A growth model for multilevel ordinal data

Journal of Educational and Behavioral Statistics

Volumn 30, Issue 4, 2005, Pages 369-396

  Segawa, Eisuke ^a  

^a UNIVERSITY OF ILLINOIS AT CHICAGO   (United States)

Author keywords

Bayesian hierarchical models; Missing data; Multi indicator model

Indexed keywords

EID: 29144517648     PISSN: 10769986     EISSN: None     Source Type: Journal    
DOI: 10.3102/10769986030004369     Document Type: Review

References (46)

1. Albert, J. H., & Chib, S. (1993). Bayesian analysis of binary and polychotomous response data. Journal of the American Statistical Association, 88, 669-679.
2. Ansari, A., & Jedidi, K. (2000). Bayesian factor analysis for multilevel binary observations. Psychometrika, 65, 475-496.
3. Arbuckle, J. L. (1996). Full information estimation in the presence of incomplete data. In G. A. Marcoulides, & R. E. Schumacker (Eds.), Advanced structural equation modeling, (pp. 243-277). Mahwah, NJ: Erlbaum.
4. Bock, R. D., & Aitken, M. (1981). Marginal maximum likelihood estimation of item parameters: Application of an EM algorithm. Psychometrika, 46, 443-459.
5. Bock, R. D., Gibbons, R., & Muraki, E. (1988). Full-information item factor analysis. Applied Psychological Measurement, 12, 261-280.
6. Brooks, S. P., & Gelman, A. (1998). Alternative methods for monitoring convergence of iterative simulations. Journal of Computational and Graphical Statistics, 7, 434-455.
7. Chib, S. (1993). Bayes regression with autoregressive errors. Journal of Econometrics, 58, 275-294.
8. Chib, S., & Greenberg, E. (1998). Analysis of mulitvariate probit models. Biometrika, 85, 347-361.
9. Congdon, P. (2001). Bayesian statistical modeling. New York: Wiley.
10. Congdon, P. (2003). Applied Bayesian statistical modeling. New York: Wiley.
11. Cowles, M. K. (1996). Accelerating Monte Carlo Markov Chain convergence for cumulativelink generalized linear models. Statistics and Computing, 6, 101-111.
12. Duncan, T. E., Duncan, S. E., Strycker, L. A., Li, Fuzhong, & Alpert, A. (1999). An introduction to latent variable growth curve modeling: concepts, issues, and applications. Mahwah, NJ: Erlbaum.
13. Flay, B. R., Graumlich, S., Segawa, E., Burns, J. L., Holliday, M. Y., & Aban Aya Investigators. (2004). Effects of two prevention programs on high-risk behaviors among African-American youth: A randomized trial. Archives of Pediatrics and Adolescent Medicine, 158, 377-384.
14. Fox, J. P., & Glas, A. W. (2001). Bayesian estimation of a multilevel IRT MODEL using Gibbs sampling. Psychometrika, 66, 271-288.
15. Fox, J. P. (2005). Multilevel IRT using dichotomous and polytomous items. British Journal of Mathematical and Statistical Psychology, 58, 145-172.
16. Gelfand, A. E., & Smith, A. F. M. (1990). Sampling-based approaches to calculating marginal densities. Journal of the American Statistical Association 85, 398-409.
17. Gelman, A., & Rubin, D. B. (1992). Inference from iterative simulation using multiple sequences (with discussion). Statistical Science 7, 457-511.
18. Gelman, A., Carlin, J. B., Stern, H. S., & and Rubin, D. B. (1995). Bayesian data analysis. New York: Chapman & Hall.
19. Graham, J. W., Hofer, S. M., & MacKinnon, D. P. (1996). Maximizing the usefulness of data obtained with planned missing value patterns: An application of maximum likelihood procedures. Multivariate Behavioral Research, 31, 197-218.
20. Goldstein, H., & Browne, W. (2002). Multilevel factor analysis modeling using Markov Chain Monte Carlo Estimation. In G. A. Marcoulides, & I. Moustaki. (Eds.), Latent variable and latent structure models (pp. 225-243). Mahwah, NJ: Erlbaum.
21. Hancock, G. R., & Kuo, W. (2001). An illustration of second-order latent growth models. Structural Equation Modeling, 8, 470-489.
22. Hastings, W. K. (1970). Monte Carlo sampling methods using Markov chains and their applications. Biometrika, 57, 97-109.
23. Jedidi, K., & Ansari, A. (2001). Bayesian structural equation models for multilevel data. In G. A. Marcoulides, & R. E. Schumacker. (Eds.), New developments and techniques in structural equation modeling (pp. 129-157). Mahwah, NJ: Erlbaum.
24. Johnson, V. E., & Albert, J. H. (1999). Ordinal data modeling. New York: Springer.
25. Kamata, A. (2001). Item analysis by the hierarchical generalized linear model. Journal of Educational Measurement, 38, 79-93.
26. Laird, N. M., & Ware, J. H. (1982). Random effects models for longitudinal data. Biometrics, 38, 963-974.
27. Littell, R. C., Milliken, G. A., Stroup, W. W., Wolfinger, R. D., & Russell, D. (1996). SAS system for mixed models. Gary, NC: SAS Institute.
28. Maier, K. S. (2001). A Rasch hierarchical measurement model. Journal of Educational and Behavioral Statistics, 26, 307-330.
29. Maier, K. S. (2002). Modeling incomplete scaled questionnaire data with a partial credit hierarchical measurement model. Journal of Educational and Behavioral Statistics, 27, 271-289.
30. Masters, G. N. (1982). A Rasch model for partial credit scoring. Psychometrika, 47, 149-174.
31. McArdle, J. J. (1988). Dynamic but structural equation modeling of repeated measures data. In R. B. Cattell & J. Nesselroade (Eds.), Handbook of multivariate experimental psychology (2nd ed., pp. 561-614). New York: Plenum Press.
32. Meredith, W. (1993). Measurement invariance, factor analysis, and factorial invariance. Psychometrika, 58, 525-543.
33. Metropolis, N., & Ulam, S. (1949). The Monte Carlo method. Journal of the American Statistical Association, 44, 335-341.
34. Muthen, L. K., & Muthen, B. O. (2001). Mplus User's Guide, 2nd ed. Los Angeles: Muthen & Muthen.
35. Nandram, B., & Chen, M. H. (1996). Reparameterizing the generalized linear model to accelerate Gibbs Sampler convergence. Journal of Statistical Computation and Simulation, 54, 129-144.
36. Neale, M. C., Boker, S. M., Xie, G, & Macs, H. H. (1999). Mx: Statistical Modeling (5th ed.). Richmond, VA: Department of Psychiatry, Virginia Commonwealth University.
37. Rasch, G. (1960). Probabilistic models for some intelligence and attainment tests. Chicago: University of Chicago Press.
38. Raudenbush, S. W., & Bryk, A. S. (2002). Hierarchical linear models (2nd ed.). Thousand Oaks, CA: Sage.
39. Rubin, D. B. (1976). Inference and missing data. Biometrika, 63, 581-592.
40. Sayer, A. G., & Cumsille, P. E. (2001). Second-order latent growth models. In L. M. Collins, & A. G. Sayer (Eds.). New methods for the analysis of change (pp. 179-200). Washington, DC: American Psychological Association.
41. Schafer, J. L. (1997). Analysis of incomplete multivariate data. New York: Chapman & Hall.
42. Spiegelhalter D., Best N. G., Carlin, B. P., & van der Linde, A. (2002). Bayesian measures of model complexity and fit (with discussion). Journal of Royal Statistical Society, Series B, 64, 583-640.
43. Spiegelhalter, D., Thomas, A., Best, N., & Lunn, D. (2003). WinBUGS version 1.4 user manual. MRC Biostatistics Unit.
44. Takane, Y., Leeuw, J. D. (1987). On the relationship between item response theory and factor analysis of discretized variables. Psychometrika, 52, 393-408.
45. Tanner, M. A., & Wong, W. H. (1987). The calculation of posterior distributions by data augmentation (with discussion). Journal of the American Statistical Association 82, 528-550.
46. Wilson, D. T., Wood, R., & Gibbons, R. T. (1984). TESTFACT: Test scoring, item statistics, and item factor analysis [computer software and manual]. Chicago: Scientific Software.