Ramsay-Curve Item Response Theory (RC-IRT) to detect and correct for nonnormal latent variables

Psychological Methods

Volumn 11, Issue 3, 2006, Pages 253-270

  Woods, Carol M ^a  

^a WASHINGTON UNIVERSITY   (United States)

Author keywords

Density estimation; Distributional assumptions; Item response theory (IRT); Latent distribution; Latent variables; Model selection; Nonnormality; Ramsay curve IRT (RC IRT)

Indexed keywords

AREA UNDER THE CURVE; ARTICLE; HUMAN; METHODOLOGY; PSYCHOLOGICAL MODEL; PSYCHOLOGICAL THEORY; PSYCHOLOGY; REACTION TIME; STATISTICAL DISTRIBUTION; STATISTICS;

AREA UNDER CURVE; HUMANS; MODELS, PSYCHOLOGICAL; PSYCHOLOGICAL THEORY; PSYCHOLOGY; REACTION TIME; STATISTICAL DISTRIBUTIONS;

EID: 33748787706     PISSN: 1082989X     EISSN: None     Source Type: Journal    
DOI: 10.1037/1082-989X.11.3.253     Document Type: Article

References (73)

1. Abdel-fattah, A. A. (1994, April). Comparing BILOG and LOGIST estimates for normal, truncated normal, and beta ability distributions. Paper presented at the annual meeting of the American Educational Research Association, New Orleans, LA.
2. Akaike, H. (1973). Information theory and an extension of the maximum likelihood principle. In B. N. Petrov & F. Csaki (Eds.), Second international symposium on information theory (pp. 267-281). Budapest, Hungary: Academiai Kiado.
3. Albert, J. H. (1992). Bayesian estimation of normal ogive item response curves using Gibbs sampling. Journal of Educational Statistics, 17, 251-269.
4. Andersen, E. B., & Madsen, M. (1977). Estimating the parameters of a latent population distribution. Psychometrika, 42, 357-374.
5. Birnbaum, A. (1968). Some latent trait models. In F. M. Lord & M. R. Novick (Eds.), Statistical theories of mental test scores (pp. 395-479). Reading, MA: Addison-Wesley.
6. Bock, R. D., & Aitkin, M. (1981). Marginal maximum likelihood estimation of item, parameters: Application of an EM algorithm. Psychometrika, 46, 443-459.
7. Bock, R. D., & Lieberman, M. (1970). Fitting a response model for n dichotomously scored items. Psychometrika, 35, 179-197.
8. Boulet, J. R. (1996). The effect of nonnormal ability distributions on IRT parameter estimation using full-information and limited-information methods (Doctoral dissertation, University of Ottawa, Ottawa, Ontario, Canada, 1996). Dissertation Abstracts International, 58, 1256.
9. Chambless, D. L., Caputo, G. C., Bright, P., & Gallagher, R. (1984). Assessment of fear of fear in agoraphobics: The Body Sensations Questionnaire and the Agoraphobic Cognitions Questionnaire. Journal of Consulting and Clinical Psychology, 52, 1090-1097.
10. Chernyshenko, O. S., Stark, S., Chan, K., Drasgow, F., & Williams, B. (2001). Fitting item response theory models to two personality inventories: Issues and insights. Multivariate Behavioral Research, 36, 523-562.
11. Cronbach, L. J. (1951). Coefficient, alpha and the internal structure of tests. Psychometrika, 16, 297-334.
12. Curry, H. B., & Schoenberg, I. J. (1947). On spline distributions and their limits: The Polya distribution functions. Bulletin of the American Mathematical Society, 53, 1114.
13. Davidian, M., & Gallant, A. R. (1993). The nonlinear mixed effects model with a smooth random effects density. Biometrika, 80, 475-488.
14. Deacon, B. J., Abramowitz, J. S., Woods, C. M., & Tolin, D. F. (2003). The Anxiety Sensitivity Index-Revised: Psychometric properties and factor structure in two nonclinical samples. Behaviour Research and Therapy, 41, 1427-1449.
15. De Ayala, R. J. (1995, April). Item parameter recovery for the nominal response model. Paper presented at the annual meeting of the American Educational Research Association, San Francisco, CA.
16. de Boor, C. (2001). A practical guide to splines (Rev. ed.). New York: Springer-Verlag.
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, Series B (Statistical Methodology), 39, 1-38.
18. Embretson, S. E., & Reise, S. P. (2000). Item response theory for psychologists. Mahwah. NJ: Erlbaum.
19. Engelen, R. J. H. (1989). Parameter estimation in the logistic item response model. Unpublished doctoral dissertation, Universiteit Twente, Enschede, the Netherlands.
20. Follman, D. (1988). Consistent estimation in the Rasch model based on nonparametric margins. Psychometrika, 53, 553-562.
21. Gray-Little, B., Williams, V. S. L., & Hancock, T. D. (1997). An item response theory analysis of the Rosenberg Self-Esteem Scale. Personality and Social Psychology Bulletin, 23, 443-451.
22. Hannan, E. J. (1987). Rational transfer function approximation. Statistical Science, 2, 135-161.
23. Holland, P. W. (1990). On the sampling theory foundations of item response theory models. Psychometrika, 55, 577-601.
24. Jamshidian, M., & Jennrich, R. I. (2000). Standard errors for EM estimation. Journal of the Royal Statistical Society, Series B (Statistical Methodology), 62, 257-270.
25. Junker, B. W., & Sijtsma, K. (2001). Nonparametric item response theory in action: An overview of the special issue. Applied Psychological Measurement, 25, 211-220.
26. Kirisci, L., & Hsu, T. C. (April, 1995). The robustness of BILOG to violations of the assumptions of unidimensionality of test items and normality of ability distribution. Paper presented at the annual meeting of the National Council on Measurement in Education, San Francisco, CA.
27. Knuth, D. E. (1981). The art of computer programming, Vol. 2: Seminumerical algorithms. Reading, MA: Addison-Wesley.
28. Kolmogorov, A. (1933). Sulla determinazione empirica di una legge di distributione. Giornale dell'Istituto Italiano degli Attuari, 4, 1-11.
29. Lord, F. N., & Novick, M. R. (Eds.). (1968). Statistical theories of mental test scores. Reading, MA: Addison-Wesley.
30. Louis, T. A. (1982). Finding the observed information matrix when using the EM algorithm. Journal of the Royal Statistical Society, Series B (Statistical Methodology), 44, 226-233.
31. Marsaglia, G., & Zaman, A. (1991). A new class of random number generators. Annals of Applied Probability, 1, 462-480.
32. Massey, F. J. (1951). The Kolmogorov-Smirnov test for goodness of fit. Journal of the American Statistical Association. 46, 68-78.
33. 2(dif) to assess relative model fit in categorical data analysis. Multivariate Behavioral Research, 41, 55-64.
34. Meijer, R. R., & Baneke, J. J. (2004). Analyzing psychopathology items: A case for nonparametric item response theory modeling. Psychological Methods, 9, 354-368.
35. Mislevy, R. (1984). Estimating latent distributions. Psychometrika, 49, 359-381.
36. Mislevy, R. J., & Bock, R. D. (1990). BILOG-3: Item analysis and test scoring with binary logistic models [Computer software]. Chicago: Scientific Software International.
37. Mokken, R. J. (1997). Nonparametric models for dichotomous responses. In W. J. van der Linden & R. K. Hambleton (Eds.), Handbook of modern item response theory (pp. 351-367). New York: Springer-Verlag.
38. Muraki, E., & Bock, R. D. (1997). PARSCALE-3: IRT based test scoring and item analysis for graded items and rating scales [Computer software]. Chicago: Scientific Software International.
39. Orlando, M., Sherboume, C. D., & Thissen, D. (2000). Summedscore linking using item response theory: Application to depression measurement. Psychological Assessment, 12, 354-359.
40. Patz, R. J., & Junker, B. W. (1999). A straightforward approach to Markov chain Monte Carlo methods for item, response models. Journal of Educational and Behavioral Statistics, 24, 146-178.
41. Ramsay, J. O. (1991). Kernel smoothing approaches to nonparametric item characteristic curve estimation. Psychometrika, 56, 611-630.
42. Ramsay, J. O. (1997). A functional approach to modeling test data. In W. J. van der Linden & R. K. Hambleton (Eds.), Handbook of modern item response theory (pp. 381-394). New York: Springer-Verlag.
43. Ramsay, J. O. (2000a). Differential equation models for statistical functions. Canadian Journal of Statistics, 28, 225-240.
44. Ramsay, J. O. (2000b). TESTGRAF98: A program for the graphical analysis of multiple choice test and questionnaire data [Computer program]. Retrieved from http://www.psych.mg.ill.ca/faculty/ramsay/ramsay.html
45. Reise, S. P., & Waller, N. G. (1990). Fitting the two-parameter model to personality data. Applied Psychological Measurement, 14, 45-58.
46. Reise, S. P., & Waller, N. G. (2003). How many IRT parameters does it take to model psychopathology items? Psychological Methods, 8, 164-184.
47. Roclebaugh, T., Woods, C. M., Thissen, D., Heimberg, R. G., Chambless, D. L., & Rapee, R. M. (2004). More information from fewer questions: The factor structure and item properties of the original and Brief Fear of Negative Evaluation scale. Psychological Assessment, 16, 169-181.
48. Rossi, N., Wang, X., & Ramsay, J. O. (2002). Nonparametric item response function estimates with the EM algorithm. Journal of Educational and Behavioral Statistics, 27, 291-317.
49. Samejima, F. (1969). Estimation of latent, ability using a response pattern of graded scores. Psychometrika Monograph (Serial No. 17).
50. Samejima, F. (1997). Graded response model. In W. J. van der Linden & R. K. Hambleton (Eds.), Handbook of modern item response theory (pp. 85-100). New York: Springer-Verlag.
51. Samejima, F. (1998). Efficient nonparametric approaches for estimaling the operating characteristics of discrete item responses. Psychometrika, 63, 111-130.
52. Santor, D. A., & Ramsay, J. O. (1998). Progress in technology of measurement: Applications of item response models. Psychological Assessment, 10, 345-359.
53. Schwarz, G. (1978). Estimating the dimension of a model. Annals of Statistics, 6, 461-464.
54. Sijtsma, K., & Molenaar, I. W. (2002). Introduction to nonparametric item response theory. Thousand Oaks, CA: Sage.
55. Silverman, B. W. (1982). On the estimation of a probability density function by the maximum penalized likelihood method. Annals of Statistics, 10, 795-810.
56. Smirnov, N. (1939). Sur les écarts de la courbe de distribution empirique. Recueil Mathématique, 6, 3-26.
57. Smith, L. L., & Reise, S. P. (1998). Gender differences on negative affectivity: An IRT study of differential item functioning on the Multidimensional Personality Questionnaire Stress Reaction scale. Journal of Personality and Social Psychology, 75, 1350-1362.
58. Steinberg, L., & Thissen, D. (1996). Uses of item response theory and the testlet concept, in the measurement of psychopathology. Psychological Methods, 1, 81-97.
59. Stone, C. A. (1992). Recovery of marginal maximum likelihood estimates in the two-parameters logistic response model: An evaluation of MULTILOG. Applied Psychological Measurement, 16, 1-16.
60. Stout, W. F. (1987). A nonparametric approach for assessing latent trait unidimensionality. Psychometrika, 52, 589-617.
61. Stout, W. F. (1990). A new item response theory modeling approach with applications to unidimensionality assessment and ability estimation. Psychometrika, 55, 293-325.
62. Thissen, D. (1991). MULTILOG user's guide: Multiple categorical item analysis and test scoring using item response theory. [Computer software and manual]. Chicago: Scientific Software International.
63. Thissen, D., & Orlando, M. (2001). Item response theory for items scored in two categories. In D. Thissen & H. Wainer (Eds.), Test scoring (pp. 73-137). Mahwah, NJ: Erlbaum.
64. Thissen, D., & Wainer, H. (Eds). (2001). Test scoring. Mahwah, NJ: Erlbaum.
65. Thurstone, L. L. (1927). A law of comparative judgment. Psychological Review, 34, 278-286.
66. van den Oord, E. J. C. G. (2005). Estimating Johnson curve population distributions in MULTILOG. Applied Psychological Measurement, 29, 45-64.
67. Woods, C. M. (2004). Item response theory with estimation of the latent population distribution using spline-based densities. Unpublished doctoral, dissertation, University of North Carolina at Chapel Hill.
68. Woods, C. M., & Thissen, D. (2004a, June). Item response theory with estimation of the latent population distribution using spline-based densities. Paper presented at the Psychometric Society meeting, Pacific Grove, CA.
69. Woods, C. M., & Thissen, D. (2004b). RCLOG v. 1: Software for Item Response Theory Parameter Estimation with the Latent Population Distribution Represented Using Spline-Based Densities. (Tech. Rep. No. 1). Chapel Hill: University of North Carolina, L. L. Thurstone Psychometric Laboratory.
70. Woods, C. M., & Thissen, D. (2006). Item response theory with estimation of the latent population distribution using splinebased densities. Psychometrika, 71, 1-22.
71. Yamamoto, K., & Muraki, E. (1991, April). Non-linear transformation of IRT scale to account for the effect of non-normal ability distribution on the item parameter estimation. Paper presented at the annual meeting of the American Educational Research Association, Chicago, IL.
72. Zhang, D., & Davidian, M. (2001). Linear mixed models with flexible distributions of random effects for longitudinal data. Biometrics, 57, 795-802.
73. Zwinderman, A. H., & van den Wollenberg, A. L. (1990). Robustness of marginal maximum likelihood estimation in the Rasch model. Applied Psychological Measurement, 14, 73-81.