Assessing the fit of structural equation models with multiply imputed data.

Area of Science:

• Statistics
• Social Sciences
• Psychometrics

Background:

• Multiple imputation is common in social sciences, but its use in structural equation modeling (SEM) inference is underexplored.
• Existing methods for SEM model fit and fit indices do not fully leverage imputation techniques.

Purpose of the Study:

• To evaluate Meng and Rubin's pooling procedure for likelihood ratio statistics in SEM model fit testing.
• To explore creating imputation-based versions of common SEM fit indices (TLI, CFI, RMSEA).

Main Methods:

• Computer simulations were used to assess the performance of the imputation-based likelihood ratio statistic.
• The study compared imputation-based fit indices to those derived from full information maximum likelihood (FIML) estimation.

Main Results:

• The pooled likelihood ratio statistic effectively tested model fit in correctly specified models, aligning with FIML.
• For misspecified models with substantial missing data (30-40%), the imputation-based statistic showed reduced power compared to FIML.
• Imputation-based TLI, CFI, and RMSEA were well-calibrated with FIML estimates.

Conclusions:

• The imputation-based pooled likelihood ratio statistic is a viable approach for SEM model fit testing.
• Imputation-based fit indices can be reliably constructed, offering alternatives to FIML.
• Recommendations for future research and implementation code (Mplus, R) are provided.