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Misspecification of the covariance structure in generalized linear mixed models
1INSERM, CESP, Centre de recherche en Épidémiologie et Santé des Populations, Villejuif, France michel.chavance@inserm.fr.
The sandwich variance is crucial for mixed models, unlike marginal models. Comparing naive and sandwich standard deviations helps detect model misspecification and ensures reliable statistical inference for fixed effects.
Area of Science:
- Statistics
- Biostatistics
- Econometrics
Background:
- Marginal models commonly use sandwich variance for correlated outcomes.
- Mixed models often lack this standard practice, potentially leading to inference issues.
Purpose of the Study:
- To highlight problems with standard variance estimation in mixed models.
- To propose the sandwich variance as a diagnostic tool for model misspecification.
Main Methods:
- Utilized two datasets to illustrate variance estimation issues.
- Compared naive and sandwich standard deviations of fixed effects estimators.
Main Results:
- Sandwich variance is consistent even with misspecified random effects.
- Ratio of naive to sandwich standard deviations can signal erroneous inference if outside [3/4, 4/3].
Conclusions:
- Sandwich variance is a valuable diagnostic for assessing model fit in mixed models.
- Broader adoption of sandwich variance for fixed effects inference in mixed models is recommended.
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