Robust Procedures in Structural Equation Modeling

Handbook of Latent Variable and Related Models

Volumn , Issue , 2007, Pages 367-397

  Yuan, Ke Hai ^a   Bentler, Peter M ^b  

^a UCLA Psychology Department ^*  (United States)

^b UNIVERSITY OF CALIFORNIA   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

MAXIMUM LIKELIHOOD; NORMAL DISTRIBUTION; STATISTICAL TESTS;

DISTRIBUTED DATA; PARAMETER ESTIMATE; ROBUST PROCEDURES; STANDARD ERRORS; STATISTICAL PROPERTIES; STRUCTURAL EQUATION MODELING; STRUCTURAL EQUATION MODELS; TEST STATISTICS;

PARAMETER ESTIMATION;

EID: 44349089208     PISSN: None     EISSN: None     Source Type: Book    
DOI: 10.1016/B978-044452044-9/50020-3     Document Type: Chapter

References (121)

1. Amemiya Y., Anderson T.W. Asymptotic chi-square tests for a large class of factor analysis models. Annals of Statistics 1990, 18:1453-1463.
2. Anderson T.W., Amemiya Y. The asymptotic normal distribution of estimators in factor analysis under general conditions. Annals of Statistics 1988, 16:759-771.
3. Anderson J.C., Gerbing D.W. The effects of sampling error on convergence, improper solutions and goodness-of-fit indices for maximum likelihood confirmatory factor analysis. Psychometrika 1984, 49:155-173.
4. Arminger G., Schoenberg R. Pseudo maximum likelihood estimation and a test for misspecification in mean and covariance structure models. Psychometrika 1989, 54:409-426.
5. Arminger G., Stein P., Wittenberg J. Mixtures of conditional mean-and covariance-structure models. Psychometrika 1999, 64:475-494.
6. Bentler P.M. Some contributions to efficient statistics in structural models: Specification and estimation of moment structures. Psychometrika 1983, 48:493-517.
7. Bentler P.M. EQS 6 Structural Equations Program Manual 2007, Multivariate Software, Encino, CA.
8. Bentler P.M., Dijkstra T. Efficient estimation via linearization in structural models. Multivariate Analysis VI 1985, 9-42. North-Holland, Amsterdam. P.R. Krishnaiah (Ed.).
9. Bentler P.M., Yuan K.-H. Structural equation modeling with small samples: Test statistics. Multivariate Behavioral Research 1999, 34:181-197.
10. Berkane M., Bentler P.M. Estimation of contamination parameters and identification of outliers in multivariate data. Sociological Methods & Research 1988, 17:55-64.
11. Birch J.B., Myers R.H. Robust analysis of covariance. Biometrics 1982, 38:699-713.
12. Bollen K.A., Arminger G. Observational residuals in factor analysis and structural equation models. Sociological Methodology 1991, 21:235-262.
13. Boomsma A. Nonconvergence, improper solutions, and starting values in LISREL maximum likelihood estimation. Psychometrika 1985, 50:229-242.
14. Browne M.W. A symptotic distribution-free methods for the analysis of covariance structures. British Journal of Mathematical and Statistical Psychology 1984, 37:62-83.
15. Browne M.W. Robustness of statistical inference in factor analysis and related models. Biometrika 1987, 74:375-384.
16. Browne M.W., Arminger G. Specification and estimation of mean and covariance structure models. Handbook of Statistical Modeling for the Social and Behavioral Sciences 1995, 185-249. Plenum, New York. G. Arminger, C.C. Clogg, M.E. Sobel (Eds.).
17. Browne M.W., Shapiro A. Robustness of normal theory methods in the analysis of linear latent variate models. British Journal of Mathematical and Statistical Psychology 1988, 41:193-208.
18. Campbell N.A. Robust procedures in multivariate analysis I: Robust covariance estimation. Applied Statistics 1980, 29:231-237.
19. Carroll R.J. On estimating variances of robust estimators when the errors are asymmetric. Journal of the American Statistical Association 1979, 74:674-679.
20. Chen F., Bollen K.A., Paxton P., Curran P., Kirby J. Improper solutions in structural equation models: Causes, consequences, and strategies. Sociological Methods & Research 2001, 29:468-508.
21. Cui H., He X., Ng K.W. Asymptotic distributions of principal components based on robust dispersions. Biometrika 2003, 90:953-966.
22. Curran P.J., West S.G., Finch J.F. The robustness of test statistics to nonnormality and specification error in confir matory factor analysis. Psychological Methods 1996, 1:16-29.
23. Devlin S.J., Gnanadesikan R., Kettenring J.R. Robust estimation of dispersion matrices and principal components. Journal of the American Statistical Association 1981, 76:354-362.
24. Fang K.-T., Kotz S., Ng K.W. Symmetric Multivariate and Related Distributions 1990, Chapman Hall, London.
25. Ferguson T. A Course in Large Sample Theory 1996, Chapman Hall, London.
26. Fung W.K. Unmasking outliers and leverage points: A confirmation. Journal of the American Statistical Association 1993, 88:515-519.
27. Geary R.C. Testing for normality. Biometrika 1947, 34:209-242.
28. Gourieroux C., Monfort A, Trognon A. Pseudo maximum likelihood methods: Theory. Econometrica 1984, 52:681-700.
29. Green P.J. Iteratively reweighted least squares for maximum likelihood estimation, and some robust and resistant alternatives (with discussion). Journal of the Royal Statistical Society B 1984, 46:149-192.
30. Gross A.M. Confidence intervals for bisquare regression estimates. Journal of the American Statistical Association 1977, 72:341-354.
31. Hampel F.R. The influence curve and its role in robust estimation. Journal of the American Statistical Association 1974, 69:383-393.
32. Hampel F.R., Ronchetti E.M., Rousseeuw P.J., Stahel W.A. Robust Statistics: The Approach Based on Influence Functions 1986, Wiley, New York.
33. Holland P.W., Welsch R.E. Robust regression using iteratively reweighted least-squares. Communications in Statistics-Theory and Methods A 1977, 6:813-827.
34. Holzinger K.J., Swineford F. A Study in Factor Analysis: The Stability of a Bi-Factor Solution. Supplementary Educational Monographs 1939, vol. 48. University of Chicago.
35. Hoshino T. Bayesian inference for finite mixtures in confirmatory factor analysis. Behaviormetrika 2001, 28:37-63.
36. Hu L.T., Bentler P.M., Kano Y. Can test statistics in covariance structure analysis be trusted?. Psychological Bulletin 1992, 112:351-362.
37. Huber P.J. Robust estimation of a location parameter. Annals of Mathematical Statistics 1964, 35:73-101.
38. Huber P.J. The behavior of maximum likelihood estimates under nonstandard conditions. Proceedings of the Fifth Berkeley Symposium on Mathematical Statistics and Probability 1967, 221-233. University of California Press, Berkeley, CA.
39. Huber P.J. Robust regression: Asymptotics, conjectures and Monte Carlo. Annals of Statistics 1973, 1:799-821.
40. Huber P.J. Robust Statistics 1981, Wiley, New York.
41. Theory and Applications of Recent Robust Methods 2004, Springer-Verlag, Berlin. M. Hubert, G. Pison, A. Struyf, S. Van Aelst (Eds.).
42. Hubert M., Rousseeuw P.J., Vanden Branden K. ROBPCA: A new approach to robust principal component analysis. Technometrics 2005, 47:64-79.
43. Ibazizen M., Dauxois J. A robust principal component analysis. Statistics 2003, 37:73-83.
44. Jöreskog K.G. A general approach to confirmatory maximum likelihood factor analysis. Psychometrika 1969, 34:183-202.
45. Jöreskog K.G., Sörbom D. LISREL 8 Users's Reference Guide 1996, Scientific Software International, Chicago.
46. Kano Y. Conditions on consistency of estimators in covariance structure model. Journal of the Japan Statistical Society 1986, 16:75-80.
47. Kano Y. Robust statistics for test-of-independence and related structural models. Statistics & Probability Letters 1992, 15:21-26.
48. Kano Y. Improper solutions in exploratory factor analysis: Causes and treatments. Advances in Data Sciences and Classification 1998, 375-382. Springer-Verlag, Berlin. A. Rizzi, M. Vichi, H. Bock (Eds.).
49. Kano Y., Berkane M., Bentler P.M. Statistical inference based on pseudo-maximum likelihood estimators in elliptical populations. Journal of the American Statistical Association 1993, 88:135-143.
50. Lee S.-Y., Song X.Y. Bayesian model selection for mixtures of structural equation models with an unknown number of components. British Journal of Mathematical and Statistical Psychology 2003, 56:145-165.
51. Lee S.-Y., Wang S.J. Sensitivity analysis of structural equation models. Psychometrika 1996, 61:93-108.
52. Lee, S.-Y., Xia, Y.-M. (In press). Maximum likelihood methods in treating outliers and symmetrically heavytailed distributions for nonlinear structural equation models with missing data. Psychometrika.
53. Lopuhaä H.P. On the relation between S-estimators and M-estimators of multivariate location and covariances. Annals of Statistics 1989, 17:1662-1683.
54. Lopuhaä H.P. τ-estimators for location and scatter. Canadian Journal of Statistics 1991, 19:307-321.
55. Handbook of Statistics 15: Robust Inference 1997, Elsevier, Amsterdam. G.S. Maddala, C.R. Rao (Eds.).
56. Mardia K.V. Measures of multivariate skewness and kurtosis with applications. Biometrika 1970, 57:519-530.
57. Maronna R.A. Robust M-estimators of multivariate location and scatter. Annals of Statistics 1976, 4:51-67.
58. Micceri T. The unicorn, the normal curve, and other improbable creatures. Psychological Bulletin 1989, 105:156-166.
59. Mooijaart A., Bentler P.M. Robustness of normal theory statistics in structural equation models. Statistica Neerlandica 1991, 45:159-171.
60. Muirhead R.J., Waternaux C.M. Asymptotic distributions in canonical correlation analysis and other multivariate procedures for nonnormal populations. Biometrika 1980, 67:31-43.
61. Muthén B. Latent variable mixture modeling. New Developments and Techniques in Structural Equation Modeling 2001, 1-34. Erlbaum, Mathwah, NJ. G.A. Marcoulides, R.E. Schumacker (Eds.).
62. Pison G., Rousseeuw P.J., Filzmoser P., Croux C. Robust factor analysis. Journal of Multivariate Analysis 2003, 84:145-172.
63. Poon W.Y., Poon Y.S. Influential observations in the estimation of mean vector and covariance matrix. British Journal of Mathematical and Statistical Psychology 2002, 55:177-192.
64. Poon W.Y., Wong Y.K. A forward search procedure to identifying influential observations in the estimation of covariance matrix. Structural Equation Modeling 2004, 11:357-374.
65. Poon W.Y., Lew S.F., Poon Y.S. A local influence approach to identity multiple multivariate outliers. British Journal of Mathematical and Statistical Psychology 2000, 53:255-273.
66. Rao C.R. Linear Statistical Inference and its Applications 1973, Wiley, New York. second ed.
67. Rindskopf D. Structural equation models: Empirical identification, Heywood cases, and related problems. Sociological Methods & Research 1984, 13:109-119.
68. Rocke D.M. Robustness properties of S-estimators of multivariate location and shape in high dimension. Annals of Statistics 1996, 24:1327-1345.
69. Rousseeuw P.J., Leroy A.M. Robust Regression and Outlier Detection 1987, Wiley, New York.
70. Rousseeuw P.J., van Zomeren B.C. Unmasking multivariate outliers and leverage points (with discussion). Journal of the American Statistical Association 1990, 85:633-651.
71. Rubin D.B. Iteratively reweighted least squares. Encyclopedia of Statistical Sciences 1983, vol. 4:272-275. Wiley, New York. N.L. Johnson, S. Kotz (Eds.).
72. Ruymgaart F.H. A robust principal component analysis. Journal of Multivariate Analysis 1981, 11:485-497.
73. Satorra A. Asymptotic robust inferences in the analysis of mean and covariance structures. Sociological Methodology 1992, 22:249-278.
74. Satorra A., Bentler P.M. Some robustness properties of goodness of fit statistics in covariance structure analysis. American Statistical Association 1986 Proceedings of Business and Economics Sections 1986, 549-554. American Statistical Association.
75. Satorra A., Bentler P.M. Scaling corrections for chi-square statistics in covariance structure analysis. American Statistical Association 1988 Proceedings of Business and Economics Sections 1988, 308-313. American Statistical Association.
76. Satorra A., Bentler P.M. Model conditions for asymptotic robustness in the analysis of linear relations. Computational Statistics & Data Analysis 1990, 10:235-249.
77. Satorra A., Bentler P.M. Corrections to test statistics and standard errors in covariance structure analysis. Latent Variables Analysis: Applications for Developmental Research 1994, 399-419. Sage, Thousand Oaks, CA. A. von Eye, C.C. Clogg (Eds.).
78. Satorra A., Saris W. Power of the likelihood ratio test in covariance structure analysis. Psychometrika 1985, 50:83-90.
79. Shapiro A. Asymptotic distribution theory in the analysis of covariance structures (a unified approach). South African Statistical Journal 1983, 17:33-81.
80. Shapiro A. A note on the consistency of estimators in the analysis of moment structures. British Journal of Mathematical and Statistical Psychology 1984, 37:84-88.
81. Shapiro A., Browne M. Analysis of covariance structures under elliptical distributions. Journal of the American Statistical Association 1987, 82:1092-1097.
82. Sörbom D. Model modification. Psychometrika 1989, 54:371-384.
83. Steiger J.H., Shapiro A., Browne M.W. On the multivariate asymptotic distribution of sequential chi-square statistics. Psychometrika 1985, 50:253-264.
84. Stone M. Cross-validation choice and assessment of statistical predictions. Journal of the Royal Statistical Society B 1974, 36:44-47.
85. Stroud T.W.F. Fixed alternatives and Wald's formulation of the noncentral asymptotic behavior of the like lihood ratio statistic. Annals of Mathematical Statistics 1972, 43:447-454.
86. Sugiura N. Asymptotic expansions of the distributions of the likelihood ratio criteria for covariance matrix. Annals of Mathematical Statistics 1969, 40:2051-2063.
87. Tyler D.E. Robustness and efficiency properties of scatter matrices. Biometrika 1983, 70:411-420.
88. van Driel O.P. On various causes of improper solutions in maximum like lihood factor analysis. Psychometrika 1978, 43:225-243.
89. Vuong Q.H. Likelihood ratio tests for model selection and nonnested hypotheses. Econometrica 1989, 57:307-333.
90. Wald A. Tests of statistical hypotheses concerning several parameters when the number of observations is large. Transactions of the American Mathematical Society 1943, 54:426-482.
91. White H. Maximum likelihood estimation of misspecified models. Econometrica 1982, 50:1-25.
92. Wilcox R.R. Introduction to Robust Estimation and Hypothesis Testing 2004, Academic Press, San Diego. second ed.
93. Yanagihara H., Tonda T., Matsumoto C. The effects of nonnormality on asymptotic distributions of some likelihood ratio criteria for testing covariance structures under normal assumption. Journal of Multivariate Analysis 2005, 96:237-264.
94. Yuan K.-H., Bentler P.M. Mean and covariance structure analysis: Theoretical and practical improvements. Journal of the American Statistical Association 1997, 92:767-774.
95. Yuan K.-H., Bentler P.M. Improving parameter tests in covariance structure analysis. Computational Statistics and Data Analysis 1997, 26:177-198.
96. Yuan K.-H., Bentler P.M. Normal theory based test statistics in structural equation modeling. British Journal of Mathematical and Statistical Psychology 1998, 51:289-309.
97. Yuan K.-H., Bentler P.M. Robust mean and covariance structure analysis. British Journal of Mathematical and Statistical Psychology 1998, 51:63-88.
98. Yuan K.-H., Bentler P.M. Structural equation modeling with robust covariances. Sociological Methodology 1998, 28:363-396.
99. Yuan K.-H., Bentler P.M. On normal theory and associated test statistics in covariance structure analysis under two classes of nonnormal distributions. Statistica Sinica 1999, 9:831-853.
100. Yuan K.-H., Bentler P.M. On asymptotic distributions of normal theory MLE in covariance structure analysis under some nonnormal distributions. Statistics & Probability Letters 1999, 42:107-113.
101. Yuan K.-H., Bentler P.M. F-tests for mean and covariance structure analysis. Journal of Educational and Behavioral Statistics 1999, 24:225-243.
102. Yuan K.-H., Bentler P.M. Inferences on correlation coefficients in some classes of nonnormal distributions. Journal of Multivariate Analysis 2000, 72:230-248.
103. Yuan K.-H., Bentler P.M. Three likelihood-based methods for mean and covariance structure analysis with nonnormal missing data. Sociological Methodology 2000, 30:167-202.
104. Yuan K.-H., Bentler P.M. Robust mean and covariance structure analysis through iteratively reweighted least squares. Psychometrika 2000, 65:43-58.
105. Yuan K.-H., Bentler P.M. A unified approach to multigroup structural equation modeling with nonstandard samples. Advanced Structural Equation Modeling: New Development and Techniques 2001, 35-56. Lawrence Erlbaum Associates, Mahwah, NJ. G.A. Marcoulides, R.E. Schumacker (Eds.).
106. Yuan K.-H., Bentler P.M. Effect of outliers on estimators and tests in covariance structure analysis. British Journal of Mathematical and Statistical Psychology 2001, 54:161-175.
107. Yuan K.-H., Bentler P.M. On robustness of the normal-theory based asymptotic distributions of three reliability coefficient estimates. Psychometrika 2002, 67:251-259.
108. Yuan K.-H., Bentler P.M. Mean comparison: Manifest variable versus latent variable. Psychometrika 2006, 71:139-159.
109. Yuan K.-H., Chan W. On nonequivalence of several procedures of structural equation modeling. Psychometrika 2005, 70:791-798.
110. Yuan K.-H., Hayashi K. Bootstrap approach to inference and power analysis based on three statistics for covariance structure models. British Journal of Mathematical and Statistical Psychology 2003, 56:93-110.
111. Yuan K.-H., Hayashi K. Standard errors in covariance structure models: Asymptotics versus bootstrap. British Journal of Mathematical and Statistical Psychology 2006, 59:397-417.
112. Yuan K.-H., Jennrich R.I. Asymptotics of estimating equations under natural conditions. Journal of Multivariate Analysis 1998, 65:245-260.
113. Yuan K.-H., Chan W., Bentler P.M. Robust transformation with applications to structural equation modeling. British Journal of Mathematical and Statistical Psychology 2000, 53:31-50.
114. Yuan K.-H., Marshall L.L., Bentler P.M. A unified approach to exploratory factor analysis with missing data, nonnormal data, and in the presence of outliers. Psychometrika 2002, 67:95-122.
115. Yuan K.-H., Marshall L.L., Weston R. Cross-validation through downweighting influential cases in structural equation modeling. British Journal of Mathematical and Statistical Psychology 2002, 55:125-143.
116. Yuan K.-H., Marshall L.L., Bentler P.M. Assessing the effect of model misspecifications on parameter estimates in structural equation models. Sociological Methodology 2003, 33:241-265.
117. Yuan K.-H., Bentler P.M., Chan W. Structural equation modeling with heavy tailed distributions. Psychometrika 2004, 69:421-436.
118. Yuan K.-H., Fung W.K., Reise S. Three Mahalanobis-distances and their role in assessing unidimensionality. British Journal of Mathematical and Statistical Psychology 2004, 57:151-165.
119. Yuan K.-H., Kouros C.D., Kelley K. Diagnosis for covariance structure models by analyzing the path. Under review 2005.
120. Yuan, K.-H., Hayashi, K., Bentler, P.M. (In press). Normal theory likelihood ratio statistic for mean and covariance structure analysis under alternative hypotheses. Journal of Multivariate Analysis.
121. Yung Y.-F. Finite mixtures in confirmatory factor-analysis models. Psychometrika 1997, 62:297-330.