A bootstrap generalization of modified parallel analysis for IRT dimensionality assessment

Applied Measurement in Education

Volumn 21, Issue 2, 2008, Pages 119-140

  Finch, Holmes ^a   Monahan, Patrick ^b  

^a BALL STATE UNIVERSITY   (United States)

^b INDIANA UNIVERSITY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 41849085226     PISSN: 08957347     EISSN: None     Source Type: Journal    
DOI: 10.1080/08957340801926102     Document Type: Article

References (49)

1. Ackerman, T. A. (1994). Using multidimensional item response theory to understand what items and tests are measuring. Applied Measurement in Education, 7(4), 255-278.
2. Ansley, R. A., & Forsyth, T. N. (1985). An examination of the characteristics of unidimensional IRT parameter estimates derived from two-dimensional data. Applied Psychological Measurement, 9, 37-48.
3. Berger, M. P. F., & Knol, D. L. (1990). On the assessment of dimensionality in multidimensional item response theory models. Paper presented at the meeting of the American Educational Research Association, Boston.
4. Bock, R. D., & Aitkin, M. (1981). Marginal maximum likelihood estimation of item parameters: Application of an EM algorithm. Psychometrika, 46(4), 443-459.
5. Bock, R. D., Gibbons, R. D., & Muraki, E. (1988). Full-Information item factor analysis. Applied Psychological Measurement, 12(3), 261-280.
6. Bock, R. D., Gibbons, R., Schilling, S. G., Muraki, E., Wilson, D. T., & Wood, R. (2003). Testfact version 4. Scientific Software.
7. Budescu, D. V., Cohen, Y., & Ben-Simon. A. (1997). A revised modified parallel analysis for the construction of unidimensional item pools. Applied Psychological Measurement, 21(3), 233-252.
8. Buja, A., & Eyuboglu, N. (1992). Remarks on parallel analysis. Multivariate Behavioral Research, 27(4), 509-540.
9. Chen, T. H., & Davison, M. L. (1996). A multidimensional scaling, paired comparisons approach to assessing unidimensionality in the Rasch Mode. In G. Englehard & M. Wilson (Eds.), Objective measurement theory into practice (Vol 3). Norwood, NJ: ABLEX.
10. Chernyshenko, O. S., Stark, S., & Chan, K. Y. (2001). Investigating the hierarchical factor structure of the fifth edition of the 16PF: An application of the Schmid-Leiman orthogonalization procedure. Educational and Psychological Measurement, 61(2), 290-302.
11. Cota, A. A., Longman, R. S., Holden. R. R., & Fekken, G. C. (1993). Comparing different methods for implementing parallel analysis: A practical index of accuracy. Educational and Psychological Measurement, 53, 865-876.
12. De Ayala, R. J., & Hertzog, M. A. (1991). The assessment of unidimensionality for use in item response theory. Multivariate Behavioral Research, 26, 765-792.
13. De Champlain, A., & Gessaroli, M. E. (1998). Assessing the dimensionality of item response matrices with small samples sizes and short test lengths. Applied Measurement in Education, 11(3), 231-253.
14. 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.
15. Finch, W. H., & Habing, B. (2005). Comparison of NOHARM and DETECT in item cluster recovery: Counting dimensions and allocating items. Journal of Educational Measurement, 42(2), 149-169.
16. Finch, W. H., Habing. B., & Huynh, H. (2003). Performance of DIMTEST and NOHARM Based Statistics for Testing Unidimensionality. Paper presented at the annual meeting of the National Council on Measurement in Education, Chicago, IL.
17. Froelich, A. G., & Habing. B. (2003). Conditional covariance based subtest selection for DIMTEST. Paper presented at the annual meeting of the National Council on Measurement in Education, Seattle, WA, April 10-14, 2001.
18. Froelich, A. G., & Stout, W. (2003). A new bias correction method for the DIMTEST procedure. Unpublished manuscript submitted for publication, based on Froelich's unpublished doctoral dissertation and Stout, Froelich, & Gao, 2001.
19. 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.
20. Gessaroli, M. E., De Champlain, A. F., & Folske, J. C. (1997). Assessing dimensionality using a likelihood-ratio chi-square test based on a non-linear factor analysis of item response data. Paper presented at the annual meeting of the National Council on Measurement in Education. Chicago, IL.
21. Haberman, S. J. (1977), Log-linear models and frequency tables with small expected cell counts. Annals of Statistics, 5, 1148-1169.
22. Hambleton, R. K., Swaminathan, H., & Rogers, H. J. (1991). Fundamentals of item response theory. Newbury Park. CA: Sage Publications.
23. Harshman, R. A. & Reddon, J. R. (1983). Determining the number of factors by comparing real with random data: A serious flaw and some possible corrections. Paper presented at the annual meeting of the Classification Society of North America, Philadelphia, PA.
24. Hattie, J., Krakowski, K., Rogers, J., & Swaminathan, H. (1996). An assessment of Stout's index of essential unidimensionality. Applied Psychological Measurement, 20, 1-14.
25. Horn, J. L. (1965). A rationale and test for the number of factors in factor analysis. Psychometrika, 30, 179-185.
26. Humphreys, L. G., & Ilgen, D. R. (1969). Note on a criterion for the number of common factors. Educational and Psychological Measurement, 29, 571-578.
27. Humphreys, L. G., & Montanelli. R. G., Jr. (1975). An investigation of the parallel analysis criterion for determining the number of common factors. Multivariate Behavioral Research, 10, 1-11.
28. Kim, H. R. (1994). New techniques for the dimensionality assessment of standardized test data. Unpublished doctoral dissertation, University of Illinois at Urbana-Champaign.
29. Longman, R. S., Cota, A. A., Holden, R. R., & Fekken, G. C. (1989). Multivariate Behavioral Research, 24(1), 59-69.
30. McDonald, R. P. (1967). Nonlinear factor analysis. Psychometric Monographs, No. 15.
31. Meara, K., Robin, F., & Sireci, S. G. (2000). Using multidimensional scaling to assess the dimensionality of dichotoinous item data. Multivariate Behavioral Research, 35, 229-259.
32. Mislevy, R. J. (1986). Recent developments in the factor analysis of categorical variables. Journal of Educational Statistics, 11, 3-31.
33. Monahan, P. O., Stump, T. E., Finch, H., & Hambleton, R. K. (2005). Bias of exploratory and crossvalidated DETECT index under null hypothesis of unidimensionality. Paper presented at the annual meeting of the National Council on Measurement in Education. Montreal, April.
34. Montanelli, R. G., & Humphreys, L. G. (1976). Latent roots of random data correlation matrices with squared multiple correlations on the diagonal: A Monte Carlo study. Psychometrika, 22, 341-348.
35. Nandakumar, R., & Stout, W. (1993). Refinements of Stout's procedure for assessing latent trait unidimensionality. Journal of Educational and Behavioral Statistics, 18, 41-68.
36. Pyo, K. H. (2000). Assessing dimensionality of a set of language test data. Paper presented at the annual meetings of the American Educational Research Association. New Orleans, LA.
37. Reckase, M. D. (1985). The difficulty of test items that measure more than one ability. Applied Psychological Measurement. 9, 401-412.
38. Roberts, J. S., & Samuel sen, K. (2002). Analyzing the structure of binary test responses using an optimal scaling approach. Paper presented at the annual meeting of the National Council on Measurement in Education, New Orleans, LA.
39. Roussos, L. A., Stout, W. F., & Marden, J. I. (1998). Using new proximity measures with hierarchical cluster analysis to detect multidimensionality. Journal of Educational Measurement, 35, 1-30.
40. Schatschneider, C., Francis, D. J., Foorman, B. R., Fletcher, J. M., & Mehta, P. (1999). The dimensionality of phonological awareness: An application of item response theory. Journal of Educational Psychology. 91(3), 439-449.
41. Shao, J., & Tu, D. (1995). The jackknife and bootstrap. New York: Springer.
42. Stout, W. F. (1987). A nonparametric approach for assessing latent trait dimensionality. Psychometrika, 52, 589-617.
43. Stout, W. F., Froelich, A. G., & Gao, F. (2001). Using resampling to produce an improved DIMTEST procedure. In A. Booinsma, M. A. J. van Duijn, & T. A. B. Snijders (Eds.), Essays on item response theory (pp. 357-375).
44. Stout, W. F., Habing, B., Douglas, J., Kim, H. R., Roussos, L., & Zhang, J. (1996). Conditional covariance-based nonparametric multidimensionality assessment. Applied Psychological Measurement, 19, 331-354.
45. Tate, R. (2003). A comparison of selected empirical methods for assessing the structure of responses to test items. Applied Psychological Measurement, 27(3), 159-203.
46. Wood, R., Wilson, D., Gibbons, R., Schilling, S., Muraki, E., & Bock, D. (2002). TESTFACT. Lincolnwood, IL: Scientific Software International.
47. Zhang, J., & Stout, W. F. (1999a). Conditional covariance structure of generalized compensatory multidimensional items. Psychometrika, 64, 129-152.
48. Zhang, J., & Stout, W. F. (1999b). The theoretical DETECT index of dimensionality and its application to approximate simple structure. Psychometrika, 64, 213-249.
49. Zimowski, M., Muraki, E., Mislevy, R., & Bock, D. (2002). BILOG-MG. Lincolnwood, IL: Scientific Software International.