Parameter estimation of multiple item response profile model

British Journal of Mathematical and Statistical Psychology

Volumn 65, Issue 3, 2012, Pages 438-466

  Cho, Sun Joo ^a   Partchev, Ivailo ^b   De Boeck, Paul ^c,d  

^a VANDERBILT UNIVERSITY   (United States)

^b Cito group   (Netherlands)

^c UNIVERSITY OF AMSTERDAM   (Netherlands)

^d UNIVERSITY OF LEUVEN   (Belgium)

Author keywords

[No Author keywords available]

Indexed keywords

AGGRESSION; ALGORITHM; ARTICLE; BAYES THEOREM; COMPUTER SIMULATION; FEMALE; HUMAN; MALE; MONTE CARLO METHOD; PSYCHOLOGICAL ASPECT; PSYCHOLOGICAL MODEL; REGRESSION ANALYSIS; STATISTICAL MODEL; STATISTICS;

AGGRESSION; ALGORITHMS; BAYES THEOREM; COMPUTER SIMULATION; FEMALE; HUMANS; MALE; MODELS, PSYCHOLOGICAL; MODELS, STATISTICAL; MONTE CARLO METHOD; REGRESSION ANALYSIS;

EID: 84865800805     PISSN: 00071102     EISSN: 20448317     Source Type: Journal    
DOI: 10.1111/j.2044-8317.2011.02036.x     Document Type: Article

References (75)

1. Akaike, A. (1974). A new look at the statistical model identification. IEEE Transactions on Automatic Control, 19, 716-723.
2. Baayen, R. H., Davidson, R. H., & Bates, D. M. (2008). Mixed-effects modeling with crossed random effects for subjects and items. Journal of Memory and Language, 59, 390-412.
3. Bates, D. M., & DebRoy, S. (2004). Linear mixed models and penalized least squares. Journal of Multivariate Analysis, 1, 1-17.
4. Bates, D., & Maechler, M. (2009). lme4: Linear mixed-effects models using s4 classes. Retrieved from http://cran.R-project.org/lme4
5. Bock, R. D., & Lieberman, M. (1970). Fitting a response model for n dichotomously scored items. Psychometrika, 33, 179-197.
6. Bock, R. D., & Schilling, S. G. (1997). High-dimensional full-information item factor analysis. In M. Berkane (Ed.), Latent variable modelling and applications to causality (pp. 164-176). New York : Springer.
7. Breslow, N. E. (2004). Whither PQL?. In D. Y. Lin & P. J. Heagerty (Eds.), Proceedings of the Second Seattle Symposium in Biostatistics: Analysis of correlated data (pp. 1-22). New York : Springer.
8. Breslow, N. E., & Clayton, D. G. (1993). Approximate inference in generalized linear mixed models. Journal of the American Statistical Association, 88, 9-25.
9. Breslow, N. E., & Lin, X. (1995). Bias correction in generalised linear mixed models with a single component of dispersion. Biometrika, 82, 81-91.
10. Browne, W. J., & Draper, D. (2006). A comparison of Bayesian and likelihood methods for fitting multilevel models. Bayesian Analysis, 3, 473-514.
11. Butler, J. S., & Moffitt, R. (1982). A computationally efficient quadrature procedure for the one-factor multinomial probit model. Econometrica, 50, 761-764.
12. Camilli, G., & Penfield, D. A. (1997). Variance estimation for differential test functioning based on Maentel-Haenszel statistics. Journal of Educational Measurement, 34, 123-139.
13. Chang, H., & Stout, W. (1993). The asymptotic posterior normality of the latent trait in an IRT model. Psychometrika, 58, 37-52.
14. Cho, S.-J., & Rabe-Hesketh, S. (2011). Alternating imputation posterior estimation of models with crossed random effects. Computational Statistics and Data Analysis, 55, 12-25.
15. Clark, H. H. (1973). The language-as-fixed effect fallacy: A critique of language statistics in psychological research. Journal of Verbal Learning and Verbal Behavior, 12, 335-359.
16. Clayton, D. G., & Rasbash, J. (1999). Estimation in large crossed random-effect models by data augmentation. Journal of the Royal Statistical Society, Series A, 162, 425-436.
17. Congdon, P. (2003). Applied Bayesian modelling. Chichester: Wiley.
18. De Boeck, P. (2008). Random item IRT models. Psychometrika, 73, 533-559.
19. De Boeck, P., & Wilson, M. (2004). Explanatory item response models: A generalized linear and nonlinear approach. New York : Springer.
20. De Boeck, P., & Wilson, M. (2010). Multidimensional (multiple) random item profile model. Denver, CO : National Council Measurement in Education.
21. Diaz, R. E. (2007). Comparison of PQL and Laplace 6 estimates of hierarchical linear models when comparing groups of small incident rates in cluster randomised trials. Computational Statistics and Data Analysis, 51, 2871-2888.
22. Doran, H., Bates, D., Bliese, P., & Dowling, M. (2007). Estimating the multilevel Rasch model: With the lme4 package. Journal of Statistical Software, 20. Retrieved from http://www.jstatsoft.org/v20/i02/
23. Forster, K. I., & Masson, M. E. J. (2008). Issue: Emerging data analysis. Journal of Memory and Language, 59, 387-556.
24. Fox, J.-P. (2010). Bayesian item response modeling: Theory and applications. New York : Springer.
25. Freeman, E., Heathcote, A., Chalmers, K., & Hockley, W. (2010). Item effects in recognition memory for words. Journal of Memory and Language, 62, 1-18.
26. Geerlings, H., Glas, C. A. W., & van der Linden, W. J. (2011). Modeling rule-based item generation. Psychometrika, 76(2), 337-359.
27. Geisser, S., & Eddy, W. F. (1979). A predictive approach to model selection. Journal of the American Statistical Association, 74, 153-160.
28. Gelfand, A. E., & Dey, D. K. (1994). Bayesian model choice: Asymptotics and exact calculations. Journal of the Royal Statistical Society, Series B, 56, 501-514.
29. Gelman, A., Carlin, J. B., Stern, H. S., & Rubin, D. B. (2004). Bayesian data analysis (2nd ed.). Boca Raton, FL: Chapman & Hall.
30. Gelman, A., & Hill, J. (2007). Data analysis using regression and multilevel/hierarchical models. New York : Cambridge University Press.
31. Gelman, A., & Rubin, D. B. (1992). Inference from iterative simulation using multiple sequences. Statistical Sceience, 7, 457-472.
32. Geman, S., & Geman, D. (1984). Stochastic relaxation, Gibbs distribution, and the Bayesian restoration of image. IEEE Transactions of Pattern Analysis and Machine Intelligence, 6, 721-741.
33. Glas, C. A. W., & van der Linden, W. J. (2003). Computerized adaptive testing with item clones. Applied Psychological Measurement, 27, 247-261.
34. Goldstein, H. (1987). Multilevel covariance component models. Biometrika, 74, 430-431.
35. Goldstein, H. (1991). Nonlinear multilevel models, with an application to discrete response data. Biometrika, 78, 45-51.
36. Goldstein, H., & Rasbash, J. (1996). Improved approximations for multilevel models with binary responses. Journal of the Royal Statistical Society, Series A, 159, 505-513.
37. Goldstein, H., Rasbash, J., Plewis, I., Draper, D., Browne, W. J., Yang, M., Woodhouse, G., & Healy, M. (1998). A user's guide to MLwiN. London : Multilevel Models Project, Institute of Education, University of London.
38. Hedeker, D., & Gibbons, R. D. (1994). A random-effects ordinal regression model for multilevel analysis. Biometrics, 50, 933-944.
39. Jaeger, T. F. (2008). Categorical data analysis: Away from ANOVAs (transformation or not) and towards logit mixed models. Journal of Memory and Language, 59, 434-446.
40. Janssen, R., Schepers, J., & Peres, D. (2004). Models with item and item group predictors. In P. De Boeck & M. Wilson (Eds.), Explanatory item response models (pp. 198-212). New York : Springer.
41. Janssen, R., Tuerlinckx, F., Meulders, M., & De Boeck, P. (2000). A hierarchical IRT model for criterion-referenced measurement. Journal of Educational and Behavioral Statistics, 25, 285-306.
42. Joe, H. (2008). Accuracy of Laplace approximation for discrete response mixed models. Computational Statistics and Data Analysis, 52, 5066-5074.
43. Johnson, M. S., & Sinharay, S. (2005). Calibration of polytomous item families using Bayesian hierarchical modeling. Applied Psychological Measurement, 29, 369-400.
44. Karim, M. R., & Zeger, S. L. (1992). Generalized linear models with random effects: Salamander mating revisited. Biometrics, 48, 631-644.
45. Lambert, P. C. (2006). Comment on article by Browne and Draper. Bayesian Analysis, 1, 543-546.
46. Lee, Y., & Nelder, J. A. (1996). Hierarchical generalized linear models. Journal of the Royal Statistical Society, Series B, 58, 619-678.
47. Lee, Y., & Nelder, J. A. (2006). Double-hierarchical generalized linear models (with discussion). Applied Statistics, 55, 1-29.
48. 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.
49. Longford, N. T., Holland, P. W., & Thayer, D. T. (1993). Stability of the MH D-DIF statistics across populations. In P. W. Holland & H. Wainer (Eds.), Differential item functioning: Theory and practice (pp. 171-196). Hillsdale, NJ : Erlbaum.
50. McCullagh, P., & Nelder, J. A. (1989). Generalized linear models (2nded.). London : Chapman & Hall.
51. McCulloch, C. E., & Searle, S. R. (2001). Generalized, linear, and mixed models. New York : Wiley.
52. Natarajan, R., & Kass, R. E. (2000). Reference Bayesian methods for generalized linear mixed model. Journal of the American Statistical Association, 95, 227-237.
53. Penfield, R. D., & Algina, J. (2006). A generalized DIF effect variance estimator for measuring unsigned differential test functioning in mixed format tests. Journal of Educational Measurement, 43, 295-312.
54. Pinheiro, J. C., & Bates, D. M. (1995). Approximation to the log-likelihood function in the nonlinear mixed-effects model. Journal of Computational and Graphics and Statistics, 4, 12-35.
55. Quené, H. (2008). Multilevel modeling of between-speaker and within-speaker variation in spontaneous speech tempo. Journal of the Acoustical Society of America, 123, 1104-1113.
56. Raaijmarkers, J. G. W. (2003). A further look at the language-as-fixed-effect fallacy. Canadian Journal of Experimental Psychology, 57, 141-151.
57. Raaijmarkers, J. G. W., Schrijnemakers, J. M. C., & Gremmen, F. (1999). How to deal with "the language-as-fixed-effect fallacy": Common misconceptions and alternative solutions. Journal of Memory and Language, 41, 416-426.
58. Rabe-Hesketh, S., & Skrondal, A. (2008). Multilevel and longitudinal modeling using Stata (2nded.). College Station, TX: Stata Press.
59. Rabe-Hesketh, S., Skrondal, A., & Pickles, A. (2004). Generalized multilevel structural equation modelling. Psychometrika, 69, 167-190.
60. Rabe-Hesketh, S., Skrondal, A., & Pickles, A. (2005). Maximum likelihood estimation of limited and discrete dependent variable models with nested random effects. Journal of Econometrics, 128, 301-323.
61. Rasbash, J., & Browne, W. J. (2007). Non-hierarchical multilevel models. In J. de Leeuw & E. Meijer (Eds.), Handbook of multilevel analysis (pp. 333-336). New York : Springer.
62. Rasbash, J., & Goldstein, H. (1994). Efficient analysis of mixed hierarchical and crossed random structures using a multilevel model. Journal of Behavioral Statistics, 337-350.
63. Raudenbush, S. W., Yang, M., & 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.
64. Rodríguez, G., & Goldman, N. (1995). An assessment of estimation procedures for multilevel models with binary responses. Journal of the Royal Statistical Society, Series A, 158, 73-89.
65. Rodríguez, G., & Goldman, N. (2001). Improved estimation procedures for multilevel models with binary response: A case study. Journal of the Royal Statistical Society, Series A, 164, 339-355.
66. Schwarz, G. (1978). Estimating the dimension of a model. Annals of Statistics, 6, 416-464.
67. Smits, D. J. M., De Boeck, P., & Vansteelandt, K. (2004). The inhibition of verbally aggressive behavior. European Journal of Personality, 18, 537-555.
68. Soares, T. M., Gonçalves, F. B., & Gamerman, D. (2009). An integrated Bayesian model for DIF analysis. Journal of Educational and Behavioral Statistics, 34, 348-377.
69. Spiegelhalter, D., Best, N. G., & Carlin, B. P. (1998). Bayesian deviance, the effective number of parameters, and the comparison of arbitrarily complex models. Technical report, MRC Biostatistics Unit, Cambridge
70. Spiegelhalter, D., Thomas, A., & Best, N. (2003). WinBUGS (Version 1.4) [Computer program]. Cambridge : MRC Biostatistics Unit, Institute of Public Health.
71. Stram, D. O., & Lee, J. W. (1994). Variance components testing in the longitudinal mixed-effects model. Biometrics, 50, 1171-1177.
72. Tanner, M. A. (1996). Tools for statistical inference: Methods for the exploration of posterior distributions and likelihood functions. New York : Springer.
73. Tanner, M. A., & Wong, W. H. (1987). The calculation of posterior distributions by data augmentation. Journal of the American Statistical Association, 82, 528-540.
74. Thomas, N., & Gan, N. (1997). Generating multiple imputations for matrix sampling data analyzed with item response models. Journal of Educational and Behavioral Statistics, 22, 425-445.
75. Tierny, L., & Kadane, J. B. (1986). Accurate approximations for posterior moments and marginal densities. Journal of the American Statistical Association, 81, 82-86.