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.