geogravity: Gravity matrix and gravity variable calculations
In McSpatial: Nonparametric spatial data analysis

Description Usage Arguments Details Value See Also Examples

Calculates a variable showing the average value for each observation of a gravity measure of the spatial interaction between the observation and the other points in a data set.

1 2	geogravity(x,longvar,latvar,alpha=1,maxd=NULL,alldata=FALSE, window=.10,outmatrix=FALSE)

`x`	The variable of interest, e.g., population or employment.
`longvar`	Longitude variable, in degrees.
`latvar`	Latitude variable, in degrees.
`alpha`	The α parameter for the distance variables. Default: alpha = 1.
`maxd`	Maximum distance, beyond which observations get zero weight. Default: all observations are included in the calculations.
`alldata`	If FALSE, interpolates between target points rather than making the calculations at every observation. Default: alldata=FALSE.
`window`	Window size used to determine a set of target points when alldata=FALSE. Default: window = .10.
`outmatrix`	If TRUE and alldata==TRUE, stores the full matrix of gravity values. Default: outmatrix=FALSE.

The gravity measure of the spatial interaction between two points i and j is g_{ij} = P_i P_j / d_{ij}^α if d_{ij} < maxd and g_{ij} = 0 if d_{ij} > maxd, where P is a variable such as population or employment that measures the importance of the observation, d_{ij} is the straight-line distance between observations i and j, and α is a parameter. The variable P is provided by the argument x. The full n x n matrix of values is stored in dmat if alldata=TRUE and outmatrix=TRUE, with the diagonal elements set to zero.

The "gravity variable" that is stored in gravity is the average value for each observation:

g_i = (1/(n-1)) ∑ g_{ij}

By default, the locfit program is used to find a set of target values for calculating g_{ij}. The full set of observations is used for the j index, but a smaller set of observations is used for the target values, i. The abbreviated set of g_i values is then interpolated to the full set of data points using the smooth12 command. The vector of target observation numbers is stored in targetobs.

`targetobs`	The vector of target observation numbers.
`gtarget`	The gravity variable at the target points.
`gravity`	The gravity variable for the full data set.
`dmat`	The full nxn matrix of results, if outmatrix=TRUE and alldata=TRUE. The diagonal elements are set to zero.

geodistance

geodensity

library(spdep)
cook <- readShapePoly(system.file("maps/CookCensusTracts.shp",package="McSpatial"))
cook <- cook[cook$POPULATION>0&cook$AREA>0,]
cook$lndens <- log(cook$POPULATION/cook$AREA)
lmat <- coordinates(cook)
longitude <- lmat[,1]
latitude  <- lmat[,2]
fit <- geogravity(cook$lndens,longitude,latitude)
cook$gravity <- fit$gravity