A Nonlinear Mixed Model Framework for Item Response Theory

Psychological Methods

Volumn 8, Issue 2, 2003, Pages 185-205

  Rijmen, Frank ^a   Tuerlinckx, Francis ^a   De Boeck, Paul ^a   Kuppens, Peter ^a  

^a UNIVERSITY OF LEUVEN   (Belgium)

Author keywords

[No Author keywords available]

Indexed keywords

ANGER; ARTICLE; BAYES THEOREM; COMPUTER PROGRAM; HUMAN; MATHEMATICS; NONLINEAR SYSTEM; PSYCHOMETRY; STATISTICAL ANALYSIS; STATISTICAL MODEL;

ANGER; BAYES THEOREM; DATA INTERPRETATION, STATISTICAL; HUMANS; LOGISTIC MODELS; MATHEMATICS; MODELS, STATISTICAL; NONLINEAR DYNAMICS; PSYCHOMETRICS; SOFTWARE;

EID: 0141640977     PISSN: 1082989X     EISSN: None     Source Type: Journal    
DOI: 10.1037/1082-989X.8.2.185     Document Type: Article

References (90)

1. Adams, R. J., Wilson, M., & Wang, W. C. (1997). The multidimensional random coefficients multinomial logit model. Applied Psychological Measurement, 21, 1-23.
2. Adams, R. J., Wilson, M., & Wu, M. L. (1997). Multilevel item response models: An approach to errors in variables regression. Journal of Educational and Behavioral Statistics, 22, 47-76.
3. Agresti, A. (1989). Tutorial on modeling ordered categorical response data. Psychological Bulletin, 89, 290-301.
4. Agresti, A. (2002). Categorical data analysis (2nd ed.). New York: Wiley.
5. Agresti, A., Booth, J. G., Hobert, J. P., & Caffo, B. (2000). Random-effects modeling of categorical response data. Sociological Methodology, 30, 27-80.
6. Andrich, D. (1978). A rating formulation for ordered response categories. Psychometrika, 43, 561-573.
7. 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.
8. Bock, R. D. (1972). Estimating item parameters and latent ability when responses are scored in two or more nominal categories. Psychometrika, 37, 29-51.
9. Bock, R. D., & Aitkin, M. (1981). Marginal maximum likelihood estimation of item parameters: An application of an EM-algorithm. Psychometrika, 46, 443-459.
10. Bock, R. D., Gibbons, R., & Muraki, E. (1988). Full-information item factor-analysis. Applied Psychological Measurement, 12, 261-280.
11. Bradlow, E. T., Wainer, H., & Wang, X. (1999). A Bayesian random effects model for testlets. Psychometrika, 64, 153-168.
12. Breslow, N. E., & Clayton, D. G. (1993). Approximate inference in generalized linear mixed models. Journal of the American Statistical Society, 88, 9-25.
13. Breslow, N. E., & Lin, X. (1995). Bias correction in generalised linear mixed models with a single component of dispersion. Biometrika, 82, 81-91.
14. Butter, R., De Boeck, P., & Verhelst, N. (1998). An item response model with internal restrictions on item difficulty. Psychometrika, 63, 47-63.
15. Clayton, D. (1996). Generalized linear mixed models. In W. R. Gilks, S. Richardson, & D. J. Spiegelhalter (Eds.), Markov chain Monte Carlo methods in practice (pp. 275-303). New York: Chapman & Hall.
16. Davidian, M., & Giltinan, D. M. (1995). Nonlinear models for repeated measurement data. London: Chapman & Hall.
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, 39, 1-38.
18. Diggle, P. J., Heagerty, P., Liang, K.-Y., & Zeger, S. L. (2002). Analysis of longitudinal data (2nd ed.). Oxford, England: Oxford University Press.
19. Embretson, S. E. (1999). Generating items during testing: Psychometric issues and models. Psychometrika, 64, 407-433.
20. Eysenck, H. J. (1953). Fragebogen als Messmittel der Persönlichkeit [Questionnaires as measures of personality]. Zeitschrift für Experimentelle and Angewandte Psychologie, 1, 291-335.
21. Fahrmeir, L., & Tutz, G. (2001). Multivariate statistical modelling based on generalized linear models (2nd ed.). New York: Springer-Verlag.
22. Fischer, G. H. (1973). Linear logistic test model as an instrument in educational research. Acta Psychologica, 37, 359-374.
23. Fox, J. P., & Glas, C. A. W. (2001). Bayesian estimation of a multilevel IRT model using Gibbs sampling. Psychometrika, 66, 271-288.
24. Gelman, A., Carlin, J. B., Stern, H. S., & Rubin, D. B. (1995). Bayesian data analysis. London: Chapman & Hall.
25. Gilks, W. R., Thomas, A., & Spiegelhalter, D. J. (1994). A language and program for complex Bayesian modelling. The Statistician, 43, 169-178.
26. Goldstein, H. (1991). Nonlinear multilevel models with an application to discrete response data. Biometrika, 78, 45-51.
27. Goldstein, H. (1995). Multilevel statistical models (2nd ed.). London: Edward Arnold.
28. Goldstein, H., & Rasbash, J. (1996). Improved approximations for multilevel models with binary responses. Journal of the Royal Statistical Society, Series A, 505-513.
29. Hedeker, D. (1999). MIXNO: A computer program for mixed-effects nominal logistic regression [Computer software and manual]. Retrieved August 24, 2001, from http//tigger.uic.edu/%7Ehedeker/manuals.html
30. Hedeker, D., & Gibbons, R. D. (1994). A random-effects ordinal regression model for multilevel analysis. Biometrics, 50, 933-944.
31. Hedeker, D., & Gibbons, R. D. (1996). MIXOR: A computer program for mixed-effects ordinal regression analysis. Computer Methods and Programs in Biomedicine, 49, 157-176.
32. Holland, P. W., & Wainer, H. (1993). Differential item functioning. Hillsdale, NJ: Erlbaum.
33. Hoskens, M., & De Boeck, P. (1997). A parametric model for local dependence among test items. Psychological Methods, 2, 261-277.
34. Jannarone, R. (1986). Conjunctive item response theory kernels. Psychometrika, 51, 357-373.
35. Janssen, R., & De Boeck, P. (2003). A random-effects version of the linear logistic test model. Manuscript submitted for publication.
36. Kamata, A. (2001). Item analysis by the hierarchical generalized linear model. Journal of Educational Measurement, 38, 79-93.
37. Kelderman, H. (1984). Loglinear Rasch model tests. Psychometrika, 49, 223-245.
38. Kuppens, P. (2003). Individual differences in appraisal and emotion: The case of anger and irritation. Unpublished manuscript.
39. Lange, K., Hunter, D. R., & Yang, I. (2000). Optimization transfer using surrogate objective functions (with discussion). Journal of Computational and Graphical Statistics, 9, 1-52.
40. Legler, J. M., & Ryan, L. M. (1997). Latent variable models for teratogenesis using multiple binary outcomes. Journal of the American Statistical Association, 92, 13-20.
41. Lin, X., & Breslow, N. E. (1996). Bias correction in generalized linear mixed models with multiple components of dispersion. Journal of the American Statistical Association, 91, 1007-1016.
42. Longford, N. T. (1993). Random coefficient models. New York: Oxford University Press.
43. Lord, F. M., & Novick, M. R. (1968). Statistical theories of mental test scores. Reading, MA: Addison-Wesley.
44. Maier, K. (2001). The Rasch hierarchical measurement model. Journal of Educational and Behavioral Statistics, 26, 307-330.
45. Masters, G. N. (1982). A Rasch model for partial credit scoring. Psychometrika, 47, 149-174.
46. McCullagh, P., & Nelder, J. A. (1989). Generalized linear models. London: Chapman & Hall.
47. McCulloch, C. E., & Searle, S. R. (2001). Generalized, linear, and mixed models. New York: Wiley.
48. McKinley, R. L. (1989). Confirmatory analysis of test structure using multidimensional item response theory (Research Report No. RR-89-31). Princeton, NJ: Educational Testing Service.
49. 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.
50. Mellenbergh, G. J. (1995). Conceptual notes on models for discrete polytomous item responses. Applied Psychological Measurement, 19, 91-100.
51. Mislevy, R. J. (1987). Exploiting auxiliary information about examinees in the estimation of item parameters. Applied Psychological Measurement, 11, 81-91.
52. Mislevy, R. J., & Verhelst, N. (1990). Modeling item responses when different persons employ different solution strategies. Psychometrika, 55, 195-215.
53. Muraki, E. (1992). A generalized partial credit model: Application of an EM algorithm. Applied Psychological Measurement, 16, 159-176.
54. Pinheiro, J. C., & Bates, D. M. (1995). Approximations to the log-likelihood function in the nonlinear mixed-effects model. Journal of Computational and Graphical Statistics, 4, 12-35.
55. Rabe-Hesketh, S., Pickles, A., & Skrondal, A. (2001). GLLAMM manual (Tech. Rep. No. 2001/01) [Software manual]. London: University of London, Department of Biostatistics and Computing.
56. Rasbash, J., Browne, W. J., Goldstein, H., & Yang, M. (2000). A user's guide to MLwiN (Version 2.1) [Software manual]. London: Institute of Education.
57. Rasch, G. (1960). Probabilistic models for some intelligence and attainment tests. Copenhagen, Denmark: Danish Institute for Educational Research.
58. S. W., & Bryk, A. S. (2002). Hierarchical linear models: Applications and data analysis method (2nd ed.). Newbury Park, CA: Sage.
59. Raudenbush, S. W., Bryk, A. S., & Congdon, R. T. (2001). HLM 5 [Computer software and manual]. Lincolnwood, IL: Scientific Software.
60. Raudenbush, S. W., Yang, M.-L., & Yosef, M. (2000). Maximum likelihood for generalized linear models with nested random effects via high-order, multivariate Laplace approximation. Journal of Computational and Graphical Statistics, 9, 141-157.
61. Rijmen, F., & De Boeck, P. (2002). The random weights linear logistic test model. Applied Psychological Measurement, 26, 269-283.
62. Rodriguez, G., & Goldman, N. (1995). An assessment of estimation procedures for multilevel models with binary response. Journal of the Royal Statistical Society, Series A, 158, 73-89.
63. Rosenbaum, P. R. (1988). Item bundles. Psychometrika, 53, 349-359.
64. Rosenberg, M. (1989). Society and the adolescent self-image (Rev. ed.). Middletown, CT: Wesleyan University Press.
65. Rost, J. (1990). Rasch models in latent classes: An integration of two approaches to item analysis. Applied Psychological Measurement, 14, 271-282.
66. Samejima, F. (1969). Estimation of latent ability using a response pattern of graded scores. Psychometrika Monograph, 34(Suppl., No. 17, pp. 100-114).
67. Scott, S. L., & Ip, E. H. (2002). Empirical Bayes and itemclustering effects in a latent variable hierarchical model: A case study from the National Assessment of Educational Progress. Journal of the American Statistical Association, 97, 409-419.
68. Self, S. G., & Liang, K. (1987). Asymptotic properties of maximum likelihood estimators and likelihood ratio tests under nonstandard conditions. Journal of the American Statistical Association, 82, 605-610.
69. Skrondal, A., & Rabe-Hesketh, S. (in press). Multilevel logistic regression for polytomous data and rankings. Psychometrika.
70. Snijders, T., & Bosker, R. (1999). An introduction to basic and advanced multilevel modeling. London: Sage.
71. Spiessens, B., Verbeke, G., Fieuws, S., & Rijmen, F. (2003). Classification of clustered data using a SAS-macro: An application to latent class models. Manuscript submitted for publication.
72. Spiessens, B., Verbeke, G., & Komárek, A. (2002). The use of mixed models for longitudinal count data when the random-effects distribution is misspecified. Manuscript submitted for publication.
73. StataCorp. (2001). Stata statistical software (Release 7) [Computer software and manual]. College Station, TX: Stata Press.
74. Stram, D. O., & Lee, J. W. (1994). Variance components testing in the longitudinal mixed-effects model. Biometrics, 50, 1171-1177.
75. Tanner, M. A. (1996). Tools for statistical inference (3rd ed.). New York: Springer-Verlag.
76. Thissen, D. (1991). MULTILOG [Software manual]. Lincolnwood, IL: Scientific Software.
77. Thissen, D., & Steinberg, L. (1984). A response model for multiple choice items. Psychometrika, 49, 501-519.
78. Thissen, D., & Steinberg, L. (1986). A taxonomy of item response models. Psychometrika, 51, 567-577.
79. Tuerlinckx, F., De Boeck, P., & Lens, W. (2002). Measuring needs with the Thematic Apperception Test: A psychometric study. Journal of Personality and Social Psychology, 82, 448-461.
80. Tutz, G. (1990). Sequential item response models with an ordered response. British Journal of Mathematical and Statistical Psychology, 43, 39-55.
81. Van der Ploeg, H. M., Defares, P. B., & Spielberger, C. D. (1982). Zelf-analyse vragenlijst [Anger trait scale]. Lisse, The Netherlands: Swets & Zeitlinger.
82. Verbeke, G., & Molenberghs, G. (1997). Linear mixed models in practice: A SAS-oriented approach. Lecture notes in statistics 126. New York: Springer-Verlag.
83. Verbeke, G., & Molenberghs, G. (2000). Linear mixed models for longitudinal data. New York: Springer-Verlag.
84. Verguts, T., & De Boeck, P. (2000). A Rasch model for learning while solving an intelligence test. Applied Psychological Measurement, 24, 151-162.
85. Verhelst, N. D., & Glas, C. A. W. (1993). A dynamic generalization of the Rasch model. Psychometrika, 58, 395-415.
86. Wolfinger, R. D., & Lin, X. (1997). Two Taylor-series approximation methods for nonlinear mixed models. Computational Statistics and Data Analysis, 25, 465-490.
87. Wu, M. L., Adams, R. J., & Wilson, M. (1998). ACER ConQuest: Generalized Item Response Modelling Software [Computer software and manual]. Melbourne, Victoria, Australia: Australian Council for Educational Research.
88. Yamamoto, K. (1987). A hybrid model for item responses. Unpublished doctoral dissertation, University of Illinois at Chicago.
89. Zeger, S. L., & Karim, M. R. (1991). Generalized linear models with random effects: A Gibbs sampling approach. Journal of the American Statistical Association, 86, 79-86.
90. Zwinderman, A. H. (1991). A generalized Rasch model for manifest predictors. Psychometrika, 56, 589-600.