Abstract
We consider the problem of sparse estimation in a factor analysis model. A traditional estimation procedure in use is the following two-step approach: the model is estimated by maximum likelihood method and then a rotation technique is utilized to find sparse factor loadings. However, the maximum likelihood estimates cannot be obtained when the number of variables is much larger than the number of observations. Furthermore, even if the maximum likelihood estimates are available, the rotation technique does not often produce a sufficiently sparse solution. In order to handle these problems, this paper introduces a penalized likelihood procedure that imposes a nonconvex penalty on the factor loadings. We show that the penalized likelihood procedure can be viewed as a generalization of the traditional two-step approach, and the proposed methodology can produce sparser solutions than the rotation technique. A new algorithm via the EM algorithm along with coordinate descent is introduced to compute the entire solution path, which permits the application to a wide variety of convex and nonconvex penalties. Monte Carlo simulations are conducted to investigate the performance of our modeling strategy. A real data example is also given to illustrate our procedure.
| Original language | English |
|---|---|
| Pages (from-to) | 863-875 |
| Number of pages | 13 |
| Journal | Statistics and Computing |
| Volume | 25 |
| Issue number | 5 |
| DOIs | |
| Publication status | Published - May 28 2014 |
| Externally published | Yes |
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Keywords
- Coordinate descent algorithm
- Factor analysis
- Nonconvex penalty
- Penalized likelihood
- Rotation technique
ASJC Scopus subject areas
- Theoretical Computer Science
- Statistics and Probability
- Statistics, Probability and Uncertainty
- Computational Theory and Mathematics
Cite this
Sparse estimation via nonconcave penalized likelihood in factor analysis model. / Hirose, Kei; Yamamoto, Michio.
In: Statistics and Computing, Vol. 25, No. 5, 28.05.2014, p. 863-875.Research output: Contribution to journal › Article
}
TY - JOUR
T1 - Sparse estimation via nonconcave penalized likelihood in factor analysis model
AU - Hirose, Kei
AU - Yamamoto, Michio
PY - 2014/5/28
Y1 - 2014/5/28
N2 - We consider the problem of sparse estimation in a factor analysis model. A traditional estimation procedure in use is the following two-step approach: the model is estimated by maximum likelihood method and then a rotation technique is utilized to find sparse factor loadings. However, the maximum likelihood estimates cannot be obtained when the number of variables is much larger than the number of observations. Furthermore, even if the maximum likelihood estimates are available, the rotation technique does not often produce a sufficiently sparse solution. In order to handle these problems, this paper introduces a penalized likelihood procedure that imposes a nonconvex penalty on the factor loadings. We show that the penalized likelihood procedure can be viewed as a generalization of the traditional two-step approach, and the proposed methodology can produce sparser solutions than the rotation technique. A new algorithm via the EM algorithm along with coordinate descent is introduced to compute the entire solution path, which permits the application to a wide variety of convex and nonconvex penalties. Monte Carlo simulations are conducted to investigate the performance of our modeling strategy. A real data example is also given to illustrate our procedure.
AB - We consider the problem of sparse estimation in a factor analysis model. A traditional estimation procedure in use is the following two-step approach: the model is estimated by maximum likelihood method and then a rotation technique is utilized to find sparse factor loadings. However, the maximum likelihood estimates cannot be obtained when the number of variables is much larger than the number of observations. Furthermore, even if the maximum likelihood estimates are available, the rotation technique does not often produce a sufficiently sparse solution. In order to handle these problems, this paper introduces a penalized likelihood procedure that imposes a nonconvex penalty on the factor loadings. We show that the penalized likelihood procedure can be viewed as a generalization of the traditional two-step approach, and the proposed methodology can produce sparser solutions than the rotation technique. A new algorithm via the EM algorithm along with coordinate descent is introduced to compute the entire solution path, which permits the application to a wide variety of convex and nonconvex penalties. Monte Carlo simulations are conducted to investigate the performance of our modeling strategy. A real data example is also given to illustrate our procedure.
KW - Coordinate descent algorithm
KW - Factor analysis
KW - Nonconvex penalty
KW - Penalized likelihood
KW - Rotation technique
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UR - http://www.scopus.com/inward/citedby.url?scp=84938416978&partnerID=8YFLogxK
U2 - 10.1007/s11222-014-9458-0
DO - 10.1007/s11222-014-9458-0
M3 - Article
AN - SCOPUS:84938416978
VL - 25
SP - 863
EP - 875
JO - Statistics and Computing
JF - Statistics and Computing
SN - 0960-3174
IS - 5
ER -