Three likelihood-based methods for mean and covariance structure analysis with nonnormal missing data

Sociological Methodology

Volumn 30, Issue 1, 2000, Pages 165-200

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

^a UNIVERSITY OF NORTH TEXAS   (United States)

^b UNIVERSITY OF CALIFORNIA   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0034555721     PISSN: 00811750     EISSN: None     Source Type: Journal    
DOI: 10.1111/0081-1750.00078     Document Type: Article

References (75)

1. Allison, Paul D. 1987. "Estimation of Linear Models with Incomplete Data." Pp. 71-103 in Sociological Methodology 1987, edited by C.C. Clogg. San Francisco: Jossey-Bass.
2. Amemiya, Yasuo, and Theodore W. Anderson. 1990. "Asymptotic Chi-Square Tests for a Large Class of Factor Analysis Models." Annals of Statistics 18:1453-63.
3. Anderson, Theodore W. 1957. "Maximum Likelihood Estimates for the Multivariate Normal Distribution When Some Observations are Missing." Journal of the American Statistical Association 52:200-203.
4. Anderson, Theodore W., and Yasuo Amemiya. 1988. "The Asymptotic Normal Distribution of Estimators in Factor Analysis Under General Conditions." Annals of Statistics 16:759-71.
5. Arbuckle, James L. 1996. "Full Information Estimation in the Presence of Incomplete Data." Pp. 243-77 in Advanced Structural Equation Modeling: Issues and Techniques, edited by G.A. Marcoulides and R.E. Schumacker. Mahwah, NJ: Lawrence Erlbaum.
6. Arminger, Gerhard, and Ronald Schoenberg. 1989. "Pseudo Maximum Likelihood Estimation and a Test for Misspecification in Mean and Covariance Structure Models." Psychometrika, 54:409-26.
7. Arminger, Gerhard, and Michael E. Sobel. 1990. "Pseudo-Maximum Likelihood Estimation of Mean and Covariance Structures with Missing Data." Journal of the American Statistical Association 85:195-203.
8. Beale, Evelyn M.L., and Roderick J.A. Little. 1975. "Missing Data in Multivariate Analysis." Journal of the Royal Statistical Society, ser. B, 37:129-45.
9. Bentler, Peter M. 1983. "Some Contributions to Efficient Statistics in Structural Models: Specification and Estimation of Moment Structures." Psychometrika 48:493-517.
10. _. 1995. EQS Structural Equations Program Manual. Encino, CA: Multivariate Software.
11. _. In press. EQS 6 Structural Equations Program Manual. Encino, CA: Multivariate Software.
12. Bentler, Peter M., and Theo K. Dijkstra. 1985. "Efficient Estimation via Linearization in Structural Models." Pp. 9-42 in Multivariate Analysis VI, edited by P.R. Krishnaiah. Amsterdam: North-Holland.
13. Bentler, Peter M., and Ke-Hai Yuan. 1999. "Structural Equation Modeling with Small Samples: Test Statistics." Multivariate Behavioral Research 34:181-97.
14. Bollen, Kenneth A. 1989. Structural Equations with Latent Variables. New York: Wiley.
15. Bollen, Kenneth A. and Robert Stine. 1993. "Bootstrapping Goodness-of-fit Measures in Structural Equation Models." Pp. 111-135 in Testing Structural Equation Models, edited by K.A. Bollen and J.S. Long. Newbury Park, CA: Sage.
16. Brown, C. Hendricks. 1983. "Asymptotic Comparison of Missing Data Procedures for Estimating Factor Loadings." Psychometrika 48:269-91.
17. Brown, Roger L. 1994. "Efficacy of the Indirect Approach for Estimating Structural Equation Models with Missing Data: A Comparison of Five Methods." Structural Equation Modeling 1:287-316.
18. Browne, Michael W. 1984. "Asymptotic Distribution-free Methods for the Analysis of Covariance Structures." British Journal of Mathematical and Statistical Psychology 37:62-83.
19. _. 1987. "Robustness of Statistical Inference in Factor Analysis and Related Models." Biometrika 74:375-84.
20. Browne, Michael W., and Gerhard Arminger. 1995. "Specification and Estimation of Mean and Covariance Structure Models." Pp. 185-249 in Handbook of Statistical Modeling for the Social and Behavioral Sciences, edited by G. Arminger, C.C. Clogg, and M.E. Sobel. New York: Plenum.
21. Browne, Michael W., and Alexander Shapiro. 1988. "Robustness of Normal Theory Methods in the Analysis of Linear Latent Variate Models." British Journal of Mathematical and Statistical Psychology 41:193-208.
22. Curran, Patrick S., Stephen G. West, and John F. Finch. 1996. "The Robustness of Test Statistics to Nonnormality and Specification Error in Confirmatory Factor Analysis." Psychological Methods 1:16-29.
23. Dempster, Arthur P., Nan M. Laird, and Donald B. Rubin. 1977. "Maximum Likelihood Estimation from Incomplete Data via the EM Algorithm" (with discussion). Journal of the Royal Statistical Society, ser. B, 39:1-38.
24. Dijkstra, Theo K. 1981. Latent Variables in Linear Stochastic Models: Reflections on "Maximum Likelihood" and "Partial Least Squares" Methods. Ph.D. dissertation, University of Groningen.
25. Fang, Kai-Tai, Samuel Kotz, and Kaiwang Ng. 1990. Symmetric Multivariate and Related Distributions. London: Chapman and Hall.
26. Ferguson, Thomas S. 1996. A Course in Large Sample Theory. London: Chapman and Hall.
27. Finkbeiner, Carl. 1979. "Estimation for the Multiple Factor Model When Data Are Missing." Psychometrika 44:409-20.
28. Godambe, Vidyadhar P., and Belvant K. Kale. 1991. "Estimating Function: An Overview." Pp. 3-20 in Estimating Functions, edited by V.P. Godambe. New York: Oxford University Press.
29. Gourieroux, Christian, Alain Monfort, and Alain Trognon. 1984. "Pseudo Maximum Likelihood Methods: Theory." Econometrica 52:681-700.
30. Hu, Litze, Peter M. Bentler, and Yutaka Kano. 1992. "Can Test Statistics in Covariance Structure Analysis Be Trusted?" Psychological Bulletin 112:351-62.
31. Jamshidian, Mortaza, and Peter M. Bentler. 1999. "Using Complete Data Routines for ML Estimation of Mean and Covariance Structures with Missing Data." Journal of Educational and Behavioral Statistics 23:21-41.
32. Jöreskog, Karl G., and Dag Sörbom. 1993. LISREL 8 User's Reference Guide, Chicago: Scientific Software International.
33. Khatri, C. G. 1966. "A Note on a MANOVA Model Applied to Problems in Growth Curves." Annals of the Institute of Statistical Mathematics 18:75-86.
34. Kline, Rex B. 1998. Principles and Practice of Structural Equation Modeling. New York: Guilford.
35. Laird, Nan M. 1988. "Missing Data in Longitudinal Studies." Statistics in Medicine 7: 305-15.
36. Lange, Kenneth L., Roderick J.A. Little, and Jeremy M.G. Taylor. 1989. "Robust Statistical Modeling Using the t Distribution." Journal of the American Statistical Association 84:881-96.
37. Lee, Sik-Yum. 1986. "Estimation for Structural Equation Models with Missing Data." Psychometrika 51:93-99.
38. Liang, Kung-Yee, and Scott L. Zeger. 1986. "Longitudinal Data Analysis Using Generalized Linear Models." Biometrika 73:13-22.
39. Little, Roderick J.A. 1988. "Robust Estimation of the Mean and Covariance Matrix from Data with Missing Values." Applied Statistics 37:23-38.
40. Little, Roderick J.A., and Donald E. Rubin. 1987. Statistical Analysis with Missing Data. New York: Wiley.
41. Magnus, Jan R., and Heinz Neudecker. 1988. Matrix Differential Calculus with Applications in Statistics and Econometrics. New York: Wiley.
42. Mardia, Kanti V., John T. Kent, and John M. Bibby. 1979. Multivariate Analysis. New York: Academic Press.
43. Marsh, Herbert W. 1998. "Pairwise Deletion for Missing Data in Structural Equation Models: Nonpositive Definite Matrices, Parameter Estimates, Goodness of Fit, and Adjusted Sample Sizes." Structural Equation Modeling 5:22-36.
44. Meng, Xiao-Li. 1994. "Multiple Imputation Inferences with Uncongenial Sources of Input" (with discussion). Statistical Science 9:538-73.
45. Meng, Xiao-Li, and Steven Pedlow. 1992. "EM: A Bibliographic Review with Missing Articles." Pp. 24-27 in Statistical Computing Section, Proceedings of the American Statistical Association.
46. Micceri, Theodore. 1989. "The Unicorn, the Normal Curve, and Other Improbable Creatures." Psychological Bulletin 105:156-66.
47. Mooijaart, Ab, and Peter M. Bentler. 1991. "Robustness of Normal Theory Statistics in Structural Equation Models." Statistica Neerlandica 45:159-71.
48. Mueller, Ralph O. 1996. Basic Principles of Structural Equation Modeling. New York: Springer Verlag.
49. Muirhead, R. J. 1982. Aspects of Multivariate Statistical Theory. New York: Wiley.
50. Muirhead, Robb J., and Christine M. Waternaux. 1980. "Asymptotic Distributions in Canonical Correlation Analysis and Other Multivariate Procedures for Nonnormal Populations." Biometrika 67:31-43.
51. Muthén, Bengt, David Kaplan, and Michael Hollis. 1987. "On Structural Equation Modeling with Data that Are Not Missing Completely at Random." Psychometrika 52:431-62.
52. Muthén, Linda, and Bengt Muthén. 1998. Mplus User's Guide. Los Angeles: Muthén and Muthén.
53. Neale, Michael C. 1994. "Mx: Statistical Modeling," 2nd ed. Box 710 MCV, Richmond, VA 23298: Department of Psychiatry, Medical College of Virginia.
54. Olkin, Ingram. 1994. "Multivariate Nonnormal Distributions and Models of Dependency." Pp. 37-53 in Multivariate Analysis and Its Applications, edited by T.W. Anderson, K.T. Fang, and I. Olkin. Hayward, CA: IMS.
55. Rotnitzky, Andrea, and David Wypij. 1994. "A Note on the Bias of Estimators with Missing Data." Biometrics 50:1163-70.
56. Rovine, Michael J. 1994. "Latent Variables Models and Missing Data Analysis." Pp. 181-225 in Latent Variables Analysis: Applications for Developmental Research, edited by A. von Eye and C.C. Clogg. Thousand Oaks, CA: Sage.
57. Rubin, Donald B. 1987. Multiple Imputation for Nonresponse in Surveys. New York: Wiley.
58. _. 1996. "Multiple Imputation after 18 Years." Journal of the American Statistical Association 91:473-89.
59. Satorra, Albert, and Peter M. Bentler. 1988. "Scaling Corrections for Chi-Square Statistics in Covariance Structure Analysis." Pp. 308-13 in American Statistical Association 1988 Proceedings of Business and Economics Sections. Alexandria, VA: American Statistical Association.
60. _. 1990. "Model Conditions for Asymptotic Robustness in the Analysis of Linear Relations." Computational Statistics and Data Analysis 10:235-49.
61. _. 1991. "Goodness-of-fit Test under IV Estimation: Asymptotic Robustness of a NT Test Statistic." Pp. 555-67 in Applied Stochastic Models and Data Analysis, edited by R. Gutiérrez and M.J. Valderrama. Singapore: World Scientific.
62. _. 1994. "Corrections to Test Statistics and Standard Errors in Covariance Structure Analysis." Pp. 399-419 in Latent Variables Analysis: Applications for Developmental Research, edited by A. von Eye and C.C. Clogg. Newbury Park, CA: Sage.
63. Schafer, Joseph L. 1997. Analysis of Incomplete Multivariate Data. London: Chapman and Hall.
64. Schoenberg, Ronald. 1989. LINCS: Linear Covariance Structure Analysis. User's Guide. Kent, WA: RJS Software.
65. Shapiro, Alexander. 1983. "Asymptotic Distribution Theory in the Analysis of Covariance Structures (a Unified Approach)." South African Statistical Journal 17:33-81.
66. _. 1987. "Robustness Properties of the MDF Analysis of Moment Structures." South African Statistical Journal 21:39-62.
67. Shapiro, Alexander, and Michael Browne. 1987. "Analysis of Covariance Structures under Elliptical Distributions." Journal of the American Statistical Association 82:1092-97.
68. Tanaka, Yutaka, Shingo Watadani, and Sung Ho Moon. 1991. "Influence in Covariance Structure Analysis: With an Application to Confirmatory Factor Analysis." Communication in Statistics-Theory and Method 20:3805-21.
69. Yuan, Ke-Hai, and Peter M. Bentler. 1996. "Mean and Covariance Structure Analysis with Missing Data." Pp. 307-26 in Multidimensional Statistical Analysis and Theory of Random Matrices: Proceedings of Sixth Eugene Lukacs Symposium, edited by A. Gupta and V. Girko. Utrecht, Netherlands: VSP.
70. _. 1997a. "Mean and Covariance Structure Analysis: Theoretical and Practical Improvements." Journal of the American Statistical Association 92:767-74.
71. _. 1997b. "Improving Parameter Tests in Covariance Structure Analysis." Computational Statistics and Data Analysis 26:177-98.
72. _. 1998. "Normal Theory Based Test Statistics in Structural Equation Modelling." British Journal of Mathematical and Statistical Psychology 51:289-309.
73. _. 1999. "On Normal Theory and Associated Test Statistics in Covariance Structure Analysis Under Two Classes of Nonnormal Distributions." Statistica Sinica 9:831-53.
74. Yuan, Ke-Hai, and Robert I. Jennrich. 1998. "Asymptotics of Estimating Equations Under Natural Conditions." Journal of Multivariate Analysis 65:245-60.
75. Yung, Yiu-Fai, and Peter M. Bentler. 1996. "Bootstrapping Techniques in Analysis of Mean and Covariance Structures." Pp. 195-226 in Advanced Structural Equation Modeling Techniques, edited by G.A. Marcoulides & R.E. Schumacker. Mahwah, NJ: Erlbaum.