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Residual-based diagnostics for structural equation models
B N Sánchez1, E A Houseman, L M Ryan
1Department of Biostatistics, University of Michigan, School of Public Health, Ann Arbor, Michigan 48104, USA. brisa@umich.edu
Biometrics
|April 1, 2008
Summary
New goodness-of-fit tests for structural equation models (SEMs) improve assumption checking. These methods, using subject-specific residuals, enhance diagnostic capabilities for latent variable models, offering graphical displays and simulation-based statistics.
Area of Science:
- Statistics
- Psychometrics
- Biostatistics
Background:
- Classical diagnostics for structural equation models (SEMs) rely on aggregate data, limiting their ability to assess distributional and linearity assumptions.
- Existing goodness-of-fit tests for correlated data often do not adequately address the complexities of latent variable models.
Purpose of the Study:
- To extend recent goodness-of-fit tests for correlated data to structural equation models (SEMs) with latent variables.
- To develop diagnostic tools for SEMs that can detect misspecified distributional or linearity assumptions.
- To provide methods suitable for graphical displays and complemented by simulation-based test statistics.
Main Methods:
- Developed goodness-of-fit tests for structural equation models (SEMs) utilizing subject-specific residuals.
- Defined test statistics and approximated their null distributions using computationally efficient simulation techniques.
- Employed graphical displays to complement the test statistics for assumption checking.
Main Results:
- The proposed tests effectively extend goodness-of-fit diagnostics to structural equation models (SEMs) with latent variables.
- Simulation studies demonstrated favorable properties of the new tests.
- The methods are capable of detecting misspecified distributional or linearity assumptions.
Conclusions:
- The newly developed goodness-of-fit tests offer enhanced diagnostic capabilities for structural equation models (SEMs), particularly those with latent variables.
- These methods provide a valuable supplement to existing diagnostic tools, aiding in the assessment of model assumptions.
- The approach was successfully illustrated using real-world data from a study on in utero lead exposure.
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