Nonparametric models and methods for ANCOVA with dependent data

Abstract

The nonparametric ANCOVA model of Akritas et al. [Akritas, M. G., Arnold, S. F. and Du, Y. (2000). Nonparametric models and methods for nonlinear analysis of covariance. Biometrika, 87(3), 507–526.] is extended to longitudinal data and for up to three covariates. In this model the response distributions need not be continuous or to comply to any parametric or semiparainetric model. The nonparametric covariate effect can be different in different factor level combinations. Nonparametric hypotheses of no main factor effects, no interaction and no simple effect, which adjust for the covariate values, are considered. The test statistics, which are based on averages over the covariate values of certain Nadaraya–Watson regression quantities, have asymptotically a central chi-squared distribution under their respective null hypotheses. Small sample corrections to the asymptotic distribution are provided. Simulation results and data analysis for a real dataset are presented.

Keywords:

• Kernel smoothing
• Mixed model
• Nonparametric hypotheses
• Nonparametric regression
• Repeated measures designs
• Longitudinal data

Acknowledgements

The authors are grateful to Dr. Vernon Chinchilli, Professor of Health Evaluation Sciences and Statistics, Penn State University, for providing the cholesterol data. This research was supported by NSF grant SES-0318200.