Nonparametric models and methods for nonlinear analysis of covariance

Citation
Mg. Akritas et al., Nonparametric models and methods for nonlinear analysis of covariance, BIOMETRIKA, 87(3), 2000, pp. 507-526
Citations number
20
Categorie Soggetti
Biology,Multidisciplinary,Mathematics
Journal title
BIOMETRIKA
ISSN journal
00063444 → ACNP
Volume
87
Issue
3
Year of publication
2000
Pages
507 - 526
Database
ISI
SICI code
0006-3444(200009)87:3<507:NMAMFN>2.0.ZU;2-R
Abstract
A fully nonparametric model for nonlinear analysis of covariance is propose d. The term nonlinear means that the covariate influences the response in a possibly nonlinear and nonpolynomial fashion, while the term fury nonparam etric implies that the distributions for each factor level combination and covariate value are not restricted to comply with ally parametric or semipa rametric model. The possibility of different shapes of covariate effect in different factor level combinations is also allowed. This generality is use ful whenever modelling assumptions such as proportional odds, or linearity and homoscedasticity appear suspect. In the context of this nonparametric m odel hypotheses, of no main effect, no interaction and no simple effect, wh ich adjust for the covariate values are defined and test statistics are dev eloped. Both the response and the covariate are allowed to be ordinal. The test statistics are based on averages over the covariate values of certain Nadaraya-Watson-type nonparametric regression quantities and asymptotically they have, under their respective null hypotheses, a central chi(2)-distri bution. Simulation results show that the statistics have good power propert ies. The procedures are demonstrated on two real datasets.