Computing confidence intervals of item fit statistics in the family of rasch models using the bootstrap method

Journal of Applied Measurement

Volumn 8, Issue 2, 2007, Pages 190-203

  Su, Ya Hui ^a   Sheu, Ching Fan ^b   Wang, Wen Chung ^a  

^a NATIONAL CHUNG CHENG UNIVERSITY   (Taiwan)

^b NATIONAL CHENG KUNG UNIVERSITY   (Taiwan)

Author keywords

[No Author keywords available]

Indexed keywords

ARTICLE; CONFIDENCE INTERVAL; HUMAN; STATISTICAL MODEL;

CONFIDENCE INTERVALS; HUMANS; MODELS, STATISTICAL;

EID: 34547462195     PISSN: 15297713     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article

References (49)

1. Adams, R. J., Wilson, M. R., and Wang, W.-C. (1997). The multidimensional random coefficients multinomial logit model. Applied Psychological Measurement, 21, 1-23.
2. Algina, J., Keselman, H. J., and Penfield, R. D. (2005). Effect sizes and their intervals: The two-level repeated measures case. Educational and Psychological Measurement, 65, 241-258.
3. Andrich, D. (1978a). A rating formulation for ordered response categories. Psychometrika, 43, 561-573.
4. Andrich, D. ( 1978b). Application of a psychometric model to ordered response categories which are scored with successive integers. Applied Psychological Measurement, 2, 581-594.
5. Baker, F. B. (1992). Item response theory: Parameter estimation techniques. New York: Marcel Dekker.
6. Birnbaum, A. (1968). Some latent trait models and their use in inferring an examinee's ability. In F. M. Lord and M. R. Novick (Eds.), Statistical theories of mental test scores (pp. 397-479). Reading, MA: Addison-Wesley.
7. Bond, T. G., and Fox, C. M. (2001). Applying the Rasch model: Fundamental measurement in the human sciences. Mahwah, NJ: Lawrence Erlbaum.
8. Brunner, M., and Süß, H. (2005). Analyzing the reliability of multidimensional measures: An example from intelligence research. Educational and Psychological Measurement, 65, 27-240.
9. Chan, W., and Chan, D. W. L. (2004). Bootstrap standard error and confidence intervals for the correlation corrected for range restriction: A simulation study. Psychological Methods, 9, 369-385.
10. Davison, A. C., and Hinkley, D. V. (1997). Boot-strap methods and their application. Cambridge, UK: Cambridge University Press.
11. Di-Nocera, F., and Ferlazzo, F. (2000). Resampling approach to statistical inference: Boot-strapping from event-related potentials data. Behavior Research Methods, Instruments and Computers, 32, 111-119.
12. Efron, B. (1979). Bootstrap methods: Another look at the jackknife. Annals of Statistics, 7, 1-26.
13. Efron, B. (1981). Nonparametric estimates of standard error: The jackknife, the bootstrap and other methods. Biometrika, 68, 589-599.
14. Efron, B., and Tibshirani, R. J. (1993). An introduction to the bootstrap. New York: Chapman and Hall.
15. Embretson, S. E., and Riese, S. P. (2000). Item response theory for psychologists. Mahwah, NJ: Lawrence Erlbaum.
16. Fischer, G. H., and Molenaar, I. W. (Eds.) (1995). Rasch models: Foundations, recent developments, and application. New York: Springer-Verlag.
17. Hambleton, R. K., and Swaminathan, H. (1985). Item response theory: Principles and applications. Boston: Kluwer.
18. Holland, P. W., and Wainer, H. (Eds.) (1993). Differential item functioning. Hillsdale, NJ: Erlbaum.
19. Hoskens, M, and De Boeck, P. (1997). A parametric model for local dependence among test items. Psychological Methods, 2, 261-277.
20. Ji, J., Porjesz, B., Chorlian, D., and Begleiter, H. (1998). Event-related potentials during digit recognition tasks. Cognitive Brain Research, 7, 179-190.
21. Linacre, J. M. (1996). FACETS: A computer program for analysis of examinations with multiple facets [Computer program]. Chicago: MESA Press.
22. Linacre, J. M. (2001). WINSTEPS: Rasch measurement computer program, Version 3.31 [Computer program]. Chicago: Winsteps. com.
23. Linacre, L. M. (2003). What do infit and outfit, mean-square and standardized mean? Rasch Measurement Transactions, 16(2), 878. Retrieved September 28, 2005, from http://209.238.26.90/rmt/rmt162f.htm
24. Loehlin, J. C., and Gough, H. G. (1990). Genetic and environmental variation on the California psychological inventory vector scales. Journal of Personality Assessment, 54, 463-468.
25. Lord, F. M. (1980). Applications of item response theory to practical testing problems. Hillsdale, NJ: Lawrence Erlbaum.
26. Masters, G. N. ( 1982). A Rasch model for partial credit scoring. Psychometrika, 47, 149-174.
27. Meehl, P. E. (1997). Theory testing in psychology and physics: A methodological paradox. Philosophy of Science, 34, 103-115.
28. Muraki, E. (1992). A generalized partial credit model: Application of an EM algorithm. Applied Psychological Measurement, 16, 159-176.
29. Nickerson, R. S. (2000). Null hypothesis significance testing: A review of an old but continuing controversy. Psychological Methods, 5, 241-301.
30. Rasch, G. (1960). Probabilistic models for some intelligence and attainment tests. Copenhagen, Denmark: Danish Institute for Educational Research. (Expanded edition, 1980. Chicago: University of Chicago Press.)
31. Rost, J., and Carstensen, C. H. (2002). Multidimensional Rasch measurement via item component models and faceted designs. Applied Psychological Measurement, 26, 42-56.
32. Schmidt, F. L. (1996). Statistical significance testing and cumulative knowledge in psychology: Implications for the training of researchers. Psychological Methods, 1, 115-129.
33. Smith, E. V., Jr., and Smith, R. M. (Eds.) (2004). Introduction to Rasch measurement. Maple Grove, MN: JAM Press.
34. Switzer, F. S., Paese, P. W., and Drasgow, F. (1992). Bootstrap estimates of standard errors in validity generalization. Journal of Applied Psychology, 77, 123-129.
35. Thompson, B. (1996). AERA editorial policies regarding statistical significance testing: Three suggested reforms. Educational Researchers, 25, 26-30.
36. Tonidandel, S., and Overall, J. E. (2004). Determining the number of clusters by sampling with replacement. Psychological Methods, 9, 238-249.
37. Tuerlinckx F., and De Boeck, P. (2001). The effect of ignoring item interactions on the estimated discrimination parameters in item response theory. Psychological Methods, 6, 181-195.
38. van der Linden, W. J., and Hambleton, R. K. (Eds.) (1997). Handbook of modern item response theory. New York: Springer.
39. Wagenmakers, E. J., Ratcliff, R., Gomez, P., and Iverson, G. J. (2004). Assessing model mimicry using the parametric bootstrap. Journal of Mathematical Psychology, 48, 28-50.
40. Wang, W.-C., and Chen, C.-T. (2005). Item parameter recovery, standard error estimate and fit statistics of the WINSTEPS program for the family of Rasch models. Educational and Psychological Measurement, 65, 376-404.
41. Wang, W.-C., and Wilson, M. R. (2005). The Rasch testlet model. Applied Psychological Measurement, 29, 126-149.
42. Wang, W.-C., and Wu, C.-I. (2004). Gain score in item response theory as an effect size measure. Educational and Psychological Measurement, 64, 758-780.
43. Wang, X., Bradlow, E. T., and Wainer, H. (2002). A general Bayesian model for testlets: Theory and applications. Applied Psychological Measurement, 26, 109-128.
44. Wei, M., Mallinckrodt, B., Russell, D. W., and Abraham, W. (2004). Maladaptive perfectionism as a mediator and moderator between adult attachment and depressive mood. Journal of Counseling Psychology, 51, 201-212.
45. Wilson, E. B., and Hilferty, M. M. (1931). The distribution of chi-square. Proceedings of the National Academy of Sciences of the United States of America, 17, 684-688.
46. Wright, B. D., and Masters, G. N. (1982). Rating scale analysis. Chicago: MESA Press.
47. Wright, B. D., and Stone, M. H. (1979). Best test design. Chicago: MESA Press.
48. Wright, B. D., Linacre, J. M., Gustafson J.-E., and Martin-Löf, P (1994). Reasonable mean-square fit values. Rasch Measurement Transactions, 8(3), 370. Retrieved December 1, 2003, from http://www.rasch.org/rmt/rmt83b. htm
49. Wu, M. L., Adams, R. J., and Wilson, M. R. (1998). ConQuest [Computer software and manual]. Camberwell, VIC, Australia: Australian Council for Educational Research.