Locmean {gamlss.demo}

Functions to fit local regression

Description

There are four function here to illustrate the fitting of local regressions. i) Locmean, which uses local means within a symmetric local window, ii) Locpoly, which uses a local polynomial fit within a symmetric local window. iii) WLocmean, which uses a Gaussian kernel and iv) WLocpoly, which uses local polynomials weighted by a Gaussian kernel

Usage

Locmean(y, x = seq(1, length(y)), w = rep(1, length(y)), span = 0.5)
Locpoly(y, x = seq(1, length(y)), w = rep(1, length(y)), span = 0.5, order = 1)
WLocmean(y, x = seq(1, length(y)), w = rep(1, length(y)), lambda = 0.5)
WLocpoly(y, x = seq(1, length(y)), w = rep(1, length(y)), lambda = 0.5, order = 1)

Arguments

y

the response variable

x

the x-variable

w

prior weights

span

the side of the local window compare as a proportion to the total number of observations

lambda

the smoothing parameter for the Gaussian kernel

order

the order of the polynomial

Details

Those functions can be used for illustration of the basic concepts of smoothing using small data sets. Do not use them with large data because are computationally inefficient.

Value

The functions return a locW object with values

fitted.values

the fitted valus

residuals

the residuals

edf

the effective degrees of freedom

rss

the residual sum of squares

lambda

the smoothing parameter

y

the y variable

x

the x variable

w

the prior weights

Author(s)

Mikis Stasinopoulos, [e-mail]

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.

See Also

loess, ksmooth

Examples

library(MASS)
data(mcycle)
# local means
m0<-Locmean(mcycle$accel, mcycle$times, span=.1)
m1<-Locmean(mcycle$accel, mcycle$times, span=.2)
m2<-Locmean(mcycle$accel, mcycle$times, span=.3)
span <- c("span=0.1", "span=0.2", "span=0.3")
plot(accel~times, data=mcycle,main="local mean")
lines(fitted(m0)~mcycle$times, col=1, lty=1)
lines(fitted(m1)~mcycle$times, col=2, lty=2)
lines(fitted(m2)~mcycle$times, col=3, lty=3)
legend(1.5,50, legend = span, col = 1:3,
       lty = 1:3, cex = .8, y.intersp = 1)
#  kernel estimation      
k0<-WLocmean(mcycle$accel, mcycle$times, lambda=1)
k1<-WLocmean(mcycle$accel, mcycle$times,  lambda=2)
k2<-WLocmean(mcycle$accel, mcycle$times,  lambda=3)
lambda <- c("lambda=1", "lambda=2", "lambda=3")
plot(accel~times, data=mcycle,main="Gaussian kernel fit")
lines(fitted(k0)~mcycle$times, col=1, lty=1)
lines(fitted(k1)~mcycle$times, col=2, lty=2)
lines(fitted(k2)~mcycle$times, col=3, lty=3)
legend(1.5,50, legend = lambda, col = 1:3,
       lty = 1:3, cex = .8, y.intersp = 1)
# local polymials
l1<-Locpoly(mcycle$accel, mcycle$times, span=.1)
l2<-Locpoly(mcycle$accel, mcycle$times, span=.2)
l3<-Locpoly(mcycle$accel, mcycle$times, span=.3)

span <- c("span=0.1", "span=0.2", "span=0.3")
plot(accel~times, data=mcycle,main="local linear fit")
lines(fitted(l1)~mcycle$times, col=1, lty=1)
lines(fitted(l2)~mcycle$times, col=2, lty=2)
lines(fitted(l2)~mcycle$times, col=3, lty=3)
legend(1.5,50, legend = span, col = 1:3,
       lty = 1:3, cex = .8, y.intersp = 1)       
# weighted local polynomials  
lw1<-WLocpoly(mcycle$accel, mcycle$times, lambda=1.5, order=1)
lw2<-WLocpoly(mcycle$accel, mcycle$times, lambda=1.5, order=2)
lw3<-WLocpoly(mcycle$accel, mcycle$times, lambda=1.5, order=3)

span <- c("linear", "quadratic", "cubic")
plot(accel~times, data=mcycle,main="Weighted local linear, quadratic and cubic fits")
lines(fitted(lw1)~mcycle$times, col=1, lty=1)
lines(fitted(lw2)~mcycle$times, col=2, lty=2)
lines(fitted(lw3)~mcycle$times, col=3, lty=3)
legend(1.5,50, legend = span, col = 1:3,
       lty = 1:3, cex = .8, y.intersp = 1)