Model Identification and Computer Algebra

Abstract

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 article, the authors outline how to use computer algebra systems (CAS) to determine the local and global identification of multiequation models with or without latent variables. They demonstrate a symbolic CAS approach to local identification and develop a CAS approach to obtain explicit algebraic solutions for each of the model parameters. The authors illustrate the procedures with several examples, including a new proof of the identification of a model for handling missing data using auxiliary variables. They present an identification procedure for structural equation models that makes use of CAS and that is a useful complement to current methods.