Maximum likelihood methods in treating outliers and symmetrically heavy-tailed distributions for nonlinear structural equation models with missing data

Psychometrika

Volumn 71, Issue 3, 2006, Pages 565-585

  Lee, Sir Yum ^a   Xia, Ye Mao ^a  

^a CHINESE UNIVERSITY OF HONG KONG   (Hong Kong)

Author keywords

Bayesian information criterion; Gibbs sampler; Heavy tailed distributions; MCEM algorithm; Outliers; Path sampling

Indexed keywords

EID: 33751224758     PISSN: 00333123     EISSN: None     Source Type: Journal    
DOI: 10.1007/s11336-006-1264-1     Document Type: Article

References (36)

1. Bentler, P.M. (2004). EQS6: Structural equations program manual. Encino, CA: Multivariate Software.
2. Berkane, M., & Bentler, P.M. (1988). Estimating of the contamination parameters and identification of outliers in multivariate data. Sociological Methods & Research, 17, 55-64.
3. Bowman, K.O., & Shenton, L.R. (1988). Properties of estimators for the gamma distribution. New York: Marcel Dekker.
4. Browne, M.W. (1987). Robustness of statistical influence in factor analysis and related models. Biometrika, 74, 375-384.
5. Browne, M.W., & Shapiro, A. (1988). Robustness of normal theory methods in the analysis of linear latent variable models. British Journal of Mathematical and Statistical Psychology, 41, 193-208.
6. Campbell, N.A. (1982). Robust procedure in multivariate analysis I: Robust covariance estimation. Applied Statistics. 29, 31-237.
7. Cowles, M.K. (1996). Accelerating Monte Carlo Markov Chains convergence for cumulative-link generalized linear modes. Statistics and Computing, 6, 101-111.
8. Dempster, A.P., Laird, N.M., & Rubin, D.B. (1977). Maximum likelihood from incomplete data via the EM algorithm (with discussion). Journal of the Royal Statistical Society, Series B, 39, 1-38.
9. Gelman, A., & Meng, X.L. (1998). Simulating normalizing constants: From importance sampling to bridge sampling to path sampling. Statistical Science, 13, 163-185.
10. Geman, S., & Geman, D. (1984). Stochastic relaxation, Gibbs distribution, and the Bayesian restoration of images. IEEE Transactions on Pattern Analysis and Machine Intelligence, 6, 721-741.
11. Hastings, W.K. (1970). Monte Carlo sampling methods using Markov chains and their applications. Biometrika, 57, 97-100.
12. Jöreskog, K.G., & Sörbom, D. (1996). LISREL 8: Structural equation modelling with the SIMPLIS command language. London: Scientific Software International.
13. Kano, Y., Berkane, M., & Bentler, P.M. (1993). Statistical inference based on pseudo-maximum likelihood estimators in elliptical populations. Journal of the American Statistical Association, 88, 135-143.
14. Kass, R.E., & Raftery, A.E. (1995). Bayes factor. Journal of the American Statistical Association, 90, 773-795.
15. Lange, K.L., Little, R.J.A., & Taylor, J. M. G. (1989). Robust statistical modelling using the t-distribution. Journal of the American Statistical Association, 84, 881-896.
16. Lee, M., & Lomax, R.G. (2005). The effects of varying degrees of nonnormality in structural equation modeling. Structural Equation Modeling, 12, 1-27.
17. Lee, S.Y., & Song, X.Y. (2004). Maximum likelihood analysis of a general latent variable model with hierarchically mixed data. Biometrics, 60, 624-636.
18. Lee, S.Y., & Song, X.Y. (2003). Model comparison of nonlinear structural equation models with fixed covariates. Psychometrika, 68, 21-47.
19. Lee, S. Y., Song, X.Y., & Lee, J.C.K. (2003). Maximum likelihood estimation of nonlinear structure models with ignorable missing data. Journal of Educational and Behavioral Statistics, 28, 111-134.
20. Lee, S.Y., & Zhu, H.T. (2002). Maximum likelihood estimation of nonlinear structural equation models. Psychometrika. 67, 189-210.
21. Little, R.J.A. (1988). Robust estimation of mean and covariance matrix from data with missing values. Applied Statistics, 37, 23-39.
22. Little, R.J.A., & Rubin, D.B. (1987). Statistical analysis with missing data. New York: Wiley.
23. Louis, T. A. (1982). Finding the observed information matrix when using the EM algorithm. Journal of the Royal Statistical Society. Series B, 44, 226-233.
24. Mardia, V.V. (1970). Measures of multivariate skewness and kurtosis with application. Biometrika, 57, 519-530.
25. Meng, X.L., & Rubin, D.B. (1993). Maximum likelihood estimation via the ECM algorithm: A general framework. Biometrika, 80, 267-278.
26. Metropolis, N., Rosenbluth, A.W., Rosenbluth, M.N., Teller, A.H., & Teller, E. (1953). Equations of state calculations by fast computing machines. Journal of Chemical Physics, 21, 1087-1092.
27. Ogasawara, H. (2005). Asymptotic robustness of the asymptotic bias in structural equation modeling. Computational Statistics & Data Analysis. 49, 771-783.
28. Schwarz, G. (1978). Estimating the dimension of a model. Annals of Statistics, 6, 461-464.
29. Song, X.Y., & Lee, S.Y. (2005). Maximum likelihood analysis of nonlinear structural equation models with dichotomons variables. Multivariate Behavioral Research, 40, 151-177.
30. Song, X.Y., & Lee, S.Y. (2004). Bayesian analysis of two-level nonlinear structural equation models with continuous and polytomous data. British Journal of Mathematical and Statistical Psychology. 57, 29-52.
31. Watanabe, M., & Yamaguchi, K. (2004). The EM algorithm and relate statistical models. New York: Marcel Dekker.
32. Wei, G.C.G., & Tanner, M.A. (1990). Monte Carlo implementation of the EM algorithm and the poor man's data augmentation algorithms (in theory and methods). Journal of the American Statistical Association, 85, 699-704.
33. Yuan, K.H., & Bentler, P.M. (1997). Mean and covariance structure analysis: theoretical and practical improvements (in theory and methods). Journal of the American Statistical Association, 92, 767-774.
34. Yuan, K.H., & Bentler, P.M. (1998a). Robust mean and covariance structure analysis. British Journal of Mathematical and Statistical Psychology, 51, 63-88.
35. Yuan, K.H., & Bentler, P.M. (1998b). Structural equation modelling with robust covariance. Sociological Methodology, 28, 363-396.
36. Yuan, K.H., & Bentler, P.M. (2000). Robust mean and covariance structure analysis through iteratively reweighted least squares. Psychometrika, 65, 43-58.