Abstract
In longitudinal studies, robust sandwich variance estimators are often used, and are especially useful when model assumptions are in doubt. However, the usual sandwich estimator does not allow for models with crossed random effects. The hierarchical likelihood extends the idea of the sandwich estimator to models not currently covered. By simulation studies, we show that the new sandwich estimator is robust against heteroscedastic errors and against misspecification of overdispersion in the y | v component.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Besag J., Green P., Higdon D., and Mengersen K. 1995. Bayesian computation and stochastic systems (with discussion). Statistical Science 10: 3-66.
Bjornstad J.F. 1996. On the generalization of the likelihood function and likelihood principle. J. Am. Statist. Ass. 91: 791-806.
Breslow N.E. and Clayton D.G. 1993. Approximate inference in generalized linear mixed models. J. Am. Statist. Ass. 88: 9-25.
Efron B. 1996. Empirical Bayes methods for combining likelihoods (with discussion). J. Am. Statist. Ass. 91: 538-565.
Ha I.D., Lee Y., and Song J. 2001. Hierarchical likelihood approach for frailty models. Biometrika 88: 233-243.
Hinkley D. 1977. Jackknifing in unbalanced situations. Technometrics 19: 285-292.
Kent J.T. 1982. Robust properties of likelihood ratio test. Biometrika 69: 19-27.
Lee Y. 1991. Jacknife variance estimators of the location estimator in the one-way random-effects model. Ann. Inst. Statist. Math. 43: 707-714.
Lee Y. 2001. Can we recover information from concordant pairs in binary matched pairs? J. Appl. Statist. 28: 239-246.
Lee Y. and Nelder J.A. 1996. Hierarchical generalized linear models (with discussion). J. R. Statist. Soc. B 58: 619-678.
Lee Y. and Nelder J.A. 2000. Two-ways of modelling overdispersion in non-normal data. Applied Statistics 49: 591-598.
Lee Y. and Nelder J.A. 2001a. Hierarchical generalized linear models: A synthesis of generalized linear models, random-effect models and structured dispersions. Biometrika 88: 987-1006.
Lee Y. and Nelder J.A. 2001b. Modelling and analysing correlated non-normal data. Statistical Modelling 1: 3-18.
Nelder J.A. and Pregibon D. 1987. An extended quasi-likelihood function. Biometrika 74: 221-231.
Pregibon D. 1983. An alternative covariance estimate for generalised linear models. GLIM Newsletter 6: 51-55.
Schall R. 1991. Estimation in generalized linear models with random effects. Biometrika 78: 719-727.
Seely J. and Hogg R.V. 1982. Symmetrically distributed and unbiased estimators in linear models. Communications in Statistics-Theory and Methods, Ser. A 11: 721-729.
Zeger S.L., Liang K.Y., and Albert P.S. 1988. Models for longititudinal data: A generalized estimating equation approach. Biometrics 44: 1049-1060.
Rights and permissions
About this article
Cite this article
Lee, Y. Robust variance estimators for fixed-effect estimates with hierarchical-likelihood. Statistics and Computing 12, 201–207 (2002). https://doi.org/10.1023/A:1020790524521
Issue Date:
DOI: https://doi.org/10.1023/A:1020790524521