# Functions to fit local regression 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 ```r 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. ## Returns 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 ## 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/](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](http://www.jstatsoft.org/v23/i07). ## Author(s) Mikis Stasinopoulos, d.stasinopoulos@londonmet.ac.uk ## See Also `loess`, `ksmooth` ## Examples ```r 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) ```

Locmean function