Sparse factor regression via penalized maximum likelihood estimation
Sparse factor regression via penalized maximum likelihood estimation
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DOI：
10.1007/s00362-016-0781-8
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发表时间：
2018-06
影响因子：
1.3
通讯作者：
K. Hirose;Miyuki Imada
中科院分区：
文献类型：
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作者：
K. Hirose;Miyuki Imada
在因子回归模型中，极大似然估计有三个缺点：（i）当变量的数目超过观测的数目时，最大似然估计是不可用的，（ii）基于最大似然估计的旋转技术产生不够稀疏的加载矩阵，以及（iii）当唯一方差的估计值时，可能会发生多重共线性（特定方差）是小的，因为回归系数对唯一方差的倒数敏感。为了处理这些问题，我们提出了一个惩罚的最大似然过程。具体来说，我们施加套索型惩罚的因素负荷，以提高解决方案的稀疏性。我们还引入了对唯一方差的惩罚，这（给定因子得分）对应于回归系数的岭惩罚。从预测的角度来看，我们的程序的理论性质进行了讨论。通过Monte Carlo模拟的程序的有效性进行了研究。我们的程序的效用证明了真实的数据收集的在线问卷。
In factor regression model, the maximum likelihood estimation suffers from three disadvantages: (i) the maximum likelihood estimates are unavailable when the number of variables exceeds the number of observations, (ii) the rotation technique based on maximum likelihood estimates produces an insufficiently sparse loading matrix, and (iii) multicollinearity can occur when the estimates of unique variances (specific variances) are small because the regression coefficients are sensitive to the inverse of unique variances. To handle these problems, we propose a penalized maximum likelihood procedure. Specifically, we impose a lasso-type penalty on the factor loadings to improve the sparseness of the solution. We also introduce a penalty on unique variances, which (given the factor scores) corresponds to the ridge penalty on the regression coefficient. Theoretical properties from a prediction viewpoint of our procedure are discussed. The effectiveness of the procedure is investigated through Monte Carlo simulations. The utility of our procedure is demonstrated on real data collected by an online questionnaire.