kdensity: K-density functions for distances between geographic...
In McSpatial: Nonparametric spatial data analysis

Description Usage Arguments Details Value References See Also Examples

Calculates K-density functions for lat-long coordinates. Calculates the distance, d, between every pair of observations and plots the density, f(d_0), at a set of target distances, d_0. The kernel density functions are calculated using the density function.

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kdensity(longitude,latitude,kilometer=FALSE,noplot=FALSE,
dmin=0,dmax=0,dlength=512,h=0,kern="gaussian",nsamp=0,
confint=TRUE,pval=.05)

`longitude`	Longitude variable, in degrees.
`latitude`	Latitude variable, in degrees.
`kilometer`	If kilometer = T, measurements are in kilometers rather than miles. Default: kilometer = F.
`noplot`	If noplot = T, does not show the graph of the K-density function.
`dmin`	Minimum value for target distances. Default: dmin=0.
`dmax`	Maximum value for target distances. Default: dmin = max(distance), specified by setting dmin=0.
`dlength`	Number of target values for density calculations. Default: dlength = 512.
`h`	Bandwidth. Default: (.9(quantile(distance,.75)-quantile(distance,.25))/1.34)(n^(-.20)), where n = 2*length(dvect).
`kern`	Kernel. Default: "gaussian ". Other options from the density function are also available, including "epanechnikov", "rectangular", "triangular", "biweight", and "optcosine". The "cosine" kernel is translated to "optcosine".
`nsamp`	If nsamp>0, draws a random sample of lat-long pairs for calculations rather than the full data set. Can be much faster for large samples. Default: use full sample.
`confint`	If TRUE, adds local confidence intervals to the graph. Default: confint=TRUE.
`pval`	p-value for confidence intervals. Default: pval=.05.

The kdensity function uses Silverman's (1986) reflection method to impose zero densities at negative densities. This method involves supplementing each distance observation with its negative value to form a pseudo data set with twice the original number of observations. The following commands are the core of the function:

dfit1 <- density(dvect,from=dmin,to=dmax,n=dlength,kernel=kern,bw=h)
dfit2 <- density(-dvect,from=dmin,to=dmax,n=dlength,kernel=kern,bw=h)
distance <- dfit1$x
dhat <- dfit1$y + dfit2$y

Local standard errors are calculated using the following asymptotic formula:

(nh)^{-.5} (f(x) \int K^2(ψ)d ψ )^{.5}

`distance`	The vector of target distances.
`dhat`	The vector of densities for the target distances.
`dvect`	The full vector of distances between observation pairs. Length is n(n-1)/2.
`h`	The bandwidth.
`se`	The vector of standard errors.

Duranton, Gilles and Henry G. Overman, "Testing for Localisation using Microgeographic Data", Review of Economic Studies 72 (2005), 1077-1106.

Klier Thomas and Daniel P. McMillen, "Evolving Agglomeration in the U.S. Auto Industry," Journal of Regional Science 48 (2008), 245-267.

Silverman, A. W., Density Estimation for Statistics and Data Analysis, Chapman and Hall, New York (1986).

ksim

data(matchdata)
lmat <- cbind(matchdata$longitude,matchdata$latitude)
# Smaller sample to reduce computation time for example
set.seed(18493)
obs <- sample(seq(1,nrow(lmat)),400)
lmat <- lmat[obs,]
fit95 <- kdensity(lmat[,1],lmat[,2],noplot=FALSE)