penReg {gamlss.util}R Documentation

Function to fit penalised regression

Description

The function penReg() can be used to fit a P-spline. It can be used as demonstration of how the penalised B-splines can be fitted to one explanatory variable. For more that explanatory variable use the function pb() in gamlss.

Usage

penReg(y, x, w = rep(1, length(y)), df = NULL, lambda = NULL, start = 10, 
      inter = 20, order = 2, degree = 3,  plot = FALSE,
      method = c("ML", "ML-1", "GAIC", "GCV", "EM"), k = 2, ...)

Arguments

y the response variable
x the unique explanatory variable
w prior weights
df effective degrees of freedom
lambda the smoothing parameter
start the lambda starting value if the local methods are used
inter the no of break points (knots) in the x-axis
order the required difference in the vector of coefficients
degree the degree of the piecewise polynomial
plot whether to plot the data and the fitted function
method The method used in the (local) performance iterations. Available methods are "ML", "ML-1", "EM", "GAIC" and "GCV"
k the penalty used in "GAIC" and "GCV"
... for extra arguments

Value

Returns a fitted object of class penReg. The object contains 1) the fitted coefficients 2) the fitted.values 3) the response variable y, 4) the label of the response variable ylabel 5) the explanatory variable x, 6) the lebel of the explanatory variable 7) the smoothing parameter lambda, 8) the effective degrees of freedom df, 9) the estimete for sigma sigma, 10) the residual sum of squares rss, 11) the Akaike information criterion aic, 12) the Bayesian information criterion sbc and 13) the deviance

Author(s)

Mikis Stasinopoulos d.stasinopoulos@londonmet.ac.uk, Bob Rigby r.rigby@londonmet.ac.uk and Paul Eilers

References

Eilers, P. H. C. and Marx, B. D. (1996). Flexible smoothing with B-splines and penalties (with comments and rejoinder). Statist. Sci, 11, 89-121.

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. (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.

See Also

penLS

Examples

set.seed(1234)
 x <- seq(0,10,length=200); y<-(yt<-1+2*x+.6*x^2-.1*x^3)+rnorm(200, 4)
 library(gamlss)
#------------------ 
# df fixed
 g1<-gamlss(y~pb(x, df=4))
 m1<-penReg(y,x, df=4) 
 cbind(g1$mu.coefSmo[[1]]$lambda, m1$lambda)
 cbind(g1$mu.df, m1$df)
 cbind(g1$aic, m1$aic)
 cbind(fitted(g1), fitted(m1))[1:10,]
# identical
#------------------
# estimate lambda using ML
g2<-gamlss(y~pb(x))
m2<-penReg(y,x) 
cbind(g2$mu.df, m2$df)
cbind(g2$mu.lambda, m2$lambda) 
cbind(g2$aic, m2$aic) # different lambda
cbind(fitted(g2), fitted(m2))[1:10,]
# identical
#------------------
#  estimate lambda using GCV
g3 <- gamlss(y~pb(x, method="GCV"))
m3 <- penReg(y,x, method="GCV") 
cbind(g3$mu.df, m3$df)
cbind(g3$mu.lambda, m3$lambda)
cbind(g3$aic, m3$aic)
cbind(fitted(g3), fitted(m3))[1:10,]
# almost identical
#------------------
# estimate lambda using EM
g4<-gamlss(y~pb(x, method="EM"))
m4<-penReg(y,x, method="EM") 
cbind(g4$mu.df, m4$df )
cbind(g4$mu.lambda, m4$lambda)
cbind(g4$aic, m4$aic)
cbind(fitted(g4), fitted(m4))[1:10,]
# almost identical
#------------------
#  estimate lambda using  GAIC(#=3)
g5<-gamlss(y~pb(x, method="GAIC", k=3))
m5<-penReg(y,x, method="GAIC", k=3) 
cbind(g5$mu.df, m5$df )
cbind(g5$mu.lambda, m5$lambda)
cbind(g5$aic, m5$aic)
cbind(g5$mu.df, m5$df)
cbind(g5$mu.lambda, m5$lambda)
cbind(fitted(g5), fitted(m5))[1:10,]
#-------------------
plot(y~x)
lines(fitted(m1)~x, col="green")
lines(fitted(m2)~x, col="red")
lines(fitted(m3)~x, col="blue")
lines(fitted(m4)~x, col="yellow")
lines(fitted(m4)~x, col="grey")


[Package gamlss.util version 3.1-0 Index]