krige (version 0.6.2)

semivariance: Semivariance for Geospatial Data

Description

This function computes the empirical semivariance for a spatially-distributed variable. Based on the user's chosen level of coarsening, the semivariance is presented for various distances.

Usage

semivariance(object, ...)
# S3 method for krige
semivariance(object, bins = 13, terms = "all", plot = FALSE, ...)
# S3 method for lm
semivariance(
  object,
  bins = 13,
  coords,
  terms = c("raw", "residual"),
  east,
  north,
  plot = FALSE,
  ...
)
# S3 method for default
semivariance(object, bins = 13, coords, data, east, north, plot = FALSE, ...)

Arguments

object

An object for which the semivariance is desired. The object can be a krige object, a lm object, or a vector of variables (or variable names in the data).

…

Additional arguments passed to semivariance methods.

bins

Number of bins into which distances should be divided. The observed distances will be split at equal intervals, and the semivariance will be computed within each interval. Defaults to 13 intervals.

terms

A vector of strings specifies for which the semivariogram is created. Options are "raw" (the semivariogram for raw data), "residual" (the semivariogram for residuals from linear regression).

plot

Logical values indicates whether a graph of the empirical semivariogram should be presented with a run of the function. Default omits the plot and only returns semivariance values. See semivariogram for additional plotting functions.

coords

A matrix of coordinates for all observations or a vector of variable names indicating the coordinates variables in the data. Alternatively, the coordinates can also be specified separately using east and north.

east

Alternative specification for the vector of eastings for all observations.

north

Alternative specification for the vector of northing for all observations.

data

If object is a variable name, a data frame must be provided.

Value

A semivariance object. It will be a numeric vector with each bin's value of the semivariance if only one kind of semivariance is computed; a list including different kinds of semivariance if both raw and residual semivariance is computed.

Details

Semivariance is equal to half of the variance of the difference in a variable's values at a given distance. That is, the semivariance is defined as: \(\gamma(h)=0.5*E[X(s+h)-X(s)]^2\), where \(X\) is the variable of interest, s is a location, and h is the distance from s to another location.

The function can be applied to a variable, a fitted linear model (lm object) before fitting a spatial model or to a krige object or semivariance object to assess the model fit. When applying to a variable, it will describes the raw data; for a lm object, the default will present empirical semivariogram for both the raw data and linear residuals. Users can also specify which semivariance is needed in the terms argument if there are multiple kinds of semivariogram can be plotted. A semivariance object can also be used to create semivariogram afterwards using generic plot function with more options.

References

Sudipto Banerjee, Bradley P. Carlin, and Alan E. Gelfand. 2015. Hierarchical Modeling and Analysis for Spatial Data. 2nd ed. Boca Raton, FL: CRC Press.

See Also

semivariogram, plot.semivariance, exponential.semivariance

Examples

# NOT RUN {
# Summarize example data
summary(ContrivedData)

# Empirical semivariance for variable y
semivariance(ContrivedData$y,coords = cbind(ContrivedData$s.1, ContrivedData$s.2))

# Initial OLS Model
contrived.ols<-lm(y~x.1+x.2,data=ContrivedData); summary(contrived.ols)

# Empirical semivariance for ols fit
(sv.ols <- semivariance(contrived.ols, coords = c("s.1","s.2"), bins=13))
plot(sv.ols)

# Estimation using metropolis.krige()
# Set seed
set.seed(1241060320)

M <- 100

contrived.run <- metropolis.krige(y ~ x.1 + x.2, coords = c("s.1","s.2"), 
  data = ContrivedData, n.iter = M, range.tol = 0.05)
  
# Parametric semivariance
(sv.krige <- semivariance(contrived.run, plot = TRUE))

# Convert to other format for further use
as.matrix(sv.krige)
as.data.frame(sv.krige)
# }
# NOT RUN {
# }