at the annual meeting of the American Educational Research Association, New Orleans LA. Google Scholar | |
|
Ackerman, T. (1996). Graphical representation of multidimensional item response theory. Applied Psychological Measurement, 20, 311-329. Google Scholar | SAGE Journals | ISI | |
|
Bock, R.D. , Gibbons, R. , & Muraki, E. (1988). Full-information item factor analysis. Applied Psychological Measurement, 12, 261-270. Google Scholar | SAGE Journals | ISI | |
|
Camilli, G. , Wang, M.M. , & Fesq, J. (1995). The effects of dimensionality on equating the Law School Admission Test. Journal of Educational Measurement , 32, 79-96. Google Scholar | Crossref | ISI | |
|
DeChamplain, A. (1994, January). Assessing the dimensionality of the LSAT at the section level. Paper presented at the University of Illinois, Department of Statistics, Champaign. Google Scholar | |
|
DeChamplain, A. (1995a, April). An overview of nonlinear factor analysis and its relationship to item response theory. Paper presented at the annual meeting of the American Educational Research Association, San Francisco. Google Scholar | |
|
DeChamplain, A. (1995b). Assessing the effect of multidimensionality on LSAT equating for subgroups of test takers (Law School Admission Council Statistical Report 95-01. New Town PA: Law School Admission Council. Google Scholar | |
|
Douglas, J. , Kim, H.R. , Roussos, L. , Stout, W.F. , & Zhang, J. (1997). LSAT dimensionality analysis for the December 1991, June 1992, and October 1992 administrations (Law School Admission Council Research Report. New Town PA: Law School Admission Council. Google Scholar | |
|
Fraser, C. (1988). NOHARM: A computer program for fitting both unidimensional and multidimensional normal ogive models of latent trait theory New South Wales, Australia: Center for Behavioral Studies, The University of New England. Google Scholar | |
|
Gao, F. , & Stout, W. (1996). Using resampling to eliminate estimation bias . Submitted for publication. Google Scholar | |
|
Hattie, J. , Krakowski, K. , Rogers, H.J. , & Swaminathan, H. (1996). An assessment of Stout's index of essential unidimensionality. Applied Psychological Measurement, 20, 1-14. Google Scholar | SAGE Journals | ISI | |
|
Hulin, C.L. , Drasgow, F. , & Parsons, L.K. (1983). Item response theory. Homewood IL: Dow Jones-Irwin. Google Scholar | |
|
Jain, A. , & Dubes, R. (1988). Algorithms for clustering data. Englewood Cliffs NJ: Prentice Hall. Google Scholar | |
|
Junker, B.W. (1993). Progress in characterizing strictly unidimensional IRT representations. The Annals of Statistics, 21, 1359-1378. Google Scholar | |
|
Junker, B. , & Stout, W.F. (1994). Robustness of ability estimation when multiple traits are present with one trait dominant. In D. Laveault , B. Zumbo , M. Gessaroli , & M. Boss (Eds.), Modern theories of measurement: Problems and issues (pp. 31-61). Ottawa, Canada: Edumetrics Research Group, University of Ottawa. Google Scholar | |
|
Kim, H.R. (1994). New techniques for the dimensionality assessment of standardized test data. (Doctoral dissertation, University of Illinois at Urbana-Champaign). Dissertation Abstracts International, 55-12B, 5598. Google Scholar | |
|
Knol, D.L. , & Berger, P.F. (1991). Empirical comparison between factor analysis and multidimensional item response models. Multivariate Behavioral Research, 26, 457-477. Google Scholar | Crossref | Medline | ISI | |
|
Law School Admission Council. (1991). The Law School Admission Test: Sources, contents, uses. New Town PA: Author. Google Scholar | |
|
McDonald, R.P. (1981). The dimensionality of tests and items. British Journal of Mathematical and Statistical Psychology, 34, 100-117. Google Scholar | Crossref | ISI | |
|
McDonald, R.P. (1982). Linear versus nonlinear models in item response theory. Applied Psychological Measurement, 6, 379-396. Google Scholar | SAGE Journals | ISI | |
|
McDonald, R.P. (1994). Testing for approximate dimensionality. In D. Laveault , B. D. Zumbo , M. E. Gessaroli , & M. W. Boss (Eds.), Modern theories in measurement: Problems and issues (pp. 31-61). Ottawa , Canada: Edumetrics Research Group, University of Ottawa. Google Scholar | |
|
Mokken, R.J. ( 1971 ). A theory and procedure of scale analysis. New York/Berlin: De Gruyter . Google Scholar | Crossref | |
|
Nandakumar, R. (1991). Traditional dimensionality versus essential dimensionality . Journal of Educational Measurement, 28, 99-117. Google Scholar | Crossref | ISI | |
|
Nandakumar, R. , & Stout, W. (1993). Refinements of Stout's procedure for assessing latent trait unidimensionality. Journal of Educational and Behavioral Statistics, 18, 41-68. Google Scholar | SAGE Journals | |
|
Reese, L.M. (1995a). A comparison of local item dependence levels for the LSAT with two other tests. Unpublished manuscript. New Town PA: Law School Admission Council. Google Scholar | |
|
Reese, L.M. (1995b). The impact of local dependencies on some LSAT outcomes (Law School Admission Council Statistical Report 95-02. New Town PA: Law School Admission Council. Google Scholar | |
|
Roussos, L. (1995a). A new dimensionality estimation tool for multiple-item tests and a new DIF analysis paradigm based on multidimensionality and construct validity. (Doctoral dissertation, University of Illinois at Urbana-Champaign). Dissertation Abstracts International, 57-04B, 2956. Google Scholar | |
|
Roussos, L. (1995b). Hierarchical agglomerative clustering computer program user's manual. Urbana-Champaign : Statistical Laboratory for Educational and Psychological Measurement, Department of Statistics, University of Illinois. Google Scholar | |
|
Roussos, L. , & Stout, W.F. (1996, April). Simulation study of the effectiveness of using new proximity measures with hierarchical cluster analysis to detect simulated dimensionality structure. Paper presented at the annual meeting of the National Council on Measurement in Education , New York. Google Scholar | |
|
Stout, W.F. (1987). A nonparametric approach for assessing latent trait dimensionality. Psychometrika, 52, 589-617. Google Scholar | Crossref | ISI | |
|
Stout, W.F. (1990). A new item response theory modeling approach with applications to unidimensional assessment and ability estimation. Psychometrika, 55, 293-326. Google Scholar | Crossref | ISI | |
|
Wang, M. (1988). Measurement bias in the application of a unidimensional model to multidimensional item response data. Unpublished manuscript, Educational Testing Service, Princeton NJ. Google Scholar | |
|
Yen, W.M. (1984). Effects of local item dependence on the fit and equating performance of the three-parameter logistic model. Applied Psychological Measurement, 8, 125-145. Google Scholar | SAGE Journals | ISI | |
|
Zhang, J. (1996). Some fundamental issues in item response theory with applications. Unpublished doctoral dissertation, Department of Statistics, University of Illinois at Urbana-Champaign. Google Scholar | |
|
Zhang, J. , & Stout, W.F. (1996a, April). A new theoretical DETECT index of dimensionality and its estimation. Paper presented at the annual meeting of the National Council on Measurement in Education, New York. Google Scholar | |
|
Zhang, J. , & Stout, W.F. (1996b). Conditional covariance structure of generalized compensatory multidi Google Scholar | |
| mensional items with applications. Manuscript submitted for publication. Google Scholar |
