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LISREL: Gradient and Hessian of the fitting function

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  • Neudecker, H
  • Satorra, A

Abstract

Latent-variable models are nowadays frequently used in economic, social and behavioral studies to analyze relationships among variables. The LISREL model is a general model that integrates the classical simultaneous-equation model developed in econometrics with the factor-analysis model developed by psychometricians. The classical "errors-in-variables" model is also a particular case of LISREL. In this paper we obtain the hessian of a general type of fitting function for the LISREL model. Although the expressions of the first derivatives are known and widely used, the expressions obtained for the second derivatives are a novelty and may have practical implications. For instance, the expressions for the hessian would be needed to implement true Newton fitting algorithms, or when using observed hessians (instead of expected) in evaluating the asymptotic distribution of statistics of interest.

Suggested Citation

  • Neudecker, H & Satorra, A, 1989. "LISREL: Gradient and Hessian of the fitting function," University of Amsterdam, Actuarial Science and Econometrics Archive 293133, University of Amsterdam, Faculty of Economics and Business.
    • Handle: RePEc:ags:amstas:293133
    DOI: 10.22004/ag.econ.293133
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    Research Methods/ Statistical Methods;

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