nn {gamlss.add}

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 [e-mail], Bob Rigby 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.

Rigby R.A., Stasinopoulos D. M., Heller G., and De Bastiani F., (2019) Distributions for Modeling Location, Scale and Shape: Using GAMLSS in R, Chapman and Hall/CRC.

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

Stasinopoulos D. M. Rigby R.A. (2007) Generalized additive models for location scale and shape (GAMLSS) in R. Journal of Statistical Software, 23(7), 1–46, doi:10.18637/jss.v023.i07

Stasinopoulos D. M., Rigby R.A., Heller G., Voudouris V., and De Bastiani F., (2017) Flexible Regression and Smoothing: Using GAMLSS in R, Chapman and Hall/CRC. (see also https://www.gamlss.com/).

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$fit <- predict(mg1, newdata=newrent, type="response")# gam
 library(lattice)
 wf1<-wireframe(fit~Fl+A, newrent1, aspect=c(1,0.5), drape=TRUE, 
                colorkey=(list(space="right", height=0.6)), main="nn()")
 wf2<-wireframe(fit~Fl+A, newrent2, aspect=c(1,0.5), drape=TRUE, 
                colorkey=(list(space="right", height=0.6)), main="ga()")
print(wf1, split=c(1,1,2,1), more=TRUE)
print(wf2, split=c(2,1,2,1))
#-------------------------------------------------------------------------
## Not run: 
data(db)
mdb1 <- gamlss(head~nn(~age,size=20, decay=0.001), data=db)
plot(head~age, data=db)
points(fitted(mdb1)~db$age, col="red")
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")

## End(Not run)