How to evaluate local fit (residuals) in large structural equation models.

Area of Science:

• Psychometrics
• Statistical Modeling

Background:

• Structural Equation Modeling (SEM) requires evaluating model fit at global and local levels.
• Global fit assesses overall model correspondence, while local fit examines residuals (differences between observed and predicted associations).
• Satisfactory global fit can mask problematic local fit, especially in large, complex models.

Purpose of the Study:

• To provide practical guidance on efficiently evaluating and describing local fit in large-scale structural equation models.
• To address the challenges of assessing local fit when dealing with numerous variables and residuals.

Main Methods:

• The study focuses on methods for evaluating local fit in structural equation models.
• It emphasizes the importance of examining residuals beyond global fit indices.
• An empirical example with freely available data and syntax is presented.

Main Results:

• Large structural equation models can exhibit good global fit despite significant local misspecification.
• Residuals, when averaged, can dilute the impact of localized model errors.
• Efficient evaluation of local fit is essential for accurate model interpretation.

Conclusions:

• Local fit evaluation is critical for identifying specific areas of model misspecification in large SEMs.
• The tutorial offers practical strategies to manage and interpret local fit diagnostics.
• Accessible examples facilitate the application of these methods by researchers.