On identification of multi-factor models with correlated residuals
On identification of multi-factor models with correlated residuals
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具有相关残差的多因素模型的识别
DOI：
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发表时间：
2004
期刊：
影响因子：
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通讯作者：
D. Chouanière
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作者：
M. Grzebyk;P. Wild;D. Chouanière
本文给出了残差相关、因子不相关和因子载荷为零约束的多因子模型的辨识条件。这些条件来自于Stanghellini（1997年）和Vicard（2000年）的结果，这些结果处理浓度矩阵中无限制的单因子模型。像这些作者一样，我们利用残差的互补图，并且条件建立在奇循环在该图中的作用上。然而，与这些作者相反，我们考虑的情况下，残差的条件依赖性表示的协方差矩阵，而不是其逆，浓度矩阵。本文首先导出了残差协方差阵为结构零点的单因子模型的相应辨识条件。这被扩展到某些因子载荷被约束为零的情况。利用这些条件得到了多因子模型可辨识的一个充分必要条件。版权所有Biometrika Trust 2004，牛津大学出版社。
We specify some conditions for the identification of a multi-factor model with correlated residuals, uncorrelated factors and zero restrictions in the factor loadings. These conditions are derived from the results of Stanghellini (1997) and Vicard (2000) which deal with single-factor models with zero restrictions in the concentration matrix. Like these authors, we make use of the complementary graph of residuals and the conditions build on the role of odd cycles in this graph. However, in contrast to these authors, we consider the case where the conditional dependencies of the residuals are expressed in terms of a covariance matrix rather than its inverse, the concentration matrix. We first derive the corresponding condition for identification of single-factor models with structural zeros in the covariance matrix of the residuals. This is extended to the case where some factor loadings are constrained to be zero. We use these conditions to obtain a sufficient and a necessary condition for identification of multi-factor models. Copyright Biometrika Trust 2004, Oxford University Press.