cparlwrgrid: Conditionally parametric LWR regression bandwidth or window...
In McSpatial: Nonparametric spatial data analysis

Description Usage Arguments Value References See Also Examples

Finds the value of a user-provided array of window or bandwidth values that provides the lowest cv or gcv for a CPAR model. Calls cparlwr and returns its full output for the chosen value of h.

1
2
3

 
cparlwrgrid(form,nonpar,window=0,bandwidth=0,kern="tcub",method="gcv",
  print=TRUE,distance="Mahal",targetobs=NULL,data=NULL)

`form`	Model formula
`nonpar`	List of either one or two variables for z. Formats: cparlwr(y~xlist, nonpar=~z1, ...) or cparlwr(y~xlist, nonpar=~z1+z2, ...). Important: note the "~" before the first z variable.
`window`	Window size. Default: not used.
`bandwidth`	Bandwidth. Default: not used.
`kern`	Kernel weighting functions. Default is the tri-cube. Options include "rect", "tria", "epan", "bisq", "tcub", "trwt", and "gauss".
`method`	Specifies "gcv" or "cv" criterion function. Default: method="gcv".
`print`	If TRUE, prints gcv or cv values for each value of the window or bandwidth.
`distance`	Options: "Euclid", "Mahal", or "Latlong" for Euclidean, Mahalanobis, or "great-circle" geographic distance. May be abbreviated to the first letter but must be capitalized. Note: cparlwr looks for the first two letters to determine which variable is latitude and which is longitude, so the data set must be attached first or specified using the data option; options like data$latitude will not work. Default: Mahal.
`targetobs`	If targetobs = NULL, uses the maketarget command to form targets. If target="alldata", each observation is used as a target value for x. A set of target can also be supplied directly by listing the observation numbers of the target data points. The observation numbers can be identified using the obs variable produced by the maketarget command.
`data`	A data frame containing the data. Default: use data in the current working directory

`target`	The target points for the original estimation of the function.
`ytarget`	The predicted values of y at the target values z.
`xcoef.target`	Estimated coefficients, B(z), at the target values of z.
`xcoef.target.se`	Standard errors for B(z) at the target values of z.
`yhat`	Predicted values of y at the original data points.
`xcoef`	Estimated coefficients, B(z), at the original data points.
`xcoef.se`	Standard errors for B(z) with z evaluated at all points in the data set.
`df1`	tr(L), a measure of the degrees of freedom used in estimation.
`df2`	tr(L'L), an alternative measure of the degrees of freedom used in estimation.
`sig2`	Estimated residual variance, sig2 = rss/(n-2df1+df2)*.
`cv`	Cross-validation measure. cv = mean(((y-yhat)/(1-infl))^2) , where yhat is the vector of predicted values for y and infl is the vector of diagonal terms for L.
`gcv`	gcv = n(nsig2)/((n-nreg)^2), where sig2 is the estimated residual variance and nreg = 2df1 - df2*.
`infl`	A vector containing the diagonal elements of L.

Cleveland, William S. and Susan J. Devlin, "Locally Weighted Regression: An Approach to Regression Analysis by Local Fitting," Journal of the American Statistical Association 83 (1988), 596-610.

Loader, Clive. Local Regression and Likelihood. New York: Springer, 1999.

McMillen, Daniel P., "One Hundred Fifty Years of Land Values in Chicago: A Nonparametric Approach," Journal of Urban Economics 40 (1996), 100-124.

McMillen, Daniel P., "Issues in Spatial Data Analysis," Journal of Regional Science 50 (2010), 119-141.

McMillen, Daniel P., "Employment Densities, Spatial Autocorrelation, and Subcenters in Large Metropolitan Areas," Journal of Regional Science 44 (2004), 225-243.

McMillen, Daniel P. and John F. McDonald, "A Nonparametric Analysis of Employment Density in a Polycentric City," Journal of Regional Science 37 (1997), 591-612.

McMillen, Daniel P. and Christian Redfearn, “Estimation and Hypothesis Testing for Nonparametric Hedonic House Price Functions,” Journal of Regional Science 50 (2010), 712-733.

Pagan, Adrian and Aman Ullah. Nonparametric Econometrics. New York: Cambridge University Press, 1999.

cparlwr

par(ask=TRUE)
n = 1000
z1 <- runif(n,0,2*pi)
z1 <- sort(z1)
z2 <- runif(n,0,2*pi)
o1 <- order(z1)
o2 <- order(z2)
ybase1 <-  z1 - .1*(z1^2) + sin(z1) - cos(z1) - .5*sin(2*z1) + .5*cos(2*z1) 
ybase2 <- -z2 + .1*(z2^2) - sin(z2) + cos(z2) + .5*sin(2*z2) - .5*cos(2*z2)
ybase <- ybase1+ybase2
sig = sd(ybase)/2
y <- ybase + rnorm(n,0,sig)
summary(lm(y~ybase))

# Single variable estimation
fit1 <- cparlwrgrid(y~z1,nonpar=~z1,window=seq(.10,.40,.10))
c(fit1$df1,fit1$df2,2*fit1$df1-fit1$df2)
plot(z1[o1],ybase1[o1],type="l",ylim=c(min(ybase1,fit1$yhat),max(ybase1,fit1$yhat)),
  xlab="z1",ylab="y")
# Make predicted and actual values have the same means
fit1$yhat <- fit1$yhat - mean(fit1$yhat) + mean(ybase1)
lines(z1[o1],fit1$yhat[o1], col="red")
legend("topright", c("Base", "LWR"), col=c("black","red"),lwd=1)
fit2 <- cparlwrgrid(y~z2,nonpar=~z2,window=seq(.10,.40,.10))
fit2$yhat <- fit2$yhat - mean(fit2$yhat) + mean(ybase2)
c(fit2$df1,fit2$df2,2*fit2$df1-fit2$df2)
plot(z2[o2],ybase2[o2],type="l",ylim=c(min(ybase2,fit2$yhat),max(ybase2,fit2$yhat)),
    xlab="z1",ylab="y")
lines(z2[o2],fit2$yhat[o2], col="red")
legend("topright", c("Base", "LWR"), col=c("black","red"),lwd=1)

#both variables
fit3 <- cparlwrgrid(y~z1+z2,nonpar=~z1+z2,window=seq(.10,.20,.05))
yhat1 <- fit3$yhat - mean(fit3$yhat) + mean(ybase1)
plot(z1[o1],yhat1[o1], xlab="z1",ylab="y")
lines(z1[o1],ybase1[o1],col="red")
yhat2 <- fit3$yhat - mean(fit3$yhat) + mean(ybase2)
plot(z2[o2],yhat2[o2], xlab="z2",ylab="y")
lines(z2[o2],ybase2[o2],col="red")