Help for package gamlss.add

Title:

Extra Additive Terms for Generalized Additive Models for Location Scale and Shape

Version:

5.1-13

Date:

2024-03-17

Description:

Interface for extra smooth functions including tensor products, neural networks and decision trees.

License:

GPL-2 | GPL-3

URL:

https://www.gamlss.com/

BugReports:

https://github.com/gamlss-dev/gamlss.add/issues

Depends:

R (≥ 2.15.0), gamlss.dist, gamlss (≥ 2.4.0), mgcv, nnet, rpart, graphics, stats, utils, grDevices, methods

Suggests:

lattice

LazyLoad:

yes

NeedsCompilation:

Packaged:

2024-03-27 09:16:11 UTC; dimitriosstasinopoulos

Author:

Mikis Stasinopoulos

[aut, cre], Robert Rigby

[aut], Vlasios Voudouris [ctb], Daniil Kiose

[ctb]

Maintainer:

Mikis Stasinopoulos <d.stasinopoulos@gre.ac.uk>

Repository:

CRAN

Date/Publication:

2024-03-28 08:50:07 UTC

Extra Additive Terms for Generalized Additive Models for Location Scale and Shape

Description

Interface for extra smooth functions including tensor products, neural networks and decision trees.

Details

The DESCRIPTION file:

Package:	gamlss.add
Title:	Extra Additive Terms for Generalized Additive Models for Location Scale and Shape
Version:	5.1-13
Date:	2024-03-17
Authors@R:	c(person("Mikis", "Stasinopoulos", role = c("aut", "cre"), email = "d.stasinopoulos@gre.ac.uk", comment = c(ORCID = "0000-0003-2407-5704")), person("Robert", "Rigby", role = "aut", email = "r.rigby@gre.ac.uk", comment = c(ORCID = "0000-0003-3853-1707")), person("Vlasios", "Voudouris", role = "ctb"), person("Daniil", "Kiose", role = "ctb", comment = c(ORCID = "0000-0002-3596-5748")) )
Description:	Interface for extra smooth functions including tensor products, neural networks and decision trees.
License:	GPL-2 \| GPL-3
URL:	https://www.gamlss.com/
BugReports:	https://github.com/gamlss-dev/gamlss.add/issues
Depends:	R (>= 2.15.0), gamlss.dist, gamlss (>= 2.4.0), mgcv, nnet, rpart, graphics, stats, utils, grDevices, methods
Suggests:	lattice
LazyLoad:	yes
Author:	Mikis Stasinopoulos [aut, cre] (<https://orcid.org/0000-0003-2407-5704>), Robert Rigby [aut] (<https://orcid.org/0000-0003-3853-1707>), Vlasios Voudouris [ctb], Daniil Kiose [ctb] (<https://orcid.org/0000-0002-3596-5748>)
Maintainer:	Mikis Stasinopoulos <d.stasinopoulos@gre.ac.uk>

Index of help topics:

centilesTwo             Centiles contour plots in GAMLSS
fitFixedKnots           Functions to Fit Univariate Break Point
                        Regression Models
fk                      A function to fit break points within GAMLSS
ga                      A interface functions to use Simon Wood's gam()
                        and bam() functions within GAMLSS
gamlss.add-package      Extra Additive Terms for Generalized Additive
                        Models for Location Scale and Shape
gamlss.fk               Support for Function fk()
gamlss.ga               Support for Function ga() and ba()
gamlss.nn               Support for Function nn()
nn                      A interface function to use nnet() function
                        within GAMLSS
plot.nnet               Plotting fitted neural networks
tr                      A interface function to use rpart() function
                        within GAMLSS

Author(s)

Mikis Stasinopoulos [aut, cre] (<https://orcid.org/0000-0003-2407-5704>), Robert Rigby [aut] (<https://orcid.org/0000-0003-3853-1707>), Vlasios Voudouris [ctb], Daniil Kiose [ctb] (<https://orcid.org/0000-0002-3596-5748>)

Maintainer: Mikis Stasinopoulos <d.stasinopoulos@gre.ac.uk>

References

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

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.

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/).

Therneau T. M., Atkinson E. J. (2015) An Introduction to Recursive Partitioning Using the RPART Routines. Vignette in package rpart.

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

Wood S.N. (2006) Generalized Additive Models: An Introduction with R. Chapman and Hall/CRC Press.

Examples

library(gamlss)
gn <- gamlss(R~ga(~te(Fl,A)), data=rent, family=GA)

Centiles contour plots in GAMLSS

Description

This function centilesTwo() plots two dimensional centiles contour plots for GAMLSS models.

Usage

centilesTwo(object, grid.x1, grid.x2, x1.name, x2.name, 
       cent = 0.05, dist = 0.01, points = TRUE, 
       other = list(), point.col = 1, point.pch = ".", 
       image = FALSE, image.col = heat.colors(12), ...)

Arguments

object

an gamlss object

grid.x1

grid values for x-variable one

grid.x2

grid values for x-variable two

x1.name

the name of x-variable on

x2.name

the name of x-variable two

cent

the required centiles

dist

the distance

points

whether to plot the data points

other

a list having other explanatory variables at fixed values

point.col

the colour of the data points

point.pch

the type of the data point

image

whether to plot using the image9 function

image.col

the colour scheme

...

for extra arguments for the contour() function

Details

The function uses the function exclude.too.far() of the package mgcv.

Value

Produce a contour plot.

Author(s)

Mikis Stasinopoulos d.stasinopoulos@londonmet.ac.uk, Bob Rigby, Fernanda De Bastiani

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.

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/).

Wood S.N. (2006) Generalized Additive Models: An Introduction with R. Chapman and Hall/CRC Press.

Examples

## Not run:  
data(plasma)
m1 <- gamlss(betadiet ~ ga(~te(age, fiber)), sigma.formula = ~1,  
    nu.formula = ~ga(~te(age, fiber)), tau.formula = ~1,  
    family = BCTo, data = plasma)
centilesTwo(m1, 18:90, seq(2.5,38, 0.5), age, fiber, cent=0.05, dist=.1,
            xlab="age", ylab='fiber') 
centilesTwo(m1, 18:90, seq(2.5,38, 0.5), age, fiber, cent=0.95, dist=.1)

## End(Not run)

Functions to Fit Univariate Break Point Regression Models

Description

There are two main functions here. The functions fitFixedKnots allows the fit a univariate regression using piecewise polynomials with "known" break points while the function fitFreeKnots estimates the break points.

Usage

fitFixedKnots(y, x, weights = NULL, knots = NULL, data = NULL, degree = 3, 
             fixed = NULL, base=c("trun","Bbase"), ...)
fitFreeKnots(y, x, weights = NULL, knots = NULL, degree = 3, fixed =
                 NULL, trace = 0, data = NULL, base=c("trun","Bbase"), ...)

Arguments

x

the x variable (explanatory)

y

the response variable

weights

the prior weights

knots

the position of the interior knots for fitFixedKnots or starting values for fitFreeKnots

data

the data frame

degree

the degree if the piecewise polynomials

fixed

this is to be able to fit fixed break points

base

The basis for the piecewise polynomials, turn for truncated (default) and Bbase for B-base piecewise polynomials

trace

controlling the trace of of optim()

...

for extra arguments

Details

The functions fitFreeKnots() is loosely based on the curfit.free.knot() function of package DierckxSpline of Sundar Dorai-Raj and Spencer Graves.

Value

The functions fitFixedKnots and fitFreeKnots return an object FixBreakPointsReg and FreeBreakPointsReg respectively with the following items:

fitted.values

the fitted values of the model

residuals

the residuals of the model

df

the degrees of freedom fitted in the model

rss

the residuals sum of squares

knots

the knots used in creating the beta-function base

fixed

the fixed break points if any

breakPoints

the interior (estimated) break points (or knots)

coef

the coefficients of the linear part of the model

degree

the degree of the piecewise polynomial

y

the y variable

x

the x variable

w

the prior weights

Note

The prediction function in piecewise polynomials using the B-spline basis is tricky because by adding the newdata for x to the current one the B-basis function for the piecewise polynomials changes. This does not seems to be the case with the truncated basis, that is, when the option base="turn" is used (see the example below).

If the newdata are outside the range of the old x then there could a considerable discrepancies between the all fitted values and the predicted ones if the option base="Bbase" is used. The prediction function for the objects FixBreakPointsReg or FreeBreakPointsReg has the option old.x.range=TRUE which allow the user two choices:

The first is to use the old end-points for the creation of the new B-basis which were determine from the original range of x. This choice is implemented as a default in the predict method for FixBreakPointsReg and FreeBreakPointsReg objects with the argument old.x.range=TRUE.

The second is to create new end-points from the new and old data x values. In this case the range of x will be bigger that the original one if the newdata has values outside the original x range. In this case (old.x.range=FALSE) the prediction could be possible better outside the x range but would not coincide with the original predictions i.e. fitted(model) since basis have changed.

Author(s)

Mikis Stasinopoulos d.stasinopoulos@londonmet.ac.uk

References

Dierckx, P. (1991) Curve and Surface Fitting with Splines, Oxford Science Publications

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.

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/).

Examples

# creating  a linear + linear function
   x <- seq(0,10, length.out=201)
knot <- 5
 set.seed(12543)
 mu <- ifelse(x<=knot,5+0.5*x,5+0.5*x+(x-knot))
  y <- rNO(201, mu=mu, sigma=.5)
# plot the data
 plot(y~x, xlim=c(-1,13), ylim=c(3,18))

# fit model using fixed break points
 m1 <- fitFixedKnots(y, x, knots=5, degree=1)
knots(m1)
lines(fitted(m1)~x, col="red")

# now estimating the knot
m2 <- fitFreeKnots(y, x, knots=5, degree=1)
knots(m2)
summary(m2)

# now predicting 
plot(y~x, xlim=c(-5,13), ylim=c(3,18))
lines(fitted(m2)~x, col="green", lwd=3)
points(-2:13,predict(m2, newdata=-2:13), col="red",pch = 21, bg="blue")
points(-2:13,predict(m2, newdata=-2:13, old.x.range=FALSE), col="red",pch = 21, bg="grey")

# fit different basis 
m21 <- fitFreeKnots(y, x, knots=5, degree=1, base="Bbase")
deviance(m2) 
deviance(m21) # should be identical

# predicting with m21 
 plot(y~x, xlim=c(-5,13), ylim=c(3,18))
lines(fitted(m21)~x, col="green", lwd=3)
points(-2:13,predict(m21, newdata=-2:13), col="red",pch = 21, bg="blue")
points(-2:13,predict(m21, newdata=-2:13, old.x.range=FALSE), col="red",pch = 21, bg="grey")

A function to fit break points within GAMLSS

Description

The fk() function is a additive function to be used for GAMLSS models. It is an interface for the fitFreeKnots() function. The functions fitFreeKnots() was first based on the curfit.free.knot() function of package DierckxSpline of Sundar Dorai-Raj and Spencer Graves. The function fk() allows the user to use the free knots function fitFreeKnots() within gamlss. The great advantage of course comes from the fact GAMLSS models provide a variety of distributions and diagnostics.

Usage

fk(x, start=NULL, control=fk.control(...), ...) 
fk.control(degree = 1, all.fixed = FALSE, fixed = NULL, base = c("trun", "Bbase"))

Arguments

x

the x-variable

start

starting values for the breakpoints. If are set the number of break points is also determined by the length of start

control

the degree of the spline function fitted

...

for extra arguments

degree

the degree of the based function

all.fixed

whether to fix all parameter

fixed

the fixed break points

base

Which base should be used

Details

Note that fk 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.fk(). Note that, finding the break points is not a trivial problem and therefore multiple maximum points can occur. More details about the free knot splines can be found in package Dierckx, (1991).

The gamlss algorithm used a modified backfitting in this case, that is, it fits the linear part fist. Note that trying to predict outside the x-range can be dangerous as the example below shows.

Value

The gamlss object saved contains the last fitted object which can be accessed using obj$par.coefSmo where obj is the fitted gamlss object par is the relevant distribution parameter.

Author(s)

Mikis Stasinopoulos d.stasinopoulos@londonmet.ac.uk, Bob Rigby

References

Dierckx, P. (1991) Curve and Surface Fitting with Splines, Oxford Science Publications

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 https://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, 23(7), 1–46, doi:10.18637/jss.v023.i07

Examples

## creating  a linear + linear function
x <- seq(0,10, length.out=201)
knot <- 5
set.seed(12543)
mu <- ifelse(x<=knot,5+0.5*x,5+0.5*x+1.5*(x-knot))
y <- rNO(201, mu=mu, sigma=.5)
## plot the data
plot(y~x, xlim=c(-1,13), ylim=c(3,23))
## fit model using curfit
m1 <- fitFreeKnots(y, x, knots=3, degree=1)
knots(m1)
## fitted values
lines(fitted(m1)~x, col="red", lwd="3")
## predict
pm1<-predict(m1, newdata=-1:12)
points(-1:12,pm1, col="red",pch = 21, bg="blue")
#------------------------------------------------
## now gamlss
#------------------------------------------------
## now negative binomial data 
knot=4
eta1 <- ifelse(x<=knot,0.8+0.08*x,.8+0.08*x+.3*(x-knot))
plot(eta1~x)
set.seed(143)
y <- rNBI(201, mu=exp(eta1), sigma=.1)
da <- data.frame(y=y,x=x)
plot(y~x, data=da)
## getting the break point using profile deviance
n1 <- quote(gamlss(y ~ x+I((x>this)*(x-this)), family=NBI, data=da))
prof.term(n1, min=1, max=9, criterion="GD", start.prev=FALSE)
## now fit the model using fk
g1 <- gamlss(y~fk(x, degree=1, start=c(4)), data=da, family=NBI)
## get the breakpoint
knots(getSmo(g1))
## summary of the gamlss object FreeBreakPointsReg object
getSmo(g1)
## plot fitted model
plot(y~x, data=da)
lines(fitted(g1)~x, data=da, col="red")
#------------------------------------------------
## the aids data as example where things can go wrong
## using fk()
data(aids)
a1<-gamlss(y~x+fk(x, degree=1, start=25)+qrt, data=aids, family=NBI)
knots(getSmo(a1))
# using profile deviance
aids.1 <- quote(gamlss(y ~ x+I((x>this)*(x-this))+qrt,family=NBI,data=aids))
prof.term(aids.1, min=16, max=21, step=.1,  start.prev=FALSE)
## The Maximum Likelihood estimator is  18.33231 not 17.37064 
## plotting the fit
with(aids, plot(x,y,pch=21,bg=c("red","green3","blue","yellow")[unclass(qrt)]))
lines(fitted(a1)~aids$x)
#-------------------------------------------------

A interface functions to use Simon Wood's gam() and bam() functions within GAMLSS

Description

The ga() and ba() functions are a additive functions to be used within GAMLSS models. They are interfaces for the gam() and the bam() functions of package mgcv of Simon Wood. The functions gam() and the bam() allows the user to use all the available smoothers of the package mcgv() within gamlss. The great advantage of course come from fitting models outside the exponential family.

Usage

ga(formula, control = ga.control(...), ...)

ba(formula, control = ba.control(...), ...)

ga.control(offset = NULL, method = "REML",
         optimizer = c("outer", "newton"), control = list(), 
         scale = 0, select = FALSE, knots = NULL, 
         sp = NULL, min.sp = NULL, H = NULL, gamma = 1, 
         paraPen = NULL, in.out = NULL, 
         drop.unused.levels = TRUE, drop.intercept = NULL, 
         discrete = FALSE, ...)
     
ba.control(offset = NULL, method = "fREML", control = list(), 
          select = FALSE, scale = 0, gamma = 1, knots = NULL, 
          sp = NULL, min.sp = NULL, paraPen = NULL, 
          chunk.size = 10000, rho = 0, AR.start = NULL, 
          discrete = TRUE, cluster = NULL, nthreads = 2, 
          gc.level = 1, use.chol = FALSE, samfrac = 1, 
          coef = NULL, drop.unused.levels = TRUE, 
          drop.intercept = NULL, ...)

Arguments

formula

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

offset

the offset in the formula

method

the method argument in gam() and bam()

optimizer

the method optimizer in gam()

control

values for the gam.control()

scale

for the scale parameter

select

the select argument in gam() and bam()

knots

the knots argument in gam() and bam()

sp

the sp argument in gam() and bam()

min.sp

the min.sp argument in gam() and bam()

H

a user supplied fixed quadratic penalty on the parameters in gam()

gamma

the gamma argument in gam() and bam()

paraPen

the paraPen argument in gam() and bam()

in.out

the in.out argument in gam()

drop.unused.levels

by default unused levels are dropped from factors before fitting for gam() and bam()

drop.intercept

set to TRUE to force the model to really not have the a constant in the parametric model part for gam() and bam()

discrete

see bam and gam for details

chunk.size

see the help for bam().

rho

for an AR1 error model, see the help for bam()

AR.start

for an AR1 error model, see the help for bam()

cluster

see the help for bam()

nthreads

Number of threads to use for non-cluster computation see the help for bam()

gc.level

keepingf the memory footprint down, see the help for bam()

use.chol

see the help for bam()

samfrac

see the help for bam()

coef

initial values for model coefficients

...

extra options to pass to gam.control()

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 back-fitting 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.

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 is experimental so please report any peculiar behaviour to the authors

Author(s)

Mikis Stasinopoulos, d.stasinopoulos@londonmet.ac.uk

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.

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/).

Wood S.N. (2006) Generalized Additive Models: An Introduction with R. Chapman and Hall/CRC Press.

Examples

library(mgcv)
data(rent)
#---------------------------------------------------------
## normal errors one x-variable
ga1 <- gam(R~s(Fl, bs="ps", k=20), data=rent, method="REML")
gn1 <- gamlss(R~ga(~s(Fl, bs="ps", k=20), method="REML"), data=rent) # additive
gb1 <- gamlss(R~pb(Fl), data=rent) # additive
AIC(ga1,gn1, gb1, k=0)
AIC(ga1,gn1, gb1)
#--------------------------------------------------------
## normal error additive in Fl and A
ga2 <- gam(R~s(Fl)+s(A), method="REML", data=rent)
gn2 <- gamlss(R~ga(~s(Fl)+s(A), method="REML"),  data=rent) # additive
gb2 <- gamlss(R~pb(Fl)+pb(A), data=rent) # additive
AIC(ga2,gn2, gb2, k=0)
AIC(ga2,gn2, gb2)
#---------------------------------------------------------
## Not run: 
## gamma error additive in Fl and A
ga3 <- gam(R~s(Fl)+s(A), method="REML", data=rent, family=Gamma(log))
gn3 <- gamlss(R~ga(~s(Fl)+s(A), method="REML"), data=rent, family=GA)# additive
gb3 <- gamlss(R~pb(Fl)+pb(A), data=rent, family=GA) # additive
AIC(ga3,gn3, gb3, k=0)
AIC(ga3,gn3, gb3)
#---------------------------------------------------------
## gamma error surface fitting
ga4 <-gam(R~s(Fl,A), method="REML", data=rent, family=Gamma(log))
gn4 <- gamlss(R~ga(~s(Fl,A), method="REML"), data=rent, family=GA) 
AIC(ga4,gn4, k=0)
AIC(ga4,gn4)
## plot the fitted surfaces
op<-par(mfrow=c(1,2))
vis.gam(ga4)
vis.gam(getSmo(gn4))
par(op)
## contour plot using mgcv's plot() function
plot(getSmo(gn4))
#---------------------------------------------------------
## predict
newrent <- data.frame(expand.grid(Fl=seq(30,120,5), A=seq(1890,1990,5 )))
newrent1 <-newrent2 <- newrent
newrent1$pred <- predict(ga4, newdata=newrent, type="response")
newrent2$pred <- predict(gn4, newdata=newrent, type="response")
library(lattice)
wf1<-wireframe(pred~Fl*A, newrent1, aspect=c(1,0.5), drape=TRUE, 
             colorkey=(list(space="right", height=0.6)), main="gam()")
wf2<-wireframe(pred~Fl*A, newrent2, 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
ga5 <-  gam(R~te(Fl,A), data=rent, family=Gamma(log))
gn5 <- gamlss(R~ga(~te(Fl,A)), data=rent, family=GA) 
AIC(ga5,gn5)
AIC(ga5,gn5, k=0)
op<-par(mfrow=c(1,2))
vis.gam(ga5)
vis.gam(getSmo(gn5))
par(op)
#----------------------------------------------------------
## use of Markov random fields 
## example from package mgcv of Simon Wood
## Load Columbus Ohio crime data (see ?columbus for details and credits)
data(columb)       ## data frame
data(columb.polys) ## district shapes list
xt <- list(polys=columb.polys) ## neighbourhood structure info for MRF
## First a full rank MRF...
b <- gam(crime ~ s(district,bs="mrf",xt=xt),data=columb,method="REML")
bb <- gamlss(crime~ ga(~s(district,bs="mrf",xt=xt), method="REML"), data=columb)
AIC(b,bb, k=0)
op<-par(mfrow=c(2,2))
plot(b,scheme=1)
plot(bb$mu.coefSmo[[1]], scheme=1)
## Compare to reduced rank version...
b <- gam(crime ~ s(district,bs="mrf",k=20,xt=xt),data=columb,method="REML")
bb <- gamlss(crime~ ga(~s(district,bs="mrf",k=20,xt=xt), method="REML"), 
             data=columb)
AIC(b,bb, k=0)
plot(b,scheme=1)
plot(bb$mu.coefSmo[[1]], scheme=1)
par(op)
## An important covariate added...
b <- gam(crime ~ s(district,bs="mrf",k=20,xt=xt)+s(income),
         data=columb,method="REML")
## x in gam() 
bb <- gamlss(crime~ ga(~s(district,bs="mrf",k=20,xt=xt)+s(income), 
             method="REML"), data=columb)
## x in gamlss()
bbb <- gamlss(crime~ ga(~s(district,bs="mrf",k=20,xt=xt), 
             method="REML")+pb(income), data=columb)
AIC(b,bb,bbb)
## ploting the fitted models
op<-par(mfrow=c(2,2))
plot(b,scheme=c(0,1))
plot(getSmo(bb), scheme=c(0,1))
par(op)
plot(getSmo(bbb, which=2))
## plot fitted values by district
op<- par(mfrow=c(1,2))
fv <- fitted(b)
names(fv) <- as.character(columb$district)
fv1 <- fitted(bbb)
names(fv1) <- as.character(columb$district)
polys.plot(columb.polys,fv)
polys.plot(columb.polys,fv1)
par(op)
## End(Not run)
## bam

Support for Function fk()

Description

This is support for the functions fk(). It is not intended to be called directly by users. T he function gamlss.fk is calling on the R function curfit.free.knot() of Sundar Dorai-Raj

Usage

gamlss.fk(x, y, w, xeval = NULL, ...)

Arguments

x

the design matrix

y

the response variable

w

prior weights

xeval

used in prediction

...

for extra arguments

Author(s)

Mikis Stasinopoulos d.stasinopoulos@londonmet.ac.uk, Bob Rigby

References

Dierckx, P. (1991) Curve and Surface Fitting with Splines, Oxford Science Publications

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.

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/).

Support for Function ga() and ba()

Description

This is support for the smoother functions ga() and ba() intefaces for Simon Woood's gam() and bam() functions from package mgcv. It is not intended to be called directly by users.

Usage

gamlss.ga(x, y, w, xeval = NULL, ...)
gamlss.ba(x, y, w, xeval = NULL, ...)

Arguments

x

the explanatory variables

y

iterative y variable

w

iterative weights

xeval

if xeval=TRUE then predicion is used

...

for extra arguments

Author(s)

Mikis Stasinopoulos d.stasinopoulos@londonmet.ac.uk, Bob Rigby

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.

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/).

Wood S.N. (2006) Generalized Additive Models: An Introduction with R. Chapman and Hall/CRC Press.

Support for Function nn()

Description

This is support for the smoother function nn() an interface for Brian Reply's nnet() function. It is not intended to be called directly by users.

Usage

gamlss.nn(x, y, w, xeval = NULL, ...)

Arguments

x

the explanatory variables

y

iterative y variable

w

iterative weights

xeval

if xeval=TRUE then predicion is used

...

for extra arguments

Author(s)

Mikis Stasinopoulos d.stasinopoulos@londonmet.ac.uk, Bob Rigby

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.

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 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)

Plotting fitted neural networks

Description

A function to plot the results of a neural network fit based on the plotnet() function of the package NeuralNetTools

Usage

## S3 method for class 'nnet'
## S3 method for class 'nnet'
plot(x, nid = TRUE, all.out = TRUE, all.in = TRUE, bias = TRUE, 
wts.only = FALSE, rel.rsc = 5, circle.cex = 5, node.labs = TRUE, 
var.labs = TRUE, x.lab = NULL, y.lab = NULL, line.stag = NULL, 
struct = NULL, cex.val = 1, alpha.val = 1, circle.col = "lightblue",
pos.col = "black", neg.col = "grey", max.sp = FALSE, ...)

Arguments

x

A neural network fitted model

nid

logical value indicating if neural interpretation diagram is plotted, default is TRUE

all.out

character string indicating names of response variables for which connections are plotted, default all

all.in

character string indicating names of input variables for which connections are plotted, default all

bias

logical value indicating if bias nodes and connections are plotted, not applicable for networks from mlp function, default TRUE

wts.only

logical value indicating if connections weights are returned rather than a plot, default FALSE

rel.rsc

numeric value indicating maximum width of connection lines, default 5

circle.cex

numeric value indicating size of nodes, passed to cex argument, default 5

node.labs

logical value indicating if text labels are plotted, default TRUE

var.labs

logical value indicating if variable names are plotted next to nodes, default TRUE

x.lab

character string indicating names for input variables, default from model object

y.lab

character string indicating names for output variables, default from model object

line.stag

numeric value that specifies distance of connection weights from nodes

struct

numeric value of length three indicating network architecture (no nodes for input, hidden, output), required only if mod.in is a numeric vector

cex.val

numeric value indicating size of text labels, default 1

alpha.val

numeric value (0-1) indicating transparency of connections, default 1

circle.col

text value indicating colour of nodes default "lighrblue"

pos.col

text value indicating colour of the possitive connections, default "black"

neg.col

text value indicating colour of the negative connections, default "gray"

max.sp

logical value indication whether the space betwwen nodes in each laers is maximised

...

for further arguments

Details

The function plot.nnet() is (almost) identical to the function plot.nnet() created by Marcus W. Beck it was first published in the web but now is part of the NeuralNetTools package in R under the name plotnet(). Here we modify the function it so it works within the gamlss.add package. This involves of borrowing the functions rescale(), zero_range() and alpha() from package scales.

Value

The function is producing a plot

Author(s)

Marcus W. Beck <mbafs2012@gmail.com> modified by Mikis Stasinopoulos

References

Marcus W. Beck (2015). NeuralNetTools: Visualization and Analysis Tools for Neural Networks. R package version 1.4.1. https://cran.r-project.org/package=NeuralNetTools

Hadley Wickham (2014). scales: Scale functions for graphics. R package version 0.4.0. https://cran.r-project.org/package=scales

Examples

r1 <- gamlss(R~nn(~Fl+A+H+loc, size=10, decay=0.2), data=rent, 
      family=GA, gd.tol=1000, n.cyc=5)
getSmo(r1)
plot(getSmo(r1), y.lab=expression(eta[1]))
plot(getSmo(r1), y.lab=expression(g[1](mu)))
## Not run: 
r2 <- gamlss(R~nn(~Fl+A+H+loc, size=10, decay=0.2), 
      sigma.fo=~nn(~Fl+A+H+loc, size=10, decay=0.2),data=rent, 
      family=GA, gd.tol=1000, n.cyc=5)
plot(getSmo(r2), y.lab=expression(g[1](mu)))
plot(getSmo(r2, what="sigma"), y.lab=expression(g[2](sigma)))

## End(Not run)

A interface function to use rpart() function within GAMLSS

Description

The tr() function is a additive function to be used for GAMLSS models. It is an interface for the rpart() function of package rpart. The function tr() allows the user to use regression trees within gamlss. The great advantage of course comes from the fact GAMLSS models provide a variety of distributions and diagnostics. Note that the function gamlss.tr is not used by the user but it needed for the backfitting.

Usage

tr(formula, method = c("rpart"), control = rpart.control(...), ...)
gamlss.tr(x, y, w, xeval = NULL, ...)

Arguments

formula

A formula containing the expolanatory variables i.e. ~x1+x2+x3.

method

only method "rpart" is supported at the moment

control

control here is equivalent to rpart.control() function od package rpart

x

object passing informatio to the function

y

the iterative y variable

w

the iterative weights

xeval

whether prediction or not is used

...

additional arguments

Details

Note that, the gamlss fit maybe would not coverged. Also occasianly the gd.tol argument in gamlss has to be increased. The

Value

Note that tr 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.tr() The result is a rpart object.

Author(s)

Mikis Stasinopoulos mikis.stasinopoulos@gamlss.org, Bob Rigby based on work of Therneau and Atkison (2015)

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/).

Therneau T. M., Atkinson E. J. (2015) An Introduction to Recursive Partitioning Using the RPART Routines. Vignette in package rpart.

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

Examples

data(rent)
#--- fitting gamlss+tree Nornal
library(rpart)
data(rent)
rg1 <- gamlss(R ~ tr(~A+Fl), data=rent, family=NO)
plot(rg1)
plot(getSmo(rg1))
text(getSmo(rg1))
## Not run: 
# fitting Gamma  errors
rg2 <- gamlss(R ~ tr(~A+Fl), data=rent, family=GA)
plot(rg2)
plot(getSmo(rg2))
text(getSmo(rg2))
#--- fitting also model in the variance
rg3 <- gamlss(R ~ tr(~A+Fl), sigma.fo=~tr(~Fl+A), data=rent, 
                family=GA, gd.tol=100, c.crit=0.1)
plot(rg3)
plot(getSmo(rg3))
text(getSmo(rg3))
plot(getSmo(rg3, what="sigma"))
text(getSmo(rg3, what="sigma"))
## End(Not run)

Extra Additive Terms for Generalized Additive Models for Location Scale and Shape

Description

Details

Author(s)

References

See Also

Examples

Centiles contour plots in GAMLSS

Description

Usage

Arguments

Details

Value

Author(s)

References

See Also

Examples

Functions to Fit Univariate Break Point Regression Models

Description

Usage

Arguments

Details

Value

Note

Author(s)

References

Examples

A function to fit break points within GAMLSS

Description

Usage

Arguments

Details

Value

Author(s)

References

See Also

Examples

A interface functions to use Simon Wood's gam() and bam() functions within GAMLSS

Description

Usage

Arguments

Details

Value

Warning

Author(s)

References

Examples

Support for Function fk()

Description

Usage

Arguments

Author(s)

References

See Also

Support for Function ga() and ba()

Description

Usage

Arguments

Author(s)

References

Support for Function nn()

Description

Usage

Arguments

Author(s)

References

See Also

A interface function to use nnet() function within GAMLSS

Description

Usage

Arguments

Details

Value

Warning

Author(s)

References

Examples

Plotting fitted neural networks

Description

Usage