Fitting Functional Generalized Kernel Additive Models.
Computes functional regression between functional explanatory variables (X(t_1),...,X(t_q)) and scalar response Y using backfitting algorithm.
fregre.gkam( formula, family = gaussian(), data, weights = rep(1, nobs), par.metric = NULL, par.np = NULL, offset = NULL, control = list(maxit = 100, epsilon = 0.001, trace = FALSE, inverse = "solve"), ... )
formula |
an object of class |
family |
a description of the error distribution and link function to
be used in the model. This can be a character string naming a family
function, a family function or the result of a call to a family function.
(See |
data |
List that containing the variables in the model. |
weights |
weights |
par.metric |
List of arguments by covariate to pass to the
|
par.np |
List of arguments to pass to the |
offset |
this can be used to specify an a priori known component to be included in the linear predictor during fitting. |
control |
a list of parameters for controlling the fitting process, by
default: |
... |
Further arguments passed to or from other methods. |
inverse |
="svd" (by default) or ="solve" method. |
The smooth functions f(.) are estimated nonparametrically using a
iterative local scoring algorithm by applying Nadaraya-Watson weighted
kernel smoothers using fregre.np.cv in each step, see
Febrero-Bande and Gonzalez-Manteiga (2011) for more details.
Consider the fitted response g(Y.est)=Hy,
where H is the weighted hat matrix.
Opsomer and Ruppert
(1997) solves a system of equations for fit the unknowns
f(.) computing the additive smoother matrix H_k
such that f.est_k(X_k)=H_k Y and
H= H_1+,...,+H_q. The additive model is fitted
as follows:
g(y.est)=∑(i:q) f.est_i(X_i)
result List of non-parametric estimation by covariate.
fitted.values Estimated scalar response.
residuals y minus fitted values.
effects The residual degrees of freedom.
alpha Hat matrix.
family Coefficient of determination.
linear.predictors Residual variance.
deviance Scalar response.
aic Functional explanatory data.
null.deviance Non functional explanatory data.
iter Distance matrix between curves.
w beta coefficient estimated
eqrank List that containing the variables in the model.
prior.weights Asymmetric kernel used.
y Scalar response.
H Hat matrix, see Opsomer and Ruppert(1997) for more details.
converged conv.
Febrero-Bande, M. and Oviedo de la Fuente, M.
Febrero-Bande M. and Gonzalez-Manteiga W. (2012). Generalized Additive Models for Functional Data. TEST. Springer-Velag. http://dx.doi.org/10.1007/s11749-012-0308-0
Opsomer J.D. and Ruppert D.(1997). Fitting a bivariate additive model
by local polynomial regression.Annals of Statistics, 25, 186-211.
See Also as: fregre.gsam, fregre.glm
and fregre.np.cv
## Not run:
data(tecator)
ab=tecator$absorp.fdata[1:100]
ab2=fdata.deriv(ab,2)
yfat=tecator$y[1:100,"Fat"]
# Example 1: # Changing the argument par.np and family
yfat.cat=ifelse(yfat<15,0,1)
xlist=list("df"=data.frame(yfat.cat),"ab"=ab,"ab2"=ab2)
f2<-yfat.cat~ab+ab2
par.NP<-list("ab"=list(Ker=AKer.norm,type.S="S.NW"),
"ab2"=list(Ker=AKer.norm,type.S="S.NW"))
res2=fregre.gkam(f2,family=binomial(),data=xlist,
par.np=par.NP)
res2
# Example 2: Changing the argument par.metric and family link
par.metric=list("ab"=list(metric=semimetric.deriv,nderiv=2,nbasis=15),
"ab2"=list("metric"=semimetric.basis))
res3=fregre.gkam(f2,family=binomial("probit"),data=xlist,
par.metric=par.metric,control=list(maxit=2,trace=FALSE))
summary(res3)
# Example 3: Gaussian family (by default)
# Only 1 iteration (by default maxit=100)
xlist=list("df"=data.frame(yfat),"ab"=ab,"ab2"=ab2)
f<-yfat~ab+ab2
res=fregre.gkam(f,data=xlist,control=list(maxit=1,trace=FALSE))
res
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