  This paper studies a very flexible model that can be used widely to analyze
the relation between a response and multiple covariates. The model is
nonparametric, yet renders easy interpretation for the effects of the
covariates. The model accommodates both continuous and discrete random
variables for the response and covariates. It is quite flexible to cover the
generalized varying coefficient models and the generalized additive models as
special cases. Under a weak condition we give a general theorem that the
problem of estimating the multivariate mean function is equivalent to that of
estimating its univariate component functions. We discuss implications of the
theorem for sieve and penalized least squares estimators, and then investigate
the outcomes in full details for a kernel-type estimator. The kernel estimator
is given as a solution of a system of nonlinear integral equations. We provide
an iterative algorithm to solve the system of equations and discuss the
theoretical properties of the estimator and the algorithm. Finally, we give
simulation results.
