Checking dimensionality in item response models with principal component analysis on standardized residuals

Educational and Psychological Measurement

Volumn 70, Issue 5, 2010, Pages 717-731

  Chou, Yeh Tai ^a   Wang, Wen Chung ^b  

^a NATIONAL TAIWAN NORMAL UNIVERSITY   (Taiwan)

^b THE EDUCATION UNIVERSITY OF HONG KONG   (Hong Kong)

Author keywords

dimensionality; item response theory; multivariate independence; principal component analysis; Rasch model

Indexed keywords

EID: 77956980099     PISSN: 00131644     EISSN: 15523888     Source Type: Journal    
DOI: 10.1177/0013164410379322     Document Type: Article

References (37)

1. Ackerman, T.A. (1989). Unidimensional IRT calibration of compensatory and noncompensatory multidimensional items. Applied Psychological Measurement, 13, 113-127.
2. Andrich, D. (1978). A rating formulation for ordered response categories. Psychometrika, 43, 561-573.
3. Bartlett, M.S. (1950). Tests of significance in factor analysis. British Journal of Psychology, 3, 77-85.
4. Bartlett, M.S. (1954). A note on multiplying factors for various chi-squared approximations. Journal of the Royal Statistical Society, Series B, 16, 296-298.
5. Berger, M.P.F., & Knol, D.L. (1990). On the assessment of dimensionality in multidimensional item response theory models. Paper presented at the annual meeting of the American Educational Research Association, Boston, MA.
6. Birnbaum, A. (1968). Some latent trait models and their use in inferring an examinee's ability. In F. M. Lord & M. R. Novick (Eds.), Statistical theories of mental test scores (pp. 397-424). Reading, MA: Addison-Wesley.
7. Bock, R.D., Gibbons, R., & Muraki, E. (1988). Full-information item factor analysis. Applied Psychological Measurement, 12, 261-280.
8. Box, G.E.P. (1949). A general distribution theory for a class of likelihood criteria. Biometrika, 36, 317-346.
9. Brien, C.J., Venables, W.N., James, A.T., & Mayo, O. (1984). An analysis of correlation matrices: Equal correlations. Biometrika, 71, 545-554.
10. Cattell, R.B. (1966). The scree test for the number of factors. Multivariate Behavioral Research, 1, 245-276.
11. Divgi, D.R. (1980). Dimensionality of binary items: Use of a mixed model. Paper presented at the annual meeting of the National Council on Measurement in Education, Boston, MA.
12. Embretson, S.E., & Reise, S.P. (2000). Item response theory for psychologists. Mahwah, NJ: Lawrence Erlbaum.
13. Fouladi, R.T., & Steiger, J.H. (1993). Tests of multivariate independence: A critical analysis of "A Monte Carlo study of testing the significance of correlation matrices" by Silver and Dunlap. Educational and Psychological Measurement, 53, 927-932.
14. Gessaroli, M.E., & De Champlain, A.F. (1996). Using an approximate chi-square statistic to test the number of dimensions underlying the responses to a set of items. Journal of Educational Measurement, 33, 157-179.
15. Hambleton, R.K., & Swaminathan, H. (1985). Item response theory: Principles and applications. Boston, MA: Kluwer-Nijhoff.
16. Hattie, J. (1985). Methodology review: Assessing unidimensionality of tests and items. Applied Psychological Measurement, 9, 139-164.
17. Kaiser, H.F. (1960). The application of electronic computers to factor analysis. Educational and Psychological Measurement, 20, 141-151.
18. Karabatsos, G. (2000). A critique of Rasch residual fit statistics. Journal of Applied Measurement, 1, 152-176.
19. Linacre, J.M. (1998a). Detecting multidimensionality: Which residual data-type works best? Journal of Outcome Measurement, 2, 266-283.
20. Linacre, J.M. (1998b). Structure in Rasch residuals: Why principal components analysis? Rasch Measurement Transactions, 12, 636.
21. Linacre, J.M. (2003). WINSTEPS Rasch measurement computer program (Version 3.6). Chicago, IL: Winsteps.com.
22. Lord, F.M. (1980). Applications of item response theory to practical testing problems. Hillside, NJ: Lawrence Erlbaum.
23. Masters, G.N. (1982). A Rasch model for partial credit scoring. Psychometrika, 47, 149-174.
24. McDonald, R.P. (1967). Nonlinear factor analysis. Psychometrika Monograph, 15.
25. McDonald, R.P. (1981). The dimensionality of test and items. British Journal of Mathematical and Statistical Psychology, 34, 100-117.
26. Muraki, E. (1992). A generalized partial credit model: Application of an EM algorithm. Applied Psychological Measurement, 16, 159-176.
27. Raîche, G. (2005). Critical eigenvalue sizes in standardized residual principal components analysis. Rasch Measurement Transactions, 19, 1012.
28. Rasch, G. (1960). Probabilistic models for some intelligence and attainment tests. Copenhagen, Denmark: Danmarks Paedogogische Institut.
29. Reckase, M.D. (1979). Unifactor latent trait models applied to multifactor tests: Results and implications. Journal of Educational and Behavioral Statistics, 4, 207-230.
30. Samejima, F. (1969). Estimation of latent ability using a response pattern of graded scores. Psychometrika Monograph Supplement, 17, 1-100.
31. Smith, E.V., Jr. (2002). Detecting and evaluating the impact of multidimensionality using item fit statistics and principal component analysis of residuals. Journal of Applied Measurement, 3, 205-231.
32. Smith, R.M. (1996). A comparison of methods for determining dimensionality in Rasch measurement. Structural Equation Modeling, 3, 25-40.
33. Smith, R.M., & Miao, C.Y. (1994). Assessing unidimensionality for Rasch measurement. In M. Wilson (Ed.), Objective measurement: Theory into practice (Vol. 2, pp. 316-327). Norwood, NJ: Albex.
34. Steiger, J.H. (1980a). Testing pattern hypotheses on correlation matrices: Alternative statistics and some empirical results. Multivariate Behavioral Research, 15, 335-352.
35. Steiger, J.H. (1980b). Tests for comparing elements of a correlation matrix. Psychological Bulletin, 87, 245-251.
36. Wright, B.D. (1996). Local dependency, correlations and principal components. Rasch Measurement Transactions, 10, 509-511.
37. 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.