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Structural equation models (SEMs) offer a rigorous approach to causal inference but global fit statistics can be misleading. Separate analysis of measurement and path models provides more reliable conclusions for complex data.

Keywords:
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Area of Science:

  • Statistics
  • Social Sciences
  • Psychometrics

Background:

  • Structural equation models (SEMs) are widely used for causal inference with nonexperimental data.
  • SEMs incorporate measurement error and multiple indicators, offering a seemingly rigorous approach.
  • Current methods focus on global model fitting and fit statistics for complex SEMs.

Purpose of the Study:

  • To evaluate the adequacy of global fit statistics in structural equation modeling.
  • To propose an alternative approach for assessing the validity of SEMs.
  • To highlight the limitations of composite SEM analyses.

Main Methods:

  • Critically examined the interpretation of global fit indices in SEMs.
  • Proposed the separation of measurement (path) models and causal (path) models for analysis.
  • Utilized recently developed methods for assessing individual model constraints.
  • Applied an empirical example to demonstrate the proposed approach.

Main Results:

  • Global fit statistics and significance tests are insufficient for judging SEM approximation adequacy.
  • Composite analysis of measurement and path models can lead to unreasonable conclusions.
  • Separate analysis of component models allows for informed judgment and assessment of constraints.
  • The conventional global treatment yielded unacceptable conclusions in the empirical example.

Conclusions:

  • The conventional global analysis of structural equation models is problematic.
  • Separating measurement and path models is crucial for accurate causal inference.
  • A more nuanced approach to model evaluation is necessary for reliable SEM application.