Variable selection via the weighted group lasso for factor analysis models

Canadian Journal of Statistics

Volumn 40, Issue 2, 2012, Pages 345-361

  Hirose, Kei ^a   Konishi, Sadanori ^b  

^a OSAKA UNIVERSITY   (Japan)

^b CHUO UNIVERSITY   (Japan)

Author keywords

Factor analysis; L 1 regularization; MSC 2010: Primary 62H25; Number of factors; Secondary 62J07; Variable selection; Weighted group lasso

Indexed keywords

EID: 84861211116     PISSN: 03195724     EISSN: 1708945X     Source Type: Journal    
DOI: 10.1002/cjs.11129     Document Type: Article

References (31)

1. Akaike, H. (1973). Information theory and an extension of the maximum likelihood principle. 2nd International Symposium on Information Theory, Petrovand, B. N. & Csaki, F., editors. Akademiai Kiado, Budapest, pp. 267-281.
2. Akaike, H. (1987). Factor analysis and AIC. Psychometrika, 52, 317-332.
3. Anderson, T. W. (2003). An Introduction to Multivariate Statistical Analysis, 3rd ed., Wiley, New York.
4. Anderson, T. W. & Rubin, H. (1956). Statistical inference in factor analysis. In Proceedings of the Third Berkeley Symposium on Mathematical Statistics and Probability, Neyman, J., editor. University of California Press, Berkeley, 5, pp. 111-150.
5. Clarke, M. R. B. (1970). A rapidly convergent method for maximum-likelihood factor analysis. British Journal of Mathematical and Statistical Psychology, 23, 43-52.
6. Efron, B., Hastie, T., Johnstone, I., & Tibshirani, R. (2004). Least angle regression (with discussion). Annals of Statistics, 32, 407-499.
7. Fan, J. & Li, R. (2001). Variable selection via nonconcave penalized likelihood and its oracle properties. Journal of the American Statistical Association, 96, 1348-1360.
8. Gorsuch, R. L. (1988). Exploratory factor analysis. Handbook of multivariate experimental psychology, 2nd ed., Plenum Press, New York and London, pp. 231-258.
9. Ichikawa, M. & Konishi, S. (1999). Model evaluation and information criteria in covariance structure analysis. British Journal of Mathematical and Statistical Psychology, 52, 285-302.
10. Jennrich, R. I. & Robinson, S. M. (1969). A Newton-Raphson algorithm for maximum likelihood factor analysis. Psychometrika, 34, 111-123.
11. Jöreskog, K. G. (1967). Some contributions to maximum likelihood factor analysis. Psychometrika, 32, 443-482.
12. Kaiser, H. F. (1958). The varimax criterion for analytic rotation in factor analysis. Psychometrika, 23, 187-200.
13. Kano, Y. & Harada, A. (2000). Stepwise variable selection in factor analysis. Psychometrika, 65, 7-22.
14. Kano, Y. & Ihara, M. (1994). Identification of inconsistent variates in factor analysis. Psychometrika, 59, 5-20.
15. Kendall, M. G. (1980). Multivariate Analysis, 2nd ed., Charles Griffin, London.
16. Konishi, S., Ando, T., & Imoto, S. (2004). Bayesian information criteria and smoothing parameter selection in radial basis function networks. Biometrika, 91, 27-43.
17. Konishi, S. & Kitagawa, G. (2008). Information Criteria and Statistical Modeling, Springer, New York.
18. Lopes, H. & West, M. (2004). Bayesian model assessment in factor analysis. Statistica Sinica, 14, 41-67.
19. Rubin, D. B. & Thayer, D. T. (1982). EM algorithms for ML factor analysis.Psychometrika, 47, 69-76.
20. Schwarz, G. (1978). Estimating the dimension of a model. Annals of Statistics, 6, 461-464.
21. Shimamura, T., Imoto, S., Yamaguchi, R., & Miyano, S. (2007). Weighted lasso in graphical Gaussian modeling for large gene network estimation based on microarray data. Genome Informatics, 19, 142-153.
22. Tanaka, Y. (1983). Some criteria for variable selection in factor analysis. Behaviormetrika, 13, 31-45.
23. Tateishi, S., Matsui, H., & Konishi, S. (2010). Nonlinear regression modeling via the lasso-type regularization. Journal of Statistical Planning and Inference, 140, 1125-1134.
24. Tibshirani, R. (1996). Regression shrinkage and selection via the lasso. Journal of the Royal Statistical Society Series B, 58, 267-288.
25. Tierny, L. & Kanade, J. B. (1986). Accurate approximations for posterior moments and marginal densities. Journal of the American Statistical Association, 81, 82-86.
26. van Driel, O. P. (1978). On various causes of improper solutions in maximum likelihood factor analysis. Psychometrika, 43, 225-243.
27. Yanai, H. (1980). A proposition of generalized method for forward selection of variables. Behaviormetrika, 7, 95-107.
28. Yuan, M. & Lin, Y. (2006). Model selection and estimation in regression with grouped variables. Journal of the Royal Statistical Society Series B, 68, 49-67.
29. Zou, H. (2006). The adaptive Lasso and its oracle properties. Journal of the American Statistical Association, 101, 1418-1429.
30. Zou, H. & Hastie, T. (2005). Regularization and variable selection via the elastic net. Journal of the Royal Statistical Society Series B, 67, 301-320.
31. Zou, H., Hastie, T., & Tibshirani, R. (2007). On the "degrees of freedom" of the lasso. Annals of Statistics, 35, 2173-2192.