semivariogram {krige}

Semivariogram for Geospatial Data

Description

This function creates semivariogram plots. It creates empirical semivariogram for raw data and lm object or parametric exponential semivariogram based on the estimation from metropolis.krige. Based on the user's chosen level of coarsening, the semivariogram is presented for various distances.

Usage

semivariogram(x, ...)

## S3 method for class 'krige'
semivariogram(x, ..., bins = 13, terms = "all", type, pch, lty, legend, col)

## S3 method for class 'krige'
plot(...)

## S3 method for class 'lm'
semivariogram(
  x,
  ...,
  coords,
  bins = 13,
  terms = c("raw", "residual"),
  east,
  north,
  type,
  legend,
  col,
  pch,
  lty
)

## Default S3 method:
semivariogram(
  x,
  ...,
  coords,
  data,
  bins = 13,
  east,
  north,
  type,
  pch,
  lty,
  col
)

## S3 method for class 'semivariance'
semivariogram(x, ..., type, pch, lty, legend, col)

## S3 method for class 'semivariance'
plot(x, ..., type, pch, lty, legend, col)

Arguments

x

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

...

Additional arguments to be passed to semivariogram methods. Further arguments that can passed to plot() function can be specified here.

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). "parametric" (the parametric powered exponential semivariogram based on the estimation from metropolis.krige). Defaults will create all the applicable plots.

type

A vector specify the type of plots for each term. Options are "l" (line plot) and "p" (scatter plot). Defaults to c(raw = "p", residual = "p", parametric = "l")

pch

A vector specify the points symbols for scatter plot. Suppressed for line plot.

lty

A vector specify the line type for line plot. Suppressed for scatter plot.

legend

A logical argument for whether legend should be presented. Defaults to TRUE.

col

A vector specify the color for each term. Defaults to c(raw = "black", residual = "blue", parametric = "red")

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.

Details

The function creates semivariograms for diagnosing the spatial relationship that best describes the data and for diagnosing the degree to which the model fits the spatial relationship. With a view of the empirical semivariogram, a user can consult images of parametric semivariograms to determine whether an exponential, Gaussian, or other powered expoential function fit the data well, or if another style of semivariogram works better. Examining this also allows the user to develop priors such as the approximate split in variance between the nugget and partial sill as well as the approximate distance of the effective range. Semivariograms are explicitly tied to a corresponding spatial correlation function, so determining the former automatically implies the latter. See Banerjee, Carlin, and Gelfand for a fuller explanation, as well as a guidebook to semivariogram diagnosis (2015, 26-30).

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; when applying to a krige object, the default will present empirical semivariogram for the raw data and the residuals from linear fit, and the parametric semivariogram given the estimates from the geospatial model fitted in metropolis.krige; for a semivariance object, it will present a plot(s) for whichever the semivariance is calculated. Users can also specify which semivariogram is needed in the terms argument if there are multiple kinds of semivariogram can be plotted. The plots are compatible to the arguments used in base R base graphics.

Value

An semivariogram plot. For krige object, it will return empirical semivariograms for raw data and residuals of linear regression as well as a parametric powered exponential semivariogram given the values of the estimates from metropolis.krige as default.

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

semivariance, exponential.semivariance

Examples

## Not run: 
# Summarize Data
summary(ContrivedData)

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

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

# Empirical semivariagram for ols fit
semivariogram(contrived.ols, coords = c("s.1","s.2"), bins=13)

# Set seed
set.seed(1241060320)

M <- 100
#M<-10000

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 semivariagram
semivariogram(contrived.run, bins=13, terms = c("raw", "residual", "parametric"),
  type= c(raw = "p", residual = "p", parametric = "l"), legend = TRUE, col = c("black", 
  "blue", "red"), pch = c(1,3,NA), lty = c(NA,NA,1))
  
# Alternatively, the generic function plot can also be applied to krige object
plot(contrived.run)

# Plot semivariance object
plot(semivariance(contrived.run, bins=13))

## End(Not run)