Maximum likelihood estimation of factor analysis using the ECME algorithm with complete and incomplete data

Statistica Sinica

Volumn 8, Issue 3, 1998, Pages 729-747

  Liu, Chuanhai ^a,b   Rubin, Donald B ^a,c  

^a HARVARD UNIVERSITY   (United States)

^b LUCENT TECHNOLOGIES   (United States)

^c HARVARD UNIVERSITY   (United States)

Author keywords

ECM; EM; Incomplete data; Missing data

Indexed keywords

EID: 0032397180     PISSN: 10170405     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article

References (26)

1. Anderson, T. W. (1984). An Introduction to Multivariate Statistical Analysis. John Wiley, New York.
2. Basilevsky, A. (1994). Statistical factor Analysis and Related Methods. John Wiley, New York.
3. Bentler, P. M. and Tanaka, J. S. (1983). Problems with EM algorithms for ML factor analysis. Psychometrika 48, 247-251.
4. Clarke, M. R. B. (1970). A rapidly convergent method for maximum-likelihood factor analysis. British J. Math. Statist. Psych. 23, 43-52.
5. Dempster, A. P., Laird, N. M. and Rubin, D. B. (1977). Maximum likelihood estimation from incomplete data via the EM algorithm (with discussion). J. Roy. Statist. Soc. Ser. B 39, 1-38.
6. Efron, B. (1994). Missing data, imputation, and the bootstrap (with discussion). J. Amer. Statist. Assoc. 89, 463-479.
7. Jamshidian, M. and Jennrich, R. I. (1993). Conjugate gradient acceleration of the EM algorithm. J. Amer. Statist. Assoc. 88, 221-228.
8. Jennrich, R. I. and Robinson, S. M. (1969). A newton-raphson algorithm for maximum likelihood factor analysis. Psychometrika 34, 111-123.
9. Jöreskog, K. G. (1967). Some contributions to maximum likelihood factor analysis. Psychometrika 32, 443-482.
10. Jöreskog, K. G. and Sörbom, D. (1988). LISREL-7: A guide to the program and applications (2nd edition). Chicago: SPSS.
11. Little, R. J. A. and Rubin, D. B. (1987). Statistical Analysis with Missing Data. John Wiley, New York.
12. Liu, C. (1996). Maximum likelihood estimation of factor analysis with fixed and random effects from incomplete data, Technical report, Statistics Research Department, Bell Laboratories, Lucent Technologies.
13. Liu, C. and Rubin, D. B. (1994). The ECME algorithm: A simple extension of EM and ECM with faster monotone convergence. Biometrika 81, 633-648.
14. Liu, C. and Rubin, D. B. (1998). Estimation of ellipsoidal distributions from singular incomplete data. Technical report. Bell-Labs.
15. Liu, C., Rubin, B. D. and Wu, Y. (1998). Parameter expansion to accelerate EM - the PX-EM algorithm. Biometrika 85, to appear.
16. Longford, N. T. and Muthén, B. O. (1992). Factor analysis for clustered observations. Psychometrika 57, 581-597.
17. Mardia, K. V., Kent, J. T. and Bibby, J. M. (1979). Multivariate Analysis. Academic Press, New York.
18. Meng, X.-L. and Rubin, D. B. (1991). Using EM to obtain asymptotic variance-covariance matrices: the SEM algorithm. J. Amer. Statist. Assoc. 86, 899-909.
19. Meng, X.-L. and Rubin, D. B. (1993). Maximum likelihood estimation via the ECM algorithm: A general framework. Biometrika 80, 267-278.
20. Meng, X.-L. and van Dyk, D. (1997). The EM algorithm - an old folk song sung to a fast new tune (with discussion). J. Roy. Statist. Soc. Ser. B 59, 511-567.
21. Meredith, W. (1993). Measurement invariance, factor analysis and factorial invariance. Psychometrika 58, 525-543.
22. Rubin, D. B. (1976). Inference and missing data. Biometrika 63, 581-592.
23. Rubin, D. B. (1994). Comment on "Missing data, imputation, and the bootstrap". J. Amer. Statist. Assoc. 89, 475-478.
24. Rubin, D. B. and Thayer, D. T. (1982). EM algorithm for ML factor analysis. Psychometrika 47, 69-76.
25. Rubin, D. B. and Thayer, D. T. (1983). More on EM for ML factor analysis. Psychometrika 48, 253-257.
26. van Dyk, D. A., Meng, X.-L. and Rubin, D. B. (1995). Maximum likelihood estimation via the ECM algorithm: computing the asymptotic variance. Statist. Sinica 5, 55-75.