kern.reg.circ.lin {NPCirc}

Nonparametric regression estimation for circular data

Description

Function kern.reg.circ.lin implements the Nadaraya-Watson estimator and the Local-Linear estimator for circular-linear data (circular covariate and linear response), as described in Di Marzio et al. (2009) and Oliveira et al. (2013), taking the von Mises distribution as kernel.

Function kern.reg.circ.circ implements the Nadaraya-Watson estimator and the Local-Linear estimator for circular-circular data (circular covariate and circular response), as described in Di Marzio et al. (2012), taking the von Mises distribution as kernel.

Function kern.reg.lin.circ implements the Nadaraya-Watson estimator and the Local-Linear estimator for linear-circular data (linear covariate and circular response), as described in Di Marzio et al. (2012), taking the Normal distribution as kernel.

Usage

kern.reg.circ.lin(x, y, t=NULL, bw, method="LL", from=circular(0),
to=circular(2*pi), len=250, tol=300)
kern.reg.circ.circ(x, y, t=NULL, bw, method="LL", from=circular(0),
to=circular(2*pi), len=250)
kern.reg.lin.circ(x, y, t=NULL, bw, method="LL", len=250)
## S3 method for class 'regression.circular'
print(x, digits=NULL, ...)

Arguments

x

Vector of data for the independent variable. The object is coerced to class circular when using functions kern.reg.circ.lin and kern.reg.circ.circ.

y

Vector of data for the dependent variable. This must be same length as x. The object is coerced to class circular when using functions kern.reg.circ.circ and kern.reg.lin.circ.

t

Points where the regression function is estimated. If NULL equally spaced points are used according to the parameters from, to and len.

bw

Smoothing parameter to be used. The value of the smoothing parameter can be chosen by using the function bw.reg.circ.lin, bw.reg.circ.circ and bw.reg.lin.circ.

method

Character string giving the estimator to be used. This must be one of "LL" for Local-Linear estimator or "NW" for Nadaraya-Watson estimator. Default method="LL".

from, to

Left and right-most points of the grid at which the regression function is to be estimated. The objects are coerced to class circular.

len

Number of equally spaced points at which the regression function is to be estimated.

tol

Tolerance parameter to avoid overflow when bw is larger than tol. Default is tol=300.

digits

Integer indicating the precision to be used.

...

further arguments

Details

See Di Marzio et al. (2012). See Section 3 in Oliveira et al. (2013). See Di Marzio et al. (2009). The NAs will be automatically removed.

Value

An object with class "regression.circular" whose underlying structure is a list containing the following components:

datax, datay

Original dataset.

x

The n coordinates of the points where the regression is estimated.

y

The estimated values.

bw

The smoothing parameter used.

N

The sample size after elimination of missing values.

call

The call which produced the result.

data.name

The deparsed name of the x argument.

has.na

Logical, for compatibility (always FALSE).

Author(s)

Maria Oliveira, Rosa M. Crujeiras and Alberto Rodriguez–Casal

References

Di Marzio, M., Panzera A. and Taylor, C. C. (2009) Local polynomial regression for circular predictors. Statistics and Probability Letters, 79, 2066–2075.

Di Marzio, M., Panzera A. and Taylor, C. C. (2012) Non–parametric regression for circular responses. Scandinavian Journal of Statistics, 40, 228–255.

Oliveira, M., Crujeiras R.M. and Rodriguez–Casal, A. (2013) Nonparametric circular methods for exploring environmental data. Environmental and Ecological Statistics, 20, 1–17.

Oliveira, M., Crujeiras R.M. and Rodriguez–Casal, A. (2014) NPCirc: an R package for nonparametric circular methods. Journal of Statistical Software, 61(9), 1–26. https://www.jstatsoft.org/v61/i09/

See Also

plot.regression.circular, lines.regression.circular

Examples

### circular-linear
data(speed.wind2)
dir <- speed.wind2$Direction
vel <- speed.wind2$Speed
nas <- which(is.na(vel))
dir <- circular(dir[-nas],units="degrees")
vel <- vel[-nas]
estLL <- kern.reg.circ.lin(dir, vel, method="LL")
estNW <- kern.reg.circ.lin(dir, vel, method="NW")
# Circular representation
res<-plot(estNW, plot.type="circle", points.plot=TRUE,
labels=c("N","NE","E","SE","S","SO","O","NO"),
label.pos=seq(0,7*pi/4,by=pi/4), zero=pi/2, clockwise=TRUE)
lines(estLL, plot.type="circle", plot.info=res, line.col=2)
# Linear representation
plot(estNW, plot.type="line", points.plot=TRUE, xlab="direction", ylab="speed (m/s)")
lines(estLL, plot.type="line", line.col=2)


### circular-circular
data(wind)
wind6 <- circular(wind$wind.dir[seq(7,1752,by=24)])
wind12 <- circular(wind$wind.dir[seq(13,1752,by=24)])
estNW <- kern.reg.circ.circ(wind6,wind12,t=NULL,bw=6.1,method="NW")
estLL <- kern.reg.circ.circ(wind6,wind12,t=NULL,bw=2.25,method="LL")
# Torus representation
plot(estNW, plot.type="circle", points.plot=TRUE, line.col=2, lwd=2, points.col=2,
units="degrees")
lines(estLL, plot.type="circle", line.col=3, lwd=2)
# Linear representation
plot(estNW, plot.type="line", points.plot=TRUE, xlab="Wind direction at 6 a.m.",
ylab="Wind direction at noon")
lines(estLL, plot.type="line", line.col=2)


### linear-circular
data(periwinkles)
dist <- periwinkles$distance
dir <- circular(periwinkles$direction, units="degrees")
estNW <- kern.reg.lin.circ(dist,dir,t=NULL,bw=12.7,method="NW")
estLL <- kern.reg.lin.circ(dist,dir,t=NULL,bw=200,method="LL")
# Cylinder representation
plot(estNW, plot.type="circle", points.plot=TRUE, line.col=2, lwd=2, points.col=2)
lines(estLL, plot.type="circle", line.col=3, lwd=2)
# Linear representation
 plot(estNW, plot.type="line", points.plot=TRUE, units="radians", main="")
 lines(estLL, plot.type="line", line.col=2, units="radians")