Abstract
We consider the problem of regression analysis for data which consist of a large number of independent small groups or clusters of correlated observations. Instead of using the standard mean regression, we regress various percentiles of each marginal response variable over its covariates to obtain a more accurate assessment of the covariate effect. Our inference procedures are derived using the generalized estimating equations approach. The new proposal is robust and can be easily implemented. Graphical and numerical methods for checking the adequacy of the fitted quantile regression model are also proposed. The new methods are illustrated with an animal study in toxicology.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
Similar content being viewed by others
References
Baker, S. G., Wax, Y. and Patterson, B. (1993). Regression analysis of grouped survival data: Informative censoring and double sampling. Biometrics 49, 379–390.
Barrodale, I. and Roberts, F. (1973). An improved algorithm for discrete L 1 linear approximations. SIAM, Journal of Numerical Analysis 10, 839–848.
Bassett, G. Jr. & Koenker, R. (1978). Asymptotic theory of least absolute error regression, J. Am. Statist. Assoc. 73, 618–622.
Bassett, G. Jr. and Koenker, R. (1982). An empirical quantile function for linear models with iid errors, J. Am. Statist. Assoc. 77, 407–415.
Bloomfield, P. & Steiger, W. L. (1983). Least Absolute Deviations: Theory, Applications, and Algorithms. Birkhauser, Boston, Mass.
Chamberlain, G. (1994). Quantile regression, censoring and the structure of wages. In Proceedings of the Sixth World Congress of the Econometrics Society (eds. C. Sims and J.J. Laffont). New York: Cambridge University Press.
Efron B. & Tibshirani, R. (1986). Bootstrap methods for standard errors, confidence intervals, and other measures of statistical accuracy. Statist. Sci. 1, 54–75.
Jung, S. (1996). Quasi-likelihood for median regression models. J. Am. Statist. Assoc. 91, 251–257.
Koenker, R. (1994). Confidence intervals for regression quantiles. Proc. of the 5th Prague Symp. on Asymptotic Stat., 349–359, Springer-Verlag.
Koenker, R. and Bassett, G. Jr. (1978). Regression quantiles. Econometrica 84, 33–50.
Koenker, R. and Bassett, G. Jr. (1982). Tests of linear hypotheses and L 1 estimation. Econometrica 50, 1577–1584.
Koenker, R. and D’Orey, V. (1987). Computing regression quantiles. AppliedStatistics 36, 383–393.
Koenker, R. and Machado, J. A. F. (1999). Goodness of fit and related inference processes for quantile regression. J. Am. Stat ist. Assoc. 94, 1296–1310.
Lai, T. L. and Ying, Z. (1988). Stochast ic integrals of empirical-type processes with applications to censored regression. Journal of Multivariate Analysis 27, 334–358.
Laird, N. M. and Ware, J. H. (1982). Random-effects models for longitudinal data. Biometrics 38, 963–974.
Liang, K. Y. and Zeger, S. L. (1986). Longitudinal data analysis using generalized linear models. Biometrika 73, 13–22.
Lin, D. Y., Wei, L. J. and Ying, Z. (2002). Model-checking techniques based on cumulative residuals. Biometrics 58, 1–12.
Lipsitz, S. R., Fitzmaurice, G. M., Molenberghs, G. and Zhao, L. P. (1997). Quantile regression models for longitudinal data with drop-out: Application to CD4 cell counts of patients infected with the human immunodeficiency virus. Applied Statistics 46, 463–476.
Mosteller, F. and Tukey, J. W. (1977). Data Analysis and Regression: A Secondary Course in Statistics. Addison-Wesley.
Parzen, M. I., Wei, L. J. and Ying, Z. (1994). A resampling method based on pivotal estimating functions. Biometrika 81, 341–350.
Portnoy, S. (1992). A regression quantile based statistic for testing non-stationary errors. In Nonparametric Statistics and Related Topics, ed. by A. Saleh, 191–203.
Rotnitzky, A. and Robins, J. M. (1995). Semi-parametric regression estimation in the presence of dependent censoring. Biometrika 82, 805–820.
Tyl, R.W., Price, M. C., Marr, M. C. and Kimmel, C. A. (1988). Developmental toxicity evaluation of dietary di(2-ethylhexyl)phthalate in Fisher 344 rats and CD-1 mice. Fundam ental and Applied Toxicology 10, 395–412.
van der Vaart, A. and Wellner, J. A. (1996). Weak Convergence and Empirical Processes, Springer.
Wei, L. J. and Johnson, W. E. (1985). Combining dependent tests with incomplete repeated measurements, Biometrika 72, 359–364.
Wu, M. C. and Carroll, R. J. (1988). Estimation and comparison of changes in the presence of informative right censoring by modeling the censoring process. Biometrics 44, 175–188.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2004 Springer Science+Business Media New York
About this chapter
Cite this chapter
Chen, L., Wei, LJ., Parzen, M.I. (2004). Quantile Regression for Correlated Observations. In: Lin, D.Y., Heagerty, P.J. (eds) Proceedings of the Second Seattle Symposium in Biostatistics. Lecture Notes in Statistics, vol 179. Springer, New York, NY. https://doi.org/10.1007/978-1-4419-9076-1_4
Download citation
DOI: https://doi.org/10.1007/978-1-4419-9076-1_4
Publisher Name: Springer, New York, NY
Print ISBN: 978-0-387-20862-6
Online ISBN: 978-1-4419-9076-1
eBook Packages: Springer Book Archive