A description of the structure of the predictor model fitted using
NGeDS, GGeDS, NGeDSgam or
NGeDSboost.
# S3 method for GeDS
formula(x, ...)# S3 method for GeDSgam
formula(x, ...)
# S3 method for GeDSboost
formula(x, ...)
Fitted "GeDS", "GeDSgam" or "GeDSboost" class
object, produced by NGeDS, GGeDS,
NGeDSgam or NGeDSboost from which the predictor model
formula should be extracted.
Unused in this case.
In GeDS GNM (GLM) regression (implemented through NGeDS and
GGeDS) the mean of the response variable, correspondingly
transformed through an appropriate link function, is modeled using a
potentially multivariate predictor model. The latter comprises two components:
a GeD variable-knot spline regression involving up to two of the independent
variables and a parametric component for the remaining independent variables.
The formula defines the structure of this potentially multivariate predictor.
The formulae that are input in NGeDS and GGeDS
are similar to those input in lm or
glm except that the function f should be
specified in order to identify which of the covariates enter the GeD spline
regression part of the predictor model. For example, if the predictor model
is univariate and it links the transformed mean of y to x1,
the predictor has only a GeD spline component and the
formula should be in the form y ~ f(x1).
As noted, there may be additional independent variables x2,
x3, ... which may enter linearly into the parametric component of the
predictor model and not be part of the GeD spline regression component. For
example one may use the formula y ~ f(x1) + x2 + x3 which assumes a
spline regression only between the transformed mean of y and x1,
while x2 and x3 enter the predictor model linearly.
Both NGeDS and GGeDS functions, generate
bivariate GeDS regression models. Therefore, if the functional dependence of
the mean of the response variable y on x1 and x2 needs
to be jointly modeled and there are no other covariates, the formula for the
corresponding two dimensional predictor model should be specified as
y ~ f(x1,x2).
Within the argument formula, similarly as in other R functions, it is
possible to specify one or more offset variables, i.e., known terms with fixed
regression coefficients equal to 1. These terms should be identified via the
function offset.
For NGeDSgam and NGeDSboost, more than one GeD spline
component can be included in the formula, e.g., y ~ f(x1) + f(x2,x3) + x4,
where f() denotes GeD spline-based (univariate or bivariate) regression smoothing
functions/base-learners, and x4 is included as a linear term in the
predictor model. Offset terms are not supported by NGeDSboost and
will be ignored if included in the formula. Known additive components can
instead be manually incorporated into the response variable prior to fitting the model.