nn {gamlss.add}R Documentation

A interface function to use nnet() function within GAMLSS

Description

The nn() function is a additive function to be used for GAMLSS models. It is an interface for the nnet() function of package nnet of Brian Ripley. The function nn() allows the user to use neural networks within gamlss. The great advantage of course comes from the fact GAMLSS models provide a variety of distributions and diagnostics.

Usage

nn(formula, control = nn.control(...), ...)
nn.control(size = 3, linout = TRUE, entropy = FALSE, softmax = FALSE, 
           censored = FALSE, skip = FALSE, rang = 0.7, decay = 0, 
           maxit = 100, Hess = FALSE, trace = FALSE, 
           MaxNWts = 1000, abstol = 1e-04, reltol = 1e-08)

Arguments

formula A formula containing the expolanatory variables i.e. ~x1+x2+x3.
control control to pass the arguments for the nnet() function
... for extra arguments
size number of units in the hidden layer. Can be zero if there are skip-layer units
linout switch for linear output units. Default is TRUE, identily link
entropy switch for entropy (= maximum conditional likelihood) fitting. Default by least-squares.
softmax switch for softmax (log-linear model) and maximum conditional likelihood fitting. linout, entropy, softmax and censored are mutually exclusive.
censored A variant on softmax, in which non-zero targets mean possible classes. Thus for softmax a row of (0, 1, 1) means one example each of classes 2 and 3, but for censored it means one example whose class is only known to be 2 or 3.
skip switch to add skip-layer connections from input to output
rang Initial random weights on [-rang, rang]. Value about 0.5 unless the inputs are large, in which case it should be chosen so that rang * max(|x|) is about 1
decay parameter for weight decay. Default 0.
maxit parameter for weight decay. Default 0.
Hess If true, the Hessian of the measure of fit at the best set of weights found is returned as component Hessian.
trace switch for tracing optimization. Default FALSE
MaxNWts The maximum allowable number of weights. There is no intrinsic limit in the code, but increasing MaxNWts will probably allow fits that are very slow and time-consuming.
abstol Stop if the fit criterion falls below abstol, indicating an essentially perfect fit.
reltol Stop if the optimizer is unable to reduce the fit criterion by a factor of at least 1 - reltol.

Details

Note that, neural networks are over parameterized models and therefor notorious for multiple maximum. There is no guarantee that two identical fits will produce identical results.

Value

Note that nn 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.nn()

Warning

You may have to fit the model several time to unsure that you obtain a reasonable minimum

Author(s)

Mikis Stasinopoulos d.stasinopoulos@londonmet.ac.uk, Bob Rigby r.rigby@londonmet.ac.uk based on work of Venables & Ripley wich also based on work by Kurt Hornik and Albrecht Gebhardt.

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.

Ripley, B. D. (1996) Pattern Recognition and Neural Networks. Cambridge.

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.

Venables, W. N. and Ripley, B. D. (2002) Modern Applied Statistics with S. Fourth edition. Springer.

Examples

library(nnet)
data(rock)
area1<- with(rock,area/10000)
peri1<- with (rock,peri/10000) 
rock1<- with(rock, data.frame(perm, area=area1, peri=peri1, shape))
# fit nnet
r1 <- nnet(log(perm)~area+peri+shape, rock1, size=3, decay=1e-3, linout=TRUE, skip=TRUE, max=1000, Hess=TRUE)
summary(r1) 
# get gamlss
library(gamlss) 
cc <- nn.control(size=3, decay=1e-3, linout=TRUE, skip=TRUE, max=1000, Hess=TRUE)
g1 <- gamlss(log(perm)~nn(~area+peri+shape,size=3, control=cc), data=rock1)
summary(g1$mu.coefSmo[[1]])
# predict
Xp <- expand.grid(area=seq(0.1,1.2,0.05), peri=seq(0,0.5, 0.02), shape=0.2)
rocknew <- cbind(Xp, fit=predict(r1, newdata=Xp))
library(lattice)
wf1<-wireframe(fit~area+peri, rocknew, screen=list(z=160, x=-60), aspect=c(1, 0.5), drape=TRUE,  main="nnet()")
rocknew1 <- cbind(Xp, fit=predict(g1, newdata=Xp))
wf2<-wireframe(fit~area+peri, rocknew1, screen=list(z=160, x=-60), aspect=c(1, 0.5), drape=TRUE,  main="nn()")
print(wf1, split=c(1,1,2,1), more=TRUE)
print(wf2, split=c(2,1,2,1))
#--------------------------------------------------------------------------------------- 
 data(rent)
 mr1 <- gamlss(R~nn(~Fl+A, size=5, decay=0.001), data=rent, family=GA)  
 library(gamlss.add)
 mg1<-gamlss(R~ga(~s(Fl,A)), data=rent, family=GA) 
 AIC(mr1,mg1)
newrent <- newrent1 <-newrent2 <- data.frame(expand.grid(Fl=seq(30,120,5), A=seq(1890,1990,5 )))
newrent1$fit <- predict(mr1, newdata=newrent, type="response") ##nn
newrent2$fit <- predict(mg1, newdata=newrent, type="response")# gam
 library(lattice)
 wf1<-wireframe(fit~Fl+A, newrent1, aspect=c(1,0.5), drape=TRUE, colorkey=(list(space="right", height=0.6)), main="nn()")
 wf2<-wireframe(fit~Fl+A, newrent2, aspect=c(1,0.5), drape=TRUE, colorkey=(list(space="right", height=0.6)), main="ga()")
print(wf1, split=c(1,1,2,1), more=TRUE)
print(wf2, split=c(2,1,2,1))
#----------------------------------------------------------------------------------------
data(db)
mdb1 <- gamlss(head~nn(~age,size=20, decay=0.001), data=db)
plot(head~age, data=db)
points(fitted(mdb1)~db$age, col="red")

# do not run
#mdb2 <- gamlss(head~nn(~age,size=20, decay=0.001), data=db, family=BCT)
#plot(head~age, data=db)
#points(fitted(mdb2)~db$age, col="red")

[Package gamlss.add version 3.1-0 Index]