Smoothes the given bivariate data using kernel regression.
Usage
locally.weighted.polynomial(x, y, h = NA, x.grid = NA,
degree = 1, kernel.type = "Normal")
Arguments
x
Vector of data for the independent variable
y
Vector of data for the dependent variable
h
The bandwidth for the kernel
x.grid
What x-values should the value of the smoother be calculated at.
degree
The degree of the polynomial to be fit at each x-value. The default is
to fit a linear regression, ie degree=1.
kernel.type
What kernel to use. Valid choices are 'Normal',
'Epanechnikov', 'biweight', and 'triweight'
Details
The confidence intervals are created using the row-wise method of Hannig and Marron (2006).
Notice that the derivative to be estimated must be less than or equal to the degree of the polynomial
initially fit to the data.
If the bandwidth is not given, the Sheather-Jones bandwidth selection method is used.
Value
Returns a LocallyWeightedPolynomial object that has the following elements:
data
A structure of the data used to generate the smoothing curve
h
The bandwidth used to generate the smoothing curve.
x.grid
The grid of x-values that we have estimated function value
and derivative(s) for.
degrees.freedom
The effective sample size at each grid point
Beta
A matrix of estimated beta values. The number of rows is
degrees+1, while the number of columns is the same as the length
of x.grid. Notice that
hat{f}(x_i) = β[1,i]
hat{f'}(x_i) = β[2,i]*1!
hat{f''}(x_i) = β[3,i]*2!
and so on...
Beta.var
Matrix of estimated variances for Beta. Same structure as Beta.
Author(s)
Derek Sonderegger
References
Chaudhuri, P., and J. S. Marron. 1999. SiZer for exploration of structures
in curves. Journal of the American Statistical Association 94 807-823.
Hannig, J., and J. S. Marron. 2006. Advanced distribution theory for SiZer.
Journal of the American Statistical Association 101 484-499.
Sonderegger, D.L., Wang, H., Clements, W.H., and Noon, B.R. 2009. Using SiZer to detect
thresholds in ecological data. Frontiers in Ecology and the Environment 7:190-195
See Also
SiZer, plot.LocallyWeightedPolynomial, spm in package 'SemiPar',
loess, smooth.spline, interpSpline
R version 3.3.1 (2016-06-21) -- "Bug in Your Hair"
Copyright (C) 2016 The R Foundation for Statistical Computing
Platform: x86_64-pc-linux-gnu (64-bit)
R is free software and comes with ABSOLUTELY NO WARRANTY.
You are welcome to redistribute it under certain conditions.
Type 'license()' or 'licence()' for distribution details.
R is a collaborative project with many contributors.
Type 'contributors()' for more information and
'citation()' on how to cite R or R packages in publications.
Type 'demo()' for some demos, 'help()' for on-line help, or
'help.start()' for an HTML browser interface to help.
Type 'q()' to quit R.
> library(SiZer)
Loading required package: splines
Loading required package: boot
> png(filename="/home/ddbj/snapshot/RGM3/R_CC/result/SiZer/locally.weighted.polynomial.Rd_%03d_medium.png", width=480, height=480)
> ### Name: locally.weighted.polynomial
> ### Title: Locally-Weighted Polynomial Regression Smoother
> ### Aliases: locally.weighted.polynomial calc.CI.LocallyWeightedPolynomial
> ### find.state find.state.changes find.states kernel.h positive.part
> ### x.grid.create
> ### Keywords: smooth
>
> ### ** Examples
>
> data(Arkansas)
> x <- Arkansas$year
> y <- Arkansas$sqrt.mayflies
>
> layout(cbind(1,2,3))
> model <- locally.weighted.polynomial(x,y)
> plot(model, main='Smoothed Function', xlab='Year', ylab='Sqrt.Mayflies')
>
> model2 <- locally.weighted.polynomial(x,y,h=.5)
> plot(model2, main='Smoothed Function', xlab='Year', ylab='Sqrt.Mayflies')
>
> model3 <- locally.weighted.polynomial(x,y, degree=1)
> plot(model3, derv=1, main='First Derivative', xlab='Year', ylab='1st Derivative')
>
>
>
>
>
> dev.off()
null device
1
>