Bollen Kenneth A, Bauldry Shawn
Department of Sociology, H. W. Odum Institute for Research in Social Science, Carolina Population Center, University of North Carolina at Chapel Hill.
Sociol Methods Res. 2010 Oct 7;39(2):127-156. doi: 10.1177/0049124110366238.
Multiequation models that contain observed or latent variables are common in the social sciences. To determine whether unique parameter values exist for such models, one needs to assess model identification. In practice analysts rely on empirical checks that evaluate the singularity of the information matrix evaluated at sample estimates of parameters. The discrepancy between estimates and population values, the limitations of numerical assessments of ranks, and the difference between local and global identification make this practice less than perfect. In this paper we outline how to use computer algebra systems (CAS) to determine the local and global identification of multiequation models with or without latent variables. We demonstrate a symbolic CAS approach to local identification and develop a CAS approach to obtain explicit algebraic solutions for each of the model parameters. We illustrate the procedures with several examples, including a new proof of the identification of a model for handling missing data using auxiliary variables. We present an identification procedure for Structural Equation Models that makes use of CAS and that is a useful complement to current methods.
包含观测变量或潜在变量的多方程模型在社会科学中很常见。为了确定此类模型是否存在唯一的参数值，需要评估模型识别。在实践中，分析人员依靠实证检验来评估在参数样本估计值处计算的信息矩阵的奇异性。估计值与总体值之间的差异、秩的数值评估的局限性以及局部识别和全局识别之间的差异，使得这种做法并不完美。在本文中，我们概述了如何使用计算机代数系统（CAS）来确定有无潜在变量的多方程模型的局部和全局识别。我们展示了一种用于局部识别的符号CAS方法，并开发了一种CAS方法来为每个模型参数获得明确的代数解。我们用几个例子说明了这些程序，包括一个使用辅助变量处理缺失数据的模型识别的新证明。我们提出了一种利用CAS的结构方程模型识别程序，它是对当前方法的有益补充。
