gamlss.add (version 4.0-0)

ga: A interface function to use Simon Wood's gam() function within GAMLSS

Description

The ga() function is a additive function to be used for GAMLSS models. It is an interface for the gam() function of package mgcv of Simon Wood. The function ga() allows the user to use all of the available smoothers of gam() within gamlss. The great advantage of course come from fitting models outside the exponential family.

Usage

ga(formula, ...)

Arguments

formula

A formula containing s() and te functions i.e. ~s(x1)+ te(x2,x3).

...

arguments used by the gam() function.

Value

• the fitted values of the smoother is returned, endowed with a number of attributes. The smoother fitted values are used in the construction of the overall fitted values of the particular distribution parameter. The attributes can be use to obtain information about the individual fit. In particular the coefSmo within the parameters of the fitted model contains the final additive fit.

Warning

The function id experimental so please report any peculiar behaviour to the authors

Details

Note that ga itself does no smoothing; it simply sets things up for the function gamlss() which in turn uses the function additive.fit() for backfitting which in turn uses gamlss.ga() Note that, in our (limited) experience, for normal errors or exponential family, the fitted models using gam() and ga() within gamlss() are identical or at least very similar. This is particularly true if the default values for gam() are used.

References

Rigby, R. A. and Stasinopoulos D. M. (2005). Generalized additive models for location, scale and shape,(with discussion), Appl. Statist., 54, part 3, pp 507-554. Stasinopoulos D. M., Rigby R.A. and Akantziliotou C. (2006) Instructions on how to use the GAMLSS package in R. Accompanying documentation in the current GAMLSS help files, (see also http://www.gamlss.com/). Stasinopoulos D. M. Rigby R.A. (2007) Generalized additive models for location scale and shape (GAMLSS) in R. Journal of Statistical Software, Vol. 23, Issue 7, Dec 2007, http://www.jstatsoft.org/v23/i07. Wood S.N. (2006) Generalized Additive Models: An Introduction with R. Chapman and Hall/CRC Press.

Examples

library(gamlss)
library(mgcv)
data(rent)
#---------------------------------------------------------
# normal errors one x-variable
ga1 <-  gam(R~s(Fl, bs="ps", k=20), data=rent, method="ML")
gn1 <- gamlss(R~pb(Fl), data=rent) # additive
gn2 <- gamlss(R~ga(~s(Fl)), data=rent) # additive
AIC(ga1,gn1,gn2,  k=0)
#--------------------------------------------------------
# normal error additive in Fl and A
# normal error additive in Fl and A
ga2 <- gam(R~s(Fl)+s(A), data=rent)
gn0 <- gamlss(R~pb(Fl)+pb(A), data=rent) # additive
gn1 <- gamlss(R~ga(~s(Fl)+s(A)), data=rent) # additive
gn2 <- gamlss(R~ga(~s(Fl))+ga(~s(A)), data=rent)
# somehow fitting 
AIC(ga2,gn0,gn1, gn2,  k=0)
#---------------------------------------------------------
# gamma errors one x-var
ga1 <-    gam(R~s(Fl), data=rent, family=Gamma)
gg1 <- gamlss(R~pb(Fl), data=rent, family=GA)
gg2 <- gamlss(R~ga(~s(Fl)), data=rent, family=GA)
AIC(ga1, gg1, gg2,  k=0)
# different degrees of freedon for mu in ga1
#---------------------------------------------------------
# gamma error two variables s() function
g22 <-gam(R~s(Fl,A), data=rent, family=Gamma)
gm22 <- gamlss(R~ga(~s(Fl,A)), data=rent, family=GA) 
AIC(g22,gm22)
# predict
newrent <- data.frame(expand.grid(Fl=seq(30,120,5), A=seq(1890,1990,5 )))
newrent$pred2 <- predict(gm22, newdata=newrent, type="response")
newrent$pred1 <- predict(g22, newdata=newrent, type="response")
library(lattice)
wf1<-wireframe(pred1~Fl*A, newrent, aspect=c(1,0.5), drape=TRUE, colorkey=(list(space="right", height=0.6)), main="gam()")
wf2<-wireframe(pred2~Fl*A, newrent, aspect=c(1,0.5), drape=TRUE, colorkey=(list(space="right", height=0.6)), main="gamlss()")
print(wf1, split=c(1,1,2,1), more=TRUE)
print(wf2, split=c(2,1,2,1))
#---------------------------------------------------------
#gamma error two variables te() function
g221 <-gam(R~te(Fl,A), data=rent, family=Gamma)
gm221 <- gamlss(R~ga(~te(Fl,A)), data=rent, family=GA) 
AIC(g221,gm221)
# predict
newrent <- data.frame(expand.grid(Fl=seq(30,120,5), A=seq(1890,1990,5 )))
newrent$pred2 <- predict(gm221, newdata=newrent, type="response")
newrent$pred1 <- predict(g221, newdata=newrent, type="response")
library(lattice)
wf1<-wireframe(pred1~Fl*A, newrent, aspect=c(1,0.5), drape=TRUE, colorkey=(list(space="right", height=0.6)), main="gam()")
wf2<-wireframe(pred2~Fl*A, newrent, aspect=c(1,0.5), drape=TRUE, colorkey=(list(space="right", height=0.6)), main="gamlss()")
print(wf1, split=c(1,1,2,1), more=TRUE)
print(wf2, split=c(2,1,2,1))
#----------------------------------------------------------