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Abstract: Parameter Influence In Structural Equation Models.

Taehun Lee1, Robert MacCallum1

  • 1a University of North Carolina at Chapel Hill .

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Understanding parameter influence in structural equation modeling (SEM) is crucial. This study introduces influence mapping to identify which parameters most impact model fit, aiding researchers in SEM analysis.

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Area of Science:

  • Statistics
  • Psychometrics
  • Social Sciences

Background:

  • Structural Equation Modeling (SEM) relies on parameter estimates optimized for model fit.
  • A key question is how parameter changes affect model fit and which parameters are most influential.

Purpose of the Study:

  • To introduce and evaluate methods for quantifying parameter influence in SEM.
  • To propose a new approach, influence mapping for single parameters, to assess individual parameter impact on model fit.

Main Methods:

  • The study builds upon the principle of likelihood displacement (LD) to quantify influence.
  • It compares an existing vector approach with a novel method of influence mapping for single parameters.
  • Influence mapping assesses model fit changes when individual parameters are perturbed.

Main Results:

  • Influence mapping identifies parameters that cause significant model fit changes under minor perturbations.
  • Flatter influence curves indicate less influential parameters.
  • The study illustrates these concepts with an empirical application.

Conclusions:

  • Parameter influence is a critical concept in SEM, impacting model interpretation and stability.
  • Influence mapping provides a practical tool for researchers to understand parameter sensitivity.
  • The findings have implications for statistical power and model diagnostics in SEM.