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Pairwise Likelihood Ratio Tests and Model Selection Criteria for Structural Equation Models with Ordinal Variables.
Myrsini Katsikatsou1, Irini Moustaki2
1Department of Statistics, London School of Economics, Houghton Street, London, WC2A 2AE , UK. m.katsikatsou@lse.ac.uk.
Psychometrika
|October 14, 2016
Summary
This study introduces new likelihood ratio test statistics for structural equation models with correlated ordinal data. These methods, implemented in R, offer a flexible framework for model fitting and testing, showing satisfactory performance in simulations.
Area of Science:
- Statistics
- Econometrics
- Psychometrics
Background:
- Correlated multivariate ordinal data analysis often employs structural equation models (SEMs).
- Limited-information methods like three-stage least squares and pairwise maximum likelihood estimation (PMLE) are common for parameter estimation.
- Existing methods for model fit testing in this context have limitations.
Purpose of the Study:
- To derive and evaluate likelihood ratio test statistics for overall goodness-of-fit and nested models within the PMLE framework for SEMs with ordinal data.
- To assess the performance of these new statistics through simulations.
- To provide model selection criteria (AIC, BIC) compatible with the PMLE framework.
Main Methods:
- Derivation of two likelihood ratio test statistics and their asymptotic distributions under PMLE.
- Monte Carlo simulations to evaluate type I error rates and statistical power.
- Application of derived statistics and model selection criteria to real-world survey data ('trust in the police').
- Implementation in the R package lavaan.
Main Results:
- The proposed likelihood ratio test statistics demonstrate satisfactory performance regarding type I error and power in simulations.
- Their performance is comparable to statistics derived under three-stage least squares methods.
- The derived AIC and BIC criteria effectively select the correct model in simulation examples.
- The methods were successfully applied to analyze 'trust in the police' data.
Conclusions:
- The derived likelihood ratio test statistics and model selection criteria offer a flexible and effective framework for fitting and testing SEMs with ordinal data using PMLE.
- These tools enhance the analysis of complex correlated ordinal data.
- The R package lavaan now includes these advanced statistical methods for broader accessibility.
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