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Area of Science:

  • Psychometrics
  • Statistical Modeling

Background:

  • Structural Equation Modeling (SEM) relies on fit indices to evaluate model adequacy.
  • The influence of the number of observed variables (p) on these indices is not fully understood.

Purpose of the Study:

  • To investigate how the number of observed variables (p) affects key SEM fit indices: CFI, TLI, and RMSEA.
  • To compare population fit indices with their sample estimates under varying conditions.

Main Methods:

  • Manipulated the number of observed variables (p), model misspecification types, sample size, and factor loading magnitudes.
  • Analyzed the behavior of population fit indices and their sample estimates.

Main Results:

  • Population CFI and TLI were influenced by p and the type of model misspecification.
  • Population RMSEA consistently decreased with higher p, irrespective of misspecification.
  • Sample estimates for all indices indicated poorer fit than population values, particularly with smaller sample sizes, higher p, and lower factor loadings.

Conclusions:

  • The number of observed variables is a critical factor influencing SEM fit indices.
  • Researchers should be cautious when interpreting fit indices, especially in studies with many variables or small sample sizes.