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Updated: Mar 27, 2026

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Structural Equation Models in a Redundancy Analysis Framework With Covariates.

Pietro Giorgio Lovaglio1, Giorgio Vittadini1

  • 1a Department of Statistics and Quantitative Methods , University of Bicocca-Milan.

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Generalized Redundancy Analysis (GRA) offers a new method for structural equation modeling, improving upon Extended Redundancy Analysis (ERA) by accounting for direct effects and covariates. This approach enhances the analysis of complex relationships between variables in statistical modeling.

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Area of Science:

  • Statistics
  • Econometrics
  • Social Sciences

Background:

  • Extended Redundancy Analysis (ERA) models relationships between exogenous and endogenous variables using unobservable composites.
  • ERA's composite estimation can be inaccurate when direct effects or concomitant indicators are present, as it ignores these specified direct effects.

Purpose of the Study:

  • To introduce Generalized Redundancy Analysis (GRA), a novel method for specifying and fitting structural equation models.
  • To extend the capabilities of ERA by allowing for a wider range of relationships, including direct effects and the influence of external covariates.

Main Methods:

  • Propose Generalized Redundancy Analysis (GRA) for structural equation modeling.
  • Develop a more suitable specification and estimation algorithm that accommodates direct effects and covariates influencing endogenous indicators directly or indirectly through composites.
  • Conduct a simulation study with small samples to compare GRA with ERA.
  • Apply GRA to model the impact of human capital on graduate earnings using economic theory.

Main Results:

  • GRA provides a more accurate estimation of composite scores by incorporating direct effects and covariates.
  • Simulation results demonstrate the advantages of GRA over ERA, particularly in small sample sizes.
  • The application successfully estimates the relationship between formal human capital and initial earnings of university graduates.

Conclusions:

  • GRA offers a flexible and robust framework for structural equation modeling, extending the utility of the Redundancy Analysis approach.
  • The method is particularly valuable when dealing with complex models involving direct effects, unobservable composites, and external covariates.
  • GRA provides a statistically sound method for economic applications, such as analyzing human capital and earnings.