Local fit evaluation of structural equation models using graphical criteria

Area of Science:

• Statistics
• Psychometrics
• Data Analysis

Background:

• Structural Equation Modeling (SEM) relies heavily on model fit evaluation.
• Current methods predominantly use global fit indices (e.g., χ², RMSEA, CFI) to assess overall model fit.
• Local fit evaluation, using graphical criteria like d-separation, is underutilized.

Purpose of the Study:

• To provide an overview of local fit evaluation for SEM practitioners.
• To highlight the utility of local fit evaluation in diagnosing model misfit and confirming model components.
• To introduce novel R software for automating local fit evaluation.

Main Methods:

• Discussion of graphical criteria (d-separation, trek-separation) for local fit assessment.
• Exploration of statistical local tests.
• Presentation of applied examples and novel R software implementation.

Main Results:

• Local fit evaluation can pinpoint specific sources of model misfit.
• It can identify well-supported parts of a correctly fitting model.
• Local tests are applicable even for underidentified models or prior to model fitting.

Conclusions:

• Local fit evaluation is a valuable, underused approach complementing global SEM fit indices.
• It offers granular insights into model performance and data corroboration.
• Automated tools enhance the practical application of local fit evaluation in SEM.