Constrained maximum likelihood estimation for two-level mean and covariance structure models

Educational and Psychological Measurement

Volumn 71, Issue 2, 2011, Pages 325-345

  Bentler, Peter M ^a   Liang, Jiajuan ^b   Tang, Man Lai ^c   Yuan, Ke Hai ^d  

^a UNIVERSITY OF CALIFORNIA   (United States)

^b UNIVERSITY OF NEW HAVEN   (United States)

^c HONG KONG BAPTIST UNIVERSITY   (Hong Kong)

^d UNIVERSITY OF NOTRE DAME   (United States)

Author keywords

EM algorithm; linear and nonlinear constraints; maximum likelihood estimation; mean and covariance structure; two level structural equation model

Indexed keywords

EID: 79952964025     PISSN: 00131644     EISSN: 15523888     Source Type: Journal    
DOI: 10.1177/0013164410381272     Document Type: Article

References (20)

1. Aitchison, J., & Silvey, S.D. (1958). Maximum likelihood estimation of parameters subject to restraints. Annals of Mathematical Statistics, 29, 813-828.
2. Bentler, P.M. (2006). EQS 6 structural equations program manual. Encino, CA: Multivariate Software.
3. Bertsekas, D.P. (1976). Multiplier method: A survey. Automatica, 12, 133-145.
4. Buse, A. (1982). The likelihood ratio, Wald and Lagrange multiplier tests: An expository note. American Statistician, 36, 153-157.
5. Dempster, A.P., Laird, N.M., & Rubin, D.B. (1977). Maximum likelihood from incomplete data via EM algorithm (with discussion). Journal of the Royal Statistical Society (Series B), 39, 1-38.
6. du Toit, S., & du Toit, M. (2008). Multilevel structural equation modeling. In J. de Leeuw & E. Meijer (Eds.), Handbook of multilevel analysis (435-478). New York, NY: Springer-Verlag.
7. Jamshidian, M. (2004). On algorithms for restricted maximum likelihood estimation. Computational Statistics & Data Analysis, 45, 137-157.
8. Kim, D.K., & Taylor, J.M.G. (1995). The restricted EM algorithm for maximum likelihood estimation under linear restrictions on parameters. Journal of the American Statistical Association, 90, 708-716.
9. Lange, K. (1995a). A gradient algorithm locally equivalent to the EM algorithm. Journal of the Royal Statistical Society (Series B), 57, 425-437.
10. Lange, K. (1995b). A quasi-Newton acceleration of the EM algorithm. Statistica Sinica, 5, 1-18.
11. Lee, S.Y. (1979). Constrained estimation in covariance structure analysis. Biometrika, 66, 539-545.
12. Lee, S.Y., & Poon, W.Y. (1998). Analysis of two-level structural equation models via EM type algorithms. Statistica Sinica, 8, 749-766.
13. Lee, S.Y., & Tsang, S.Y. (1999). Constrained maximum likelihood estimation of two-level covariance structure model via EM type algorithms. Psychometrika, 64, 435-450.
14. Liang, J., & Bentler, P.M. (2004). A new EM algorithm for fitting two-level structural equation models. Psychometrika, 69, 101-122.
15. McDonald, R.P., & Goldstein, H. (1989). Balanced versus unbalanced designs for linear structural relations in two-level data. British Journal of Mathematical and Statistical Psychology, 42, 215-232.
16. Muthén, B.O. (1994). Multilevel covariance structure analysis. Sociological Methods & Research, 22, 376-398.
17. Muthén, L.K., & Muthén, B.O. (2004). Mplus User's Guide (Version 3) [Computer software]. Los Angeles, CA: Muthén & Muthén.
18. Raudenbush, S.W. (1995). Maximum likelihood estimation for unbalanced multilevel covariance structure models via the EM algorithm. British Journal of Mathematical and Statistical Psychology, 48, 359-370.
19. Yuan, K.-H., & Bentler, P.M. (2006). Asymptotic robustness of standard errors in multilevel structural equation models. Journal of Multivariate Analysis, 97, 1121-1141.
20. Yung, Y.F., & Bentler, P.M. (1999). On added information for ML factor analysis with mean and covariance structures. Journal of Educational and Behavioral Statistics, 24, 1-20.