Direct estimation of correlation as a measure of association strength using multidimensional item response models

Educational and Psychological Measurement

Volumn 64, Issue 6, 2004, Pages 937-955

  Wang, Wen Chung ^a  

^a NATIONAL CHUNG CHENG UNIVERSITY   (Taiwan)

Author keywords

Bootstrap; Classical test theory; Item response theory; Measurement error; Rasch model

Indexed keywords

EID: 10044253349     PISSN: 00131644     EISSN: None     Source Type: Journal    
DOI: 10.1177/0013164404268671     Document Type: Article

References (63)

1. Adams, R. J., Wilson, M. R., & Wang, W.-C. (1997). The multidimensional random coefficients multinomial logit model. Applied Psychological Measurement, 21, 1-23.
2. American Psychological Association. (2001). Publication manual of the American Psychological Association (5th ed.). Washington, DC: Author.
3. Andrich, D. (1978). A rating formulation for ordered response categories. Psychometrika, 43, 561-573.
4. Baker, F. B. (1992). Item response theory: Parameter estimation techniques. New York: Dekker.
5. Baugh, F. (2002). Correcting effect sizes for score reliability: A reminder that measurement and substantive issues are linked inextricably. Educational and Psychological Measurement, 62, 254-263.
6. Béguin, A. A., & Glas, C. A. W. (2001). MCMC estimation and model-fit analysis of multidimensional IRT models. Psychometrika, 66, 541-562.
7. Bickel, P., & Freedman, D. (1981). Some asymptotic theory for the bootstrap. Annals of Statistics, 9, 1196-1217.
8. 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. 397-479). Reading, MA: Addison-Wesley.
9. Bock, R. D., & Aitkin, M. (1981). Marginal maximum likelihood estimation of item parameters: Application of the EM algorithm. Psychometrika, 46, 443-459.
10. Bock, R. D., Gibbons, R., & Muraki, E. J. (1988). Full information item factor analysis. Applied Psychological Measurement, 12, 261-280.
11. Bock, R. D., & Mislevy, R. J. (1982). Adaptive EAP estimation of ability in a microcomputer environment. Applied Psychological Measurement, 6, 431-444.
12. Bond, T. G., & Fox, C. M. (2001). Applying the Rasch model: Fundamental measurement in the human sciences. Mahwah, NJ: Lawrence Erlbaum.
13. Cohen, J. (1969). Statistical power analysis for the behavioral sciences. Hillsdale, NJ: Lawrence Erlbaum.
14. Davison, A. C., & Hinkley, D. V. (1997). Bootstrap methods and their application. Cambridge, UK Cambridge University Press.
15. De Boeck, P., & Wilson, M. R. (Eds.). (2004). Explanatory item response models: A generalized linear and nonlinear approach. New York: Springer-Verlag.
16. DeMars, C. (2001). Group difference based on IRT scores: Does the model matter? Educational and Psychological Measurement, 61, 60-70.
17. Dempster, A. P., Laird, N. M.,& Rubin, D. B. (1977). Maximum likelihood from incomplete data via the EM algorithm. Journal of the Royal Statistical Society, 39B, 1-38.
18. DiCicco, T. J., & Efron, B. (1996). Bootstrap confidence intervals. Statistical Science, 11, 189-228.
19. Efron, B. (1979). Bootstrap methods: Another look at the jackknife. The Annals of Statistics, 7, 1-26.
20. Efron, B., & Tibshirani, R. J. (1993). An introduction to the bootstrap. New York: Chapman & Hall.
21. Eliason, S. R. (1993). Maximum likelihood estimation: Logic and practice. Newbury Park, CA: Sage.
22. Embretson, S. E., & Reise, S. P. (2000). Item response theory for psychologists. Mahwah, NJ: Lawrence Erlbaum.
23. Fischer, G. H. (1973). The linear logistic test model as instrument in educational research. Acta Psychologica, 37, 359-374.
24. Fischer, G. H., & Molenaar, I. W. (Eds.). (1995). Rasch models: Foundations, recent developments, and applications. New York: Springer.
25. Fischer, G. H., & Pononcy, I. (1994). An extension of the partial credit model with an application to the measurement of change. Psychometrika, 59, 177-192.
26. Fisher, R. A. (1915). Frequency distribution of the values of the correlation coefficient in samples from an indefinitely large population. Biometrika, 10, 507-521.
27. Fisher, R. A. (1921). On the probable error of a coefficient of correlation deduced from a small sample. Metron, 1, 1-32.
28. Fraser, C. (1988). NOHARM: A Fortran program for fitting unidimensional and multidimensional normal ogive models of latent trait theory [Computer software]. Armidale, Australia: University of New England, Centre for Behavioral Studies.
29. Hambleton, R. K., & Swaminathan, H. (1985). Item response theory: Principles and applications. Boston: Kluwer-Nijhoff.
30. Hedges, L. V., & Olkin, L. (1985). Statistical methods for meta-analysis. Orlando, FL: Academic Press.
31. Henson, R. K. (2001). Understanding internal consistency reliability estimates: A conceptual primer on coefficient alpha. Measurement and Evaluation in Counseling and Development, 34, 177-189.
32. Hotelling, H. (1953). New light on the correlation coefficient and its transforms. Journal of the Royal Statistical Society, 15B, 193-232.
33. LePage, R., & Billiard, L. (1992). Exploring the limits of bootstrap. New York: John Wiley.
34. Linacre, J. M. (1989). Many-facet Rasch measurement. Chicago: Measurement, Evaluation, Statistics, and Assessment Press.
35. Lord, F. M. (1980). Applications of item response theory to practical testing problems. Hillsdale, NJ: Lawrence Erlbaum.
36. Lord, F. M., & Novick, M. R. (1968). Statistical theories of mental test scores. Reading MA: Addison-Wesley.
37. Masters, G. N. (1982). A Rasch model for partial credit scoring. Psychometrika, 47, 149-174.
38. Maxwell, S. E., & Delaney, H. D. (1990). Designing experiments and analyzing data: A model comparison perspective. Belmont, CA: Wadsworth.
39. McCullagh, P., & Nelder, J. A. (1989). Generalized linear models (2nd ed.). London: Chapman & Hall.
40. McCulloch, C. E., & Searle, S. R. (2001). Generalized, linear, and mixed models. New York: John Wiley.
41. McDonald, R. P. (1982). Linear versus nonlinear models in latent trait theory. Applied Psychological Measurement, 6, 379-396.
42. McKinley, R. L., & Reckase, M. D. (1983). MAXLOG: A computer program for the estimation of the parameters of a multidimensional logistic model. Behavior Research Methods and Instrumentation, 15, 389-390.
43. Muraki, E. (1993). POLYFACT [Computer software and manual]. Princeton, NJ: Education Testing Service.
44. Muraki, E., & Carlson, J. E. (1995). Full-information factor analysis for polytomous item responses. Applied Psychological Measurement, 19, 73-90.
45. Neider, J. A., & Wedderburn, R.W.M. (1972). Generalized linear models. Journal of the Royal Statistical Society, 135A, 370-384.
46. Pearson, F. (1896). Mathematical contributions to the theory of evolution, III. Regression heredity and panmixia. Philosophical Transactions of the Royal Society of London, 187A,253-318.
47. Rasch, G. (1960). Probabilistic models for some intelligence and attainment tests. Copenhagen, Denmark: Institute of Educational Research.
48. Reckase, M. D. (1985). The difficulty of test items that measure more than one dimension. Applied Psychological Measurement, 9, 401-412.
49. Rijmen, F., Tuerlinckx, F., De Boeck, P., & Kuppens, R (2003). A nonlinear mixed model framework for item response theory. Psychological Methods, 8, 185-205.
50. SAS Institute, Inc. (1999). The NLMIXED procedure [Computer software]. Cary, NC: Author.
51. Thompson, B., & Snyder, R. A. (1998). Statistical significance and reliability analyses in recent JCD research articles. Journal of Counseling and Development, 76, 431-436.
52. Thompson, B., & Vacha-Haase, T. (2000). Psychometrics is datametrics: The test is not reliable. Educational and Psychological Measurement, 60, 174-195.
53. Vacha-Haase, T., Ness, C., Nilsson, J., & Reetz, D. (1999). Practices regarding reporting of reliability coefficients: A review of three journals. Journal of Experimental Education. 67, 335-341.
54. van der Linden, W. J., & Hambleton, R. K. (Eds.). (1997). Handbook of modern item response theory. New York: Springer.
55. Volodin, N., & Adams, R. J. (1995, April). Identifying and estimating a D-dimensional Rasch model. Paper presented at the International Objective Measurement Workshop, University of California at Berkeley.
56. Wang, W.-C. (1999). Direct estimation of correlations among latent traits within IRT framework. Methods of Psychological Research Online, 4(2), 47-68.
57. Wang, W.-C., & Chen, H.-C. (2004). The standardized mean difference within the framework of item response theory. Educational and Psychological Measurement, 64, 201-223.
58. Wang, W.-C., & Wu, C.-I. (2004). Gain score in item response theory as an effect size measure. Educational and Psychological Measurement, 64, 758-780.
59. Wilson, D. T., Wood, R., & Gibbons, R. (1991). TESTFACT: Test scoring, item statistics, and item factor analysis [Computer software]. Mooresville, IN: Scientific Software.
60. Wilson, M. R. (1992). The partial order model: An extension of the partial credit model. Applied Psychological Measurement, 16, 309-325.
61. Wolfinger, R. D., & SAS Institute, Inc. (n.d.). Fitting nonlinear mixed models with the new NLMIXED procedure. Retrieved August 17, 2003. from http://support.sas.com/rnd/app/papers/nlmixedsugi.pdf
62. Wright, B. D., & Masters, G. N. (1982). Rating scale analysis. Chicago: Measurement, Evaluation, Statistics, and Assessment Press.
63. Wu, M. L., Adams, R. J., & Wilson, M. R. (1998). ACER ConQuest: Generalized item response modeling software [Computer software and manual]. Camberwell, Australia: Australian Council for Educational Research.