Fitting full-information item factor models and an empirical investigation of bridge sampling

Journal of the American Statistical Association

Volumn 91, Issue 435, 1996, Pages 1254-1267

  Meng, Xiao Li ^a   Schilling, Stephen ^b  

^a UNIVERSITY OF CHICAGO   (United States)

^b VANDERBILT UNIVERSITY   (United States)

Author keywords

Factor analysis; Gibbs sampler; Item response theory; Latent variables; Monte Carlo expectation maximization algorithm; Normalizing constants; Probit model

Indexed keywords

EID: 0030336223     PISSN: 01621459     EISSN: 1537274X     Source Type: Journal    
DOI: 10.1080/01621459.1996.10476995     Document Type: Article

References (52)

1. Albert, J. H. (1992), “Bayesian Estimation of Normal Ogive Item Response Curves Using Gibbs Sampling,” Journal of Educational Statistics, 17, 251-269.
2. Albert, J. H., and Chib, S. (1993), “Bayesian Analysis of Binary and Poly- chotomous Response Data,” Journal of the American Statistical Association, 88, 669-679.
3. Bennett, C. H. (1976), “Efficient Estimation of Free Energy Differences from Monte Carlo Data,” Journal of Computational Physics, 22, 245-268.
4. Bartholomew, D. J. (1987), Latent Variable Models and Factor Analysis, New York: Oxford University Press.
5. Bock, R. D., and Aitkin, M. (1981), “Marginal Maximum Likelihood Estimation of Item Parameters: Application of an EM Algorithm,” Psy- chometrika, 37, 29-51.
6. Bock, R. D., Gibbons, R., and Muraki, E. (1988), “Full-Information Item Factor Analysis,” Applied Psychological Measurement, 12, 261-280.
7. Bock, R. D., and Lieberman, M. (1970), "Fitting a Response Model for Dichotomously Scored Items,” Psychometrika, 35, 179-197.
8. Campbell, A., and Converse, P. E. (1980), The Quality of American Life, 1978, Ann Arbor, MI: Inter-University Consortium for Political and Social Research.
9. Campbell, A., Converse, P. E., and Rodgers, W. L. (1976), The Quality of American Life, New York: Russel Sage Foundation.
10. Cristoffcrson, A. (1975), “Factor Analysis of Dichotomized Variables,” Psychometrika, 37, 29-51.
11. Dempster, A. P., Laird, N. M., and Rubin, D. B. (1977), “Maximum Likelihood From Incomplete Data via the EM Algorithm" (with discussion), Journal of the Royal Statistical Society, Ser. B, 39, 1-38.
12. Gelfand, A. E., and Dey, D. K. (1994), “Bayesian Model Choice: Asymptotics and Exact Calculations,” Journal of the Royal Statistical Society, Ser. B, 56, 501-514.
13. Gelfand, A. E., and Smith, A. F. M. (1990), “Sampling-Based Approaches to Calculating Marginal Densities,” Journal of the American Statistical Association, 85, 398-409.
14. Gelman, A., and Meng, X. L. (1994), “Path Sampling for Computing Normalizing Constants: Identities and Theory," Technical Report 376, University of Chicago, Dept, of Statistics.
15. Gelman, A., Meng, X. L., and Stem, H. (1996), “Posterior Predictive Assessment of Model Fitness via Realized Discrepancies” (with discussion), Statistica Sínica, 6, to appear.
16. Gelman, A., and Rubin, D. B. (1992), “Inference From Iterative Simulation Using Multiple Sequences" (with discussion). Statistical Science, 7, 457-511.
17. Geman, S., and Geman, D. (1984), “Stochastic Simulation. Gibbs Distributions, and the Bayesian Restoration of Images,” IEEE Transactions on Pattern Analysis and Machine Intelligence, PAM1-6, 721-741.
18. Geyer, C. J. (1994), “Estimating Normalizing Constants and Reweighting Mixtures in Markov Chain Monte Carlo,” Technical Report 568, University of Minnesota, School of Statistics.
19. Geyer, C. J., and Thompson, E. A. (1992), “Constrained Monte Carlo Maximum Likelihood for Dependent Data" (with discussion). Journal of the Royal Statistical Society, Ser. B, 54, 657-699.
20. Guo, S. W., and E. A. Thompson (1992), “A Monte Carlo Method for Combined Segregation and Linkage Analysis,” American Journal of Human Genetics, 51, 1111-1126.
21. Gupta, A. K., and Tracy, D. S. (1976), “Recurrence Relations for the Moments of Truncated Multinormal Distribution,” Communications in Statistics, Part A—Theory and Methods, 5, 855-865.
22. Harman, H. H. (1976), Modem Factor Analysis, Chicago: University of Chicago Press.
23. Irwin, M. E. (1994), “Sequential Imputation and Multilocus Linkage Analysis,” Ph.D. thesis, University of Chicago, Dept, of Statistics.
24. Kaiser, H. F. (1958), “The Varimax Criterion for Analytic Rotation in Factor Analysis,” Psychometrika, 23, 187-200.
25. Little, J. A., and Rubin, D. B. (1987), Statistical Analysis with Missing Data, New York: John Wiley.
26. Liu, C., and Rubin, D. B. (1994), ‘The ECME Algorithm: A Simple Extension of EM and ECM With Fast Monotone Convergence,” Biometrika, 81, 633-648.
27. Liu, J. S., Wong, W. H., and Kong, A. (1994), "Covariance Structure of the Gibbs Sampler With Applications to Comparisons of Estimators and Augmentation Schemes,” Biometrika, 81, 27-40.
28. Liu, J. S., Wong, W. H., and Kong, A. (1995), “Correlation Structure and Convergence Rate of the Gibbs Sampler With Various Scans,” Journal of the Royal Statistical Society, Ser. B, 57, 157-169.
29. Maxwell, A. E. (1983), “Factor Analysis,” in Encyclopedia of Statistical Sciences, Vol. 3, eds. S. Kotz, N. L. Johnson, and C. B. Read, New York: John Wiley, pp. 2-8.
30. McCullough, R., and Rossi, P. E. (1991), “An Exact Likelihood Analysis of the Multinomial Probit Model," Working Paper 91-102, University of Chicago, Graduate School of Business.
31. Meng, X. L. (1994a), “On the Rate of Convergence of the ECM Algorithm," The Annals of Statistics, 22, 326-339.
32. Meng, X. L. (1994b), “Posterior Predictive p-Value,” The Annals of Statistics, 22, 1142-1160.
33. Meng, X. L., and Pedlow, S. (1992), “EM: A Bibliographic Review with Missing Articles," in Proceedings of the Statistical Computing Section, American Statistical Association, pp. 24-27.
34. Meng, X. L., and Rubin, D. B. (1991), “Using EM to Obtain Asymptotic Variance-Covariance Matrices: The SEM Algorithm," Journal of the American Statistical Association, 86, 899-909.
35. Meng, X. L., and Rubin, D. B. (1992), “Recent Extensions to the EM Algorithm” (with discussion), Bayesian Statistics 4, eds. J. M. Bernardo, J. O. Berger, A. P. Dawid, and A. F. M. Smith, Clarendon Press, Oxford, pp. 307-320.
36. Meng, X. L., and Rubin, D. B. (1993), “Maximum Likelihood Estimation via the ECM Algorithm: A General Framework,” Biometrika, 80, 267-278.
37. Meng, X. L., and Rubin, D. B. (1994), "On the Global and Component-wise Rates of Convergence of the EM Algorithm," Linear Algebra and Its Applications (special issue honoring Ingram Olkin), 199, 413-425.
38. Meng, X. L., and Rubin, D. B. (1996), “Efficient Methods for Estimating and Testing With Seemingly Unrelated Regressions in the Presence of Latent Variables and Missing Data,” in Bayesian Analysis in Statistics and Econometrics: Essays in Honor of Arnold Ze liner, eds. D. A. Berry, K. M. Chalonera, and J. K. Gewcke, New York: John Wiley, pp. 213-226.
39. Meng, X. L., and Wong, W. H. (1996), “Simulating Ratios of Normalizing Constants via a Simple Identity: A Theoretical Exploration,” Statistica Sinica, 6, to appear.
40. Newton, M. A., and Raftery, A. E. (1994), “Approximate Bayesian Inference by the Weighted Likelihood Bootstrap” (with discussion), Journal of the Royal Statistical Society, Ser. B, 56, 3-48.
41. Muthen, B. (1978), “Contributions to Factor Analysis of Dichotomized Variables,” Psychometrika, 43, 551-560.
42. Rubin, D. B. (1984), “Bayesianly Justifiable and Relevant Frequency Calculations for the Applied Statistician," The Annals of Statistics, 12, 1151-1172.
43. Rubin, D. B., and Thayer (1982), “EM Algorithms for ML Factor Analysis,” Psychometrika, 47, 69-76.
44. Stein, M. L. (1992), “Prediction and Inference for Truncated Spatial Data,” Journal of Computational and Graphical Statistics, 1, 91-110.
45. Tanner, M. A. (1991), Tools for Statistical Inference: Observed Data and Data Augmentation Methods, New York: Springer-Verlag.
46. Tanner, M. A., and Wong, W. H. (1987), “The Calculation of Posterior Distributions by Data Augmentation” (with discussion), Journal of the American Statistical Association, 82, 528-550.
47. Thurstone, L. L. (1947), Multiple Factor Analysis, Chicago: University of Chicago Press.
48. van Dyk, D. A., Meng, X. L., and Rubin, D. B. (1995), “Maximum Likelihood Estimation via the ECM Algorithm: Computing the Asymptotic Variance,” Statistica Sinica, 5, 55-75.
49. Voter, A. F. (1985), “A Monte Carlo Method for Determining Free-Energy Differences and Transition State Theory Rate Constants," J. Chemical Physics, 82, 1890-1899.
50. Weeks, D. E., and Lange, K. (1989), “Trials, Tribulations, and Triumphs of the EM Algorithm in Pedigree Analysis,” IMA Journal of Mathematics Applied in Medicine & Biology, 6, 209-232.
51. Wei, G. C. G., and Tanner, M. A. (1990), “A Monte Carlo Implementation of the EM Algorithm and the Poor Man’s Data Augmentation Algorithm,” Journal of the American Statistical Association, 85, 699-704.
52. Wichura, M. J. (1989), “An Algorithm for Patterson Gaussian Quadrature,” Technical Report 257, University of Chicago, Dept, of Statistics.