The Robustness of 2SLS Estimation of a Non-normally Distributed Confirmatory Factor Analysis Model
Multivariate Behavioral Research
|January 29, 2016
Summary
This Monte Carlo simulation found that limited information two-stage least squares (2SLS) and full information maximum likelihood (FIML) estimation methods are robust for confirmatory factor analysis models with non-normal data. Both methods yielded similar, efficient results across tested conditions.
Area of Science:
- Statistics
- Econometrics
- Psychometrics
Background:
- Confirmatory Factor Analysis (CFA) is widely used in social sciences.
- Robustness of estimation methods under non-normality is crucial for valid inference.
- Limited Information Maximum Likelihood (LIML) and Full Information Maximum Likelihood (FIML) are common CFA estimators.
Purpose of the Study:
- To evaluate the robustness of the two-stage least squares (2SLS) estimation procedure in CFA models with non-normal distributions.
- To compare the performance of 2SLS against Full Information Maximum Likelihood (FIML) under various asymmetry conditions.
Main Methods:
- A Monte Carlo simulation study was designed.
- Two estimation procedures, 2SLS and FIML, were applied to a CFA model.
- Data were generated across four distribution conditions: normal, small asymmetry, medium asymmetry, and large asymmetry (kurtosis constant).
- Model loadings were set at two levels: small and large.
Main Results:
- Both 2SLS and FIML estimators demonstrated robustness against moderate deviations from normality.
- Estimates from both procedures were comparable across all simulated conditions.
- The 2SLS procedure exhibited high relative efficiency compared to FIML.
Conclusions:
- The 2SLS estimation method is a robust alternative for CFA models, even with non-normal data.
- FIML and 2SLS provide similar parameter estimates under moderate non-normality.
- The findings support the use of 2SLS in situations where distributional assumptions are violated.
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