ridge: Specify Ridge regression In A GAMLSS Formula

Description

The function ri() allow the user to fit a ridge regression within GAMLSS. It allows the coefficients of a set of explanatory variables to be shrunk towards an overall zero, where the amount of shrinking depends either on lambda, or on the equivalent degrees of freedom (df). The function ri() can estimate lambda a local REML-algorithm.

Usage

ridge(X, df = NULL, lambda = NULL, order = 0)
ri(X, df = NULL, lambda = NULL, order = 0, start = 10)

Arguments

A standardized (mean=0, sd-1) matrix X of explanatory variables

the effective degrees of freedom df

lambda

the smoothing parameter lambda

order

the order of the difference applied to the coefficients

start

the lambda starting value if the Schall's EM-algorithm is used

Value

x is returned with class "smooth", with an attribute named "call" which is to be evaluated in the backfitting additive.fit() called by gamlss()

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.org/). 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.

Examples

Run this code

data(usair)
# standarized the x's
for (i in 2:7) usair[,i] <- (usair[,i]-mean(usair[,i]))/sd(usair[,i])
# create a matrix 
usair$X <-as.matrix(usair[,c("x1","x2", "x3","x4", "x5", "x6")])
m1<- gamlss(y~ridge(X, df=3), data=usair, family=GA)
m2<- gamlss(y~ridge(X, lambda=10), data=usair, family=GA)
# plotting the coeficients as function of the df 
df <- seq(0,6,0.5)
resmat<-matrix(0, nrow=length(df), ncol=6)
for (i in 1:length(df)) 
{
resmat[i,] <- gamlss(y~ridge(X, df=df[i]), data=usair)$mu.coefSmo[[1]][["coef"]]
}
colnames(resmat)<-colnames(usair$X)
plot(1:length(df), type="n", xlim=c(-.5,6.5), ylim=c(-23, 38))
for (i in 1:6)
{
lines(resmat[,i]~df, col="purple")
points(resmat[,i]~df)
}
lines(rep(0,length(df))~df, col="black")
# now estimating the lambda
 g1<-gamlss(y~ri(X), data=usair)
  m1$mu.coefSmo