Abstract
In this chapter, we are considering L 1-type estimation for multivariate clustered data. Although valid, using the direct L 1 estimation of the regression coefficients in the clustered data setting is likely to lack efficiency since it does not use the intracluster correlation structure. A transformation–retransformation method is proposed to overcome this problem. This method first transforms the original model in an attempt to eliminate the intracluster correlation. Secondly, the L 1 estimates are obtained with the transformed data, which are then transformed back to the original scale. One particular implementation of this method is investigated in a simulation study which shows that it is more efficient than using the direct L 1 estimators.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Similar content being viewed by others
References
Datta, S., Satten, G.A.: Rank-sum tests for clustered data. J. Am. Stat. Assoc. 471, 908–915 (2005)
Diggle, P., Heagerty, P., Liang, K.-Y., Zeger, S.: Analysis of Longitudinal Data, 2nd edn. Oxford University Press, Oxford (2002)
Fu, L., Wang, Y.-G.: Efficient estimation for rank-based regression with clustered data. Biometrics 68, 1074–1082 (2012)
Fu, L., Wang, Y.-G., Bai, Z.: Rank regression for analysis of clustered data: a natural induced smothing approach. Comput. Stat. Data Anal. 54, 1036–1050 (2010)
Jung, S.-H., Ying, Z.: Rank-based regression with repeated measurements data. Biometrika 90, 732–740 (2003)
Jurěcková, J.: Asymptotic linearity of a rank statistic in regression parameter. Ann. Math. Stat. 40, 1889–1900 (1969)
Jurěcková, J.: Non-parametric estimate of regression coefficients. Ann. Math. Stat. 42, 1328–1338 (1971)
Kloke, J.D., McKean, J.W., Mushfiqur Rashid, M.: Rank-based estimation and associated inferences for linear models with cluster correlated errors. J. Am. Stat. Assoc. 485, 384–390 (2009)
Nevalainen, J., Larocque, D., Oja, H., Pörsti, I.: Nonparametric analysis of clustered multivariate data. J. Am. Stat. Assoc. 490, 864–872 (2010)
Nordhausen, K., Oja, H.: Multivariate L 1 methods: the package MNM. J. Stat. Softw. 43, 1–28 (2011)
Oja, H.: Multivariate Nonparametric Methods with R: An Approach Based on Spatial Signs and Ranks. Springer, New York (2010)
Pinheiro, J., Bates, D., DebRoy, S., Sarkar, D., R Core Team: nlme: Linear and Nonlinear Mixed Effects Models. R package version 3.1-117. http://CRAN.R-project.org/package=nlme (2014)
R Core Team: R: A Language and Environment for Statistical Computing. R Foundation for Statistical Computing. http://www.R-project.org (2013)
Wang, Y.-G., Zhao, Y.: Weighted rank regression for clustered data analysis. Biometrics 64, 39–45 (2008)
Wang, Y.-G., Zhu, M.: Rank-based regression for analysis of repeated measures. Biometrika 93, 459–464 (2006)
Acknowledgements
This research was supported by NSERC, FRQNT, and the Academy of Finland. The authors also thank two anonymous reviewers for helpful comments.
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2015 Springer International Publishing Switzerland
About this chapter
Cite this chapter
Nevalainen, J., Larocque, D. (2015). L1-Regression for Multivariate Clustered Data. In: Nordhausen, K., Taskinen, S. (eds) Modern Nonparametric, Robust and Multivariate Methods. Springer, Cham. https://doi.org/10.1007/978-3-319-22404-6_13
Download citation
DOI: https://doi.org/10.1007/978-3-319-22404-6_13
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-22403-9
Online ISBN: 978-3-319-22404-6
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)