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Nonparametric ANCOVA with two and three covariates

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  • Tsangari, Haritini
  • Akritas, Michael G.

Abstract

Fully nonparametric analysis of covariance with two and three covariates is considered. The approach is based on an extension of the model of Akritas et al. (Biometrika 87(3) (2000) 507). The model allows for possibly nonlinear covariate effect which can have different shape in different factor level combinations. All types of ordinal data are included in the formulation. In particular, the response distributions are not restricted to comply to any parametric or semiparametric model. In this nonparametric model, hypotheses of no main effect no interaction and no simple effect, which adjust for the covariate values, are defined through a decomposition of the conditional distribution functions of the response given to the factor level combination and covariate values. The test statistics are based on averages over the covariate values of certain Nadaraya-Watson regression quantities. Under their respective null hypotheses, such test statistics are shown to have a central [chi]2 distribution. Small sample corrections are also provided. Simulation results and the analysis of two real datasets are also presented.

Suggested Citation

  • Tsangari, Haritini & Akritas, Michael G., 2004. "Nonparametric ANCOVA with two and three covariates," Journal of Multivariate Analysis, Elsevier, vol. 88(2), pages 298-319, February.
    • Handle: RePEc:eee:jmvana:v:88:y:2004:i:2:p:298-319
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    1. Tershakovec, A.M. & Shannon, B.M. & Achterberg, C.L. & McKenzie, J.M. & Martel, J.K. & Smiciklas-Wright, H. & Pammer, S.E. & Cortner, J.A., 1998. "One-year follow-up of nutrition education for hypercholesterolemic children," American Journal of Public Health, American Public Health Association, vol. 88(2), pages 258-261.
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    Cited by:

    1. Debajit Chatterjee & Uttam Bandyopadhyay, 2019. "Testing in nonparametric ANCOVA model based on ridit reliability functional," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 71(2), pages 327-364, April.
    2. Jan De Neve & Olivier Thas, 2015. "A Regression Framework for Rank Tests Based on the Probabilistic Index Model," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 110(511), pages 1276-1283, September.

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