SpatialPosition (version 1.0)

stewart: Stewart Potentials

Description

This function computes the potentials as defined by J.Q. Stewart (1942).

Usage

stewart(knownpts, unknownpts = NULL, matdist = NULL, varname,
  typefct = "exponential", span, beta, resolution = 2000, longlat = FALSE,
  mask = NULL)

Arguments

knownpts

sp object (SpatialPointsDataFrame or SpatialPolygonsDataFrame); this is the set of known observations to estimate the potentials from.

unknownpts

sp object (SpatialPointsDataFrame or SpatialPolygonsDataFrame); this is the set of unknown units for which the function computes the estimates. Not used when resolution is set up. (optional)

matdist

matrix; a distance matrix. Row names match the first column of the knownpts object dataframe. Column names match the first column of the unknownpts object dataframe. (optional)

varname

character; name of the variable in the knownpts dataframe from which potentials are computed. Quantitative variable with no negative values.

typefct

character; spatial interaction function. Options are "pareto" (means power law) or "exponential". If "pareto" the interaction is defined as: (1 + alpha * mDistance) ^ (-beta). If "exponential" the interaction is defined as: exp(- alpha * mDistance ^ bet

span

numeric; distance where the density of probability of the spatial interaction function equals 0.5.

beta

numeric; impedance factor for the spatial interaction function.

resolution

numeric; resolution of the output SpatialPointsDataFrame (in map units).

longlat

logical; euclidean distance (FALSE, default) or Great Circle distance (TRUE). If TRUE inputs are expected in the WGS84 reference system.

mask

sp object; the spatial extent of this object is used to create the regularly spaced SpatialPointsDataFrame output. (optional)

Value

• SpatialPointsDataFrame with the computed potentials in a new field nammed OUTPUT

Details

If unknownpts is NULL then resolution must be used.

References

STEWART J.Q. (1942) "Measure of the influence of a population at a distance", Sociometry, 5(1): 63-71.

See Also

stewart, rasterStewart, plotStewart, contourStewart, CreateGrid, CreateDistMatrix.

Examples

# Create a SpatialPointsDataFrame grid of spatMask extent and 200 meters 
# resolution
data(spatData)
mygrid <- CreateGrid(w = spatMask, resolution = 200)
# Create a distance matrix between known points (spatPts) and mygrid
mymat <- CreateDistMatrix(knownpts = spatPts, unknownpts = mygrid, 
                          longlat = FALSE)
# Compute Stewart potentials from known points (spatPts) on a given 
# grid (mygrid) using a given distance matrix (mymat)
mystewart <- stewart(knownpts = spatPts, unknownpts = mygrid, 
                     matdist = mymat, varname = "Capacite", 
                     typefct = "exponential", span = 1250, 
                     beta = 3, longlat = FALSE, mask = spatMask)
# Compute Stewart potentials from known points (spatPts) on a 
# grid defined by its resolution
mystewart2 <- stewart(knownpts = spatPts, varname = "Capacite", 
                      typefct = "exponential", span = 1250, beta = 3, 
                      resolution = 200, longlat = FALSE, mask = spatMask)
# The two methods have the same result
identical(mystewart, mystewart2)
# the function output a SpatialPointsDataFrame
class(mystewart)
# Computed values
summary(mystewart$OUTPUT)