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Detection of Architectural Distortion in Prior Mammograms via Analysis of Oriented Patterns
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MODEL IDENTIFICATION AND COMPUTER ALGEBRA.

Kenneth A Bollen1, Shawn Bauldry

  • 1Department of Sociology, H. W. Odum Institute for Research in Social Science, Carolina Population Center, University of North Carolina at Chapel Hill.

Sociological Methods & Research
|July 20, 2011
PubMed
Summary
This summary is machine-generated.

This study introduces computer algebra systems (CAS) to precisely assess model identification in multiequation models. This symbolic approach overcomes limitations of empirical checks, ensuring accurate parameter estimation in social science research.

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Area of Science:

  • Social Sciences
  • Statistics
  • Econometrics

Background:

  • Multiequation models with observed or latent variables are prevalent in social sciences.
  • Assessing model identification is crucial for determining unique parameter values.
  • Current empirical checks for identification have limitations, including numerical inaccuracies and distinguishing local from global identification.

Purpose of the Study:

  • To outline the use of computer algebra systems (CAS) for determining local and global identification of multiequation models.
  • To demonstrate a symbolic CAS approach for local identification and explicit algebraic solutions for model parameters.
  • To present a CAS-based identification procedure for Structural Equation Models (SEMs) as a complement to existing methods.

Main Methods:

  • Utilizing computer algebra systems (CAS) for symbolic computation.
  • Developing a CAS approach to derive explicit algebraic solutions for model parameters.
  • Applying the CAS procedure to various examples, including a model for missing data using auxiliary variables.

Main Results:

  • Demonstrated a symbolic CAS approach to determine local identification.
  • Developed a CAS method to obtain explicit algebraic solutions for model parameters.
  • Provided a new proof for the identification of a missing data model using auxiliary variables.

Conclusions:

  • CAS offers a robust method for assessing both local and global identification in multiequation models.
  • The symbolic approach overcomes limitations associated with empirical and numerical methods.
  • This CAS-based procedure enhances the identification analysis of Structural Equation Models.