Nonparametric (cross-)correlation function for spatio-temporal data

Description

Sncf is the function to estimate the nonparametric (cross-)correlation function using a smoothing spline as an equivalent kernel. The function requires multiple observations at each location (use spline.correlog otherwise).

Usage

Sncf(
  x,
  y,
  z,
  w = NULL,
  df = NULL,
  type = "boot",
  resamp = 1000,
  npoints = 300,
  save = FALSE,
  filter = FALSE,
  fw = 0,
  max.it = 25,
  xmax = FALSE,
  na.rm = FALSE,
  latlon = FALSE,
  circ = FALSE,
  quiet = FALSE
)

Arguments

Details

Missing values are allowed – values are assumed missing at random.

The circ argument computes a circular version of the Pearson's product moment correlation (see cor2). This option is to calculate the 'nonparametric phase coherence function' (Grenfell et al. 2001)

Value

An object of class "Sncf" is returned, consisting of the following components:

Author(s)

Ottar N. Bjornstad onb1@psu.edu

References

Hall, P. and Patil, P. (1994) Properties of nonparametric estimators of autocovariance for stationary random fields. Probability Theory and Related Fields, 99:399-424. <doi:10.1007/BF01199899>

Hall, P., Fisher, N.I. and Hoffmann, B. (1994) On the nonparametric estimation of covariance functions. Annals of Statistics, 22:2115-2134 <doi:10.1214/aos/1176325774>.

Bjornstad, O.N. and Falck, W. (2001) Nonparametric spatial covariance functions: estimation and testing. Environmental and Ecological Statistics, 8:53-70 <doi:10.1023/A:1009601932481>.

Bjornstad, O.N., Ims, R.A. and Lambin, X. (1999) Spatial population dynamics: Analysing patterns and processes of population synchrony. Trends in Ecology and Evolution, 11:427-431 <doi:10.1016/S0169-5347(99)01677-8>.

Bjornstad, O. N., and J. Bascompte. (2001) Synchrony and second order spatial correlation in host-parasitoid systems. Journal of Animal Ecology 70:924-933 <doi:10.1046/j.0021-8790.2001.00560.x>.

Grenfell, B.T., Bjornstad, O.N., & Kappey, J. (2001) Travelling waves and spatial hierarchies in measles epidemics. Nature 414:716-723. <doi:10.1038/414716a>

See Also

Sncf2D, Sncf.srf

Examples

# first generate some sample data
x <- expand.grid(1:20, 1:5)[, 1]
y <- expand.grid(1:20, 1:5)[, 2]
# z data from an exponential random field
z <- cbind(
   rmvn.spa(x = x, y = y, p = 2, method = "exp"),
   rmvn.spa(x = x, y = y, p = 2, method = "exp")
  )
# w data from a gaussian random field
w <- cbind(
  rmvn.spa(x = x, y = y, p = 2, method = "gaus"), 
  rmvn.spa(x = x, y = y, p = 2, method = "gaus")
  )
# multivariate nonparametric covariance function
fit1 <- Sncf(x = x, y = y, z = z, resamp = 0)
## Not run: plot.Sncf(fit1)
summary(fit1)

# multivariate nonparametric cross-covariance function
fit2 <- Sncf(x = x, y = y, z = z, w = w, resamp = 0)
## Not run: plot(fit2)
summary(fit2)

Nonparametric (Cross-)Covariance Function from stationary random fields

Description

Sncf.srf is the function to estimate the nonparametric for spatio-temporal data from fully stationary random fields (i.e. marginal expectation and variance identical for all locations; use Sncf otherwise).

Usage

Sncf.srf(
  x,
  y,
  z,
  w = NULL,
  avg = NULL,
  avg2 = NULL,
  corr = TRUE,
  df = NULL,
  type = "boot",
  resamp = 0,
  npoints = 300,
  save = FALSE,
  filter = FALSE,
  fw = 0,
  max.it = 25,
  xmax = FALSE,
  jitter = FALSE,
  quiet = FALSE
)

Arguments

Details

If corr = F, an object of class "Sncf.cov" is returned. Otherwise the class is "Sncf".

Sncf.srf is a function to estimate the nonparametric (cross-)covariance function (as discussed in Bjornstad and Bascompte 2001) for data from a fully stationary random fields. I have found it useful to estimate the (cross-)covariance functions in synthetic data.

Value

An object of class "Sncf" (or "Sncf.cov") is returned. See Sncf for details.

Author(s)

Ottar N. Bjornstad onb1@psu.edu

References

Bjornstad, O. N., and J. Bascompte. (2001) Synchrony and second order spatial correlation in host-parasitoid systems. Journal of Animal Ecology 70:924-933. <doi:10.1046/j.0021-8790.2001.00560.x>

See Also

Sncf, summary.Sncf, plot.Sncf, plot.Sncf.cov

Examples

# first generate some sample data
x <- expand.grid(1:20, 1:5)[, 1]
y <- expand.grid(1:20, 1:5)[, 2]

# z data from an exponential random field
z <- cbind(
  rmvn.spa(x = x, y = y, p = 2, method = "exp"), 
  rmvn.spa(x = x, y = y, p = 2, method = "exp")
  )

# w data from a gaussian random field
w <- cbind(
  rmvn.spa(x = x, y = y, p = 2, method = "gaus"), 
  rmvn.spa(x = x, y = y, p = 2, method = "gaus")
  )

# multivariate nonparametric covariance function
fit1 <- Sncf.srf(x = x, y = y, z = z, avg = NULL, corr = TRUE, resamp = 0) 
## Not run: plot(fit1) 
summary(fit1)

# multivariate nonparametric cross-covariance function (with known
# marginal expectation of zero for both z and w
fit2 <- Sncf.srf(x = x, y = y, z = z, w = w, avg = 0, avg2 = 0, corr = FALSE, 
                 resamp = 0)
## Not run: plot(fit2) 
summary(fit2)

Anisotropic nonparametric (cross-)correlation function for spatio-temporal data

Description

Sncf2D is the function to estimate the anisotropic nonparametric correlation function in 8 (or arbitrary) directions (North - Southeast). Correlation functions are calculated for each different bearing. The function requires multiple observations at each location. (use spline.correlog2D otherwise).

Usage

Sncf2D(
  x,
  y,
  z,
  w = NULL,
  df = NULL,
  type = "boot",
  resamp = 1000,
  npoints = 300,
  save = FALSE,
  max.it = 25,
  xmax = FALSE,
  na.rm = FALSE,
  jitter = FALSE,
  quiet = FALSE,
  angle = c(0, 22.5, 45, 67.5, 90, 112.5, 135, 157.5)
)

Arguments

Details

Correlation functions are calculated on projected distances onto the different bearings so ALL data are used for each direction. The (obsolete?) oldncf2D used the alternative of slicing up the data like pieces of a pie.

Latitude-longitude coordinates can NOT be used.

Missing values are allowed - values are assumed missing at random.

I have implemented an optional argument: jitter if TRUE this jitters the distance matrix, to avoid some problems I've had with spline-smoothing data from regular grid-data.

Value

An object of class "Sncf2D" is returned, consisting of a list of estimates for each cardinal direction :

Note

The function to estimate the anisotropic nonparametric (cross-)correlation function in arbitrary directions. In particular it was developed to calculate the lagged cross-correlation function (Bjornstad et al. 2002).

Author(s)

Ottar N. Bjornstad onb1@psu.edu

References

Bjornstad, O. N., M. Peltonen, A. M. Liebhold, and W. Baltensweiler. 2002. Waves of larch budmoth outbreaks in the European Alps. Science 298:1020-1023. <doi:10.1126/science.1075182>

See Also

summary.Sncf2D, plot.Sncf2D, cc.offset , Sncf, spline.correlog2D

Examples

# first generate some sample data
x <- expand.grid(1:20, 1:5)[, 1]
y <- expand.grid(1:20, 1:5)[, 2]
# z data from an exponential random field
z <- cbind(
  rmvn.spa(x = x, y = y, p = 2, method = "exp"),
  rmvn.spa(x = x, y = y, p = 2, method = "exp")
  )
# anisotorpic nonparametric covariance function at 30 and 60 degrees
fit1 <- Sncf2D(x = x, y = y, z = z, resamp = 0, angle = c(30, 60))
## Not run: plot(fit1)
summary(fit1)

# What distance is the peak in correlation
cc.offset(fit1)

Function to calculate the distance at which the cross-correlation peaks for Sncf objects

Description

Alternative summary method for class "Sncf2D".

Usage

cc.offset(object, xmax = NULL)

Arguments

Value

An matrix of class "cc.offset" is returned with columns:

See Also

Sncf2D, summary.Sncf2D, plot.cc.offset

Circular correlation

Description

A vectorized function to calculate a correlation matrix for panels of data.

Usage

circ.cor2(x, y = NULL)

Arguments

Details

Missing values are not allowed.

Value

A correlation matrix is returned.

References

Jammalamadaka, S. Rao and SenGupta, A. (2001). Topics in Circular Statistics, Section 8.2, World Scientific Press, Singapore.

Utility function

Description

Called by various functions to calculate Pearson or angular correlation matrices.

Usage

cor2(x, y = NULL, circ = FALSE)

Arguments

Details

An auxilliary function to ease the maintenance.

Value

A correlation matrix is returned.

References

Jammalamadaka, S. Rao and SenGupta, A. (2001). Topics in Circular Statistics, Section 8.2, World Scientific Press, Singapore.

Uni- and multivariate spatial correlograms

Description

correlog is the function to estimate spatial (cross-)correlograms. Either univariate or multivariate (time seres) for each site can be used.

Usage

correlog(
  x,
  y,
  z,
  w = NULL,
  increment,
  resamp = 999,
  latlon = FALSE,
  na.rm = FALSE,
  quiet = FALSE
)

Arguments

Details

The spatial (cross-)correlogram and Mantel (cross-)correlogram estimates the spatial dependence at discrete distance classes.

The region-wide similarity forms the reference line (the zero-line); the x-intercept is thus the distance at which object are no more similar than that expected by-chance-alone across the region.

If the data are univariate, the spatial dependence is measured by Moran's I. If it is multivariate, it is measured by the centred Mantel statistic. (Use correlog.nc if the non-centered multivariate correlogram is desired).

Missing values are allowed – values are assumed missing at random.

Value

An object of class "correlog" is returned, consisting of the following components:

Author(s)

Ottar N. Bjornstad onb1@psu.edu

References

Bjornstad, O.N., Ims, R.A. & Lambin, X. (1999) Spatial population dynamics: Analysing patterns and processes of population synchrony. Trends in Ecology and Evolution, 11, 427-431. <doi:10.1016/S0169-5347(99)01677-8>

Bjornstad, O.N. & Falck, W. (2001) Nonparametric spatial covariance functions: estimation and testing. Environmental and Ecological Statistics, 8:53-70. <doi:10.1023/A:1009601932481>

Epperson, B.K. (1993) Recent advances in correlation studies of spatial patterns of genetic variation. Evolutionary Biology, 27, 95-155. <doi:10.1007/978-1-4615-2878-4_4>

See Also

plot.correlog, spline.correlog, correlog.nc

Examples

# first generate some sample data
x <- expand.grid(1:20, 1:5)[, 1]
y <- expand.grid(1:20, 1:5)[, 2]

# z data from an exponential random field
z <- cbind(
  rmvn.spa(x = x, y = y, p = 2, method = "exp"), 
  rmvn.spa(x = x, y = y, p = 2, method = "exp")
  )

# w data from a gaussian random field
w <- cbind(
  rmvn.spa(x = x, y = y, p = 2, method = "gaus"), 
  rmvn.spa(x = x, y = y, p = 2, method = "gaus")
  )

# Spatial correlogram 
fit1 <- correlog(x = x, y = y, z = z[, 1], increment = 2, resamp = 0) 
## Not run: plot(fit1)

# Mantel correlogram 
fit2 <- correlog(x = x, y = y, z = z, increment = 2, resamp = 0) 
## Not run: plot(fit2)

# Mantel cross-correlogram 
fit3 <- correlog(x = x, y = y, z = z, w = w, increment = 2, resamp = 0) 
## Not run: plot(fit3)

Non-centered spatial (cross-)correlogram

Description

correlog.nc is the function to estimate the non-centered (cross-)correlogram. The non-centered correlogram provides estimates of the spatial correlation for discrete distance classes. The function requires multiple observations at each location (use correlog otherwise).

Usage

correlog.nc(
  x,
  y,
  z,
  w = NULL,
  increment,
  resamp = 999,
  na.rm = FALSE,
  latlon = FALSE,
  quiet = FALSE
)

Arguments

Details

The non-centered correlogram estimates spatial dependence at discrete distance classes. The method corresponds to the modified correlogram of Koenig & Knops(1998), but augmented to potentially estimate the cross-correlogram). The function requires multiple observations at each location. Missing values is allowed in the multivariate case (pairwise deletion will be used).

Missing values are allowed – values are assumed missing at random.

Value

An object of class "correlog" is returned, consisting of the following components:

Author(s)

Ottar N. Bjornstad onb1@psu.edu

References

Bjornstad, O.N., Ims, R.A. & Lambin, X. (1999) Spatial population dynamics: Analysing patterns and processes of population synchrony. Trends in Ecology and Evolution, 11, 427-431. <doi:10.1016/S0169-5347(99)01677-8>

Koenig, W.D. & Knops, J.M.H. (1998) Testing for spatial autocorrelation in ecological studies. Ecography, 21, 423-429. <doi:10.1111/j.1600-0587.1998.tb00407.x>

See Also

plot.correlog, correlog

Examples

# first generate some sample data
x <- expand.grid(1:20, 1:5)[, 1]
y <- expand.grid(1:20, 1:5)[, 2]

# z data from an exponential random field
z <- cbind(
  rmvn.spa(x = x, y = y, p = 2, method = "exp"), 
  rmvn.spa(x = x, y = y, p = 2, method = "exp")
  )

# w data from a gaussian random field
w <- cbind(
  rmvn.spa(x = x, y = y, p = 2, method = "gaus"), 
  rmvn.spa(x = x, y = y, p = 2, method = "gaus")
  )

# noncentered (Mantel) correlogram 
fit1 <- correlog.nc(x = x, y = y, z = z, increment = 2, resamp = 499)
## Not run: plot(fit1)

Fourier filter for correlation functions.

Description

Fourier filter to ensure positive semi-definite correlation functions. Called by various functions.

Usage

ff.filter(x)

Arguments

Value

A vector is returned whose Fourier-transform has no non-negative coefficients.

See Also

Sncf

Utility function

Description

Called by various functions to calculate various intercepts.

Usage

gather(u, v, w, moran, df, xpoints, filter, fw)

Arguments

Details

An auxiliary function to ease maintenance.

Value

A list is returned.

Great-circle distance

Description

Great-circle distance function to calculate spatial distance from lat-long data. Called by various functions.

Usage

gcdist(x, y)

Arguments

Value

The distance in km is returned

Spatio-temporal data panel of Larch Budmoth defoliation

Description

This is the data in Bjornstad et al. (2002).

Usage

data(lbm)

Format

A data-frame with 135 rows and 40 columns. The first two are the x- and y-coordinates (in m), the following 38 represents the defoliation in years 1961 through 1998.

References

Bjornstad, O.N., Peltonen, M., Liebhold, A.M., and Baltensweiler, W. (2002) Waves of larch budmoth outbreaks in the European Alps. Science, 298, 1020-1023. <doi:10.1126/science.1075182>

Local indicator of spatial association

Description

lisa is a function to estimate the local indicators of spatial association. The function assumes univariate data at each location. For multivariate data use lisa.nc

Usage

lisa(x, y, z, neigh, resamp = 999, latlon = FALSE, quiet = FALSE)

Arguments

Details

This is the function to estimate the local indicators of spatial association modified form Anselin (1995). The statistic is the average autocorrelation within a neighborhood.

Value

An object of class "lisa" is returned, consisting of the following components:

Author(s)

Ottar N. Bjornstad onb1@psu.edu

References

Anselin, L. 1995. Local indicators of spatial association - LISA. Geographical Analysis 27:93-115. <doi:10.1111/j.1538-4632.1995.tb00338.x>

See Also

plot.lisa

Examples

# first generate some sample data
x <- expand.grid(1:20, 1:5)[, 1]
y <- expand.grid(1:20, 1:5)[, 2]

# z data from an exponential random field
z <- rmvn.spa(x = x, y = y, p = 2, method = "gaus")

# lisa analysis
fit1 <- lisa(x = x, y = y, z = z, neigh = 3, resamp = 499)
## Not run: plot(fit1, neigh.mean=FALSE)

Non-centered indicators of spatial association

Description

lisa.nc is a function to estimate the (non-centred) multivariate local indicators of spatial association. The function requires multiple observations at each location. For single observations at each location use lisa.

Usage

lisa.nc(
  x,
  y,
  z,
  neigh,
  na.rm = FALSE,
  resamp = 999,
  latlon = FALSE,
  quiet = FALSE
)

Arguments

Details

This is the function to estimate the (non-centered) local indicators of spatial association modified form Anselin (1995). 'correlation' is the average correlation within a neighborhood. The function requires multiple observations at each location.

Missing values are allowed – values are assumed missing at random, and pairwise complete observations will be used.

Value

An object of class "lisa" is returned, consisting of the following components:

Author(s)

Ottar N. Bjornstad onb1@psu.edu

References

Anselin, L. 1995. Local indicators of spatial association - LISA. Geographical Analysis 27:93-115. <doi:10.1111/j.1538-4632.1995.tb00338.x>

See Also

lisa

Examples

# first generate some sample data
x <- expand.grid(1:20, 1:5)[, 1]
y <- expand.grid(1:20, 1:5)[,2]

# z data from an exponential random field
z <- cbind(
  rmvn.spa(x = x, y = y, p = 2, method = "exp"), 
  rmvn.spa(x = x, y = y, p = 2, method = "exp")
  )

# lisa.nc analysis
fit1 <- lisa.nc(x = x, y = y, z = z, neigh = 3)
## Not run: plot(fit1)

The mean (cross-)correlation (with bootstrapp CI) for a panel of spatiotemporal data

Description

mSynch is the function to estimate the mean (cross-)correlation in a spatiotemporal dataset as discussed in Bjornstad et al. (1999). The function requires multiple observations at each location.

Usage

mSynch(x, y = NULL, resamp = 999, na.rm = FALSE, circ = FALSE, quiet = FALSE)

Arguments

Details

Missing values are allowed – values are assumed missing at random.

The circ argument computes a circular version of the Pearson's product moment correlation (see cor2).

Value

An object of class "mSynch" is returned, consisting of a list with two components:

Author(s)

Ottar N. Bjornstad onb1@psu.edu

References

Bjornstad, O.N., Ims, R.A. & Lambin, X. (1999) Spatial population dynamics: Analysing patterns and processes of population synchrony. Trends in Ecology and Evolution, 11, 427-431. <doi:10.1016/S0169-5347(99)01677-8>

See Also

print.mSynch

Examples

# first generate some sample data
x <- expand.grid(1:20, 1:5)[, 1]
y <- expand.grid(1:20, 1:5)[, 2]
# z data from an exponential random field
z <- cbind(
  rmvn.spa(x = x, y = y, p = 2, method = "exp"), 
  rmvn.spa(x = x, y = y, p = 2, method = "exp")
  )

# mean correlation analysis
fit1 <- mSynch(x = z, resamp = 500)
print(fit1)

Mantel (cross-)correlograms

Description

mantel.correlog is the function to calculate a Mantel (cross-)correlogram. The function requires two (or three) matrices.

Usage

mantel.correlog(
  dmat,
  zmat,
  wmat = NULL,
  increment,
  resamp = 999,
  quiet = FALSE
)

Arguments

Details

The function calculates Mantel (cross-)correlograms at discrete distance classes from two (or three) matrixes. The first is the matrix of distances and the second is a matrix of similarities. The optional third matrix is an additional similarity matrix to be used to calculate a Mantel cross-correlogram. Missing values are allowed – values are assumed missing at random.

Value

An object of class "correlog" is returned, consisting of the following components:

Author(s)

Ottar N. Bjornstad onb1@psu.edu

See Also

plot.correlog

Examples

# first generate some sample data
x <- expand.grid(1:20, 1:5)[, 1]
y <- expand.grid(1:20, 1:5)[, 2]

# z data from an exponential random field
z <- cbind(
  rmvn.spa(x = x, y = y, p = 2, method = "exp"), 
  rmvn.spa(x = x, y = y, p = 2, method = "exp")
  )

# w data from a gaussian random field
w <- cbind(rmvn.spa(
  x = x, y = y, p = 2, method = "gaus"), 
  rmvn.spa(x = x, y = y, p = 2, method = "gaus")
  )

# Make distance and similarity matrices
zmat <- cor(t(z))
wmat <- cor(t(w))
dmat <- sqrt(outer(x, x, "-")^2 + outer(y, y, "-")^2)

# Mantel correlogram 
fit1 <- mantel.correlog(dmat = dmat, zmat = zmat, increment = 2, quiet = TRUE, 
                        resamp = 0)
## Not run: plot(fit1)

# Mantel cross-correlogram 
fit2 <- mantel.correlog(dmat = dmat, zmat = zmat, wmat = wmat, increment = 2, 
                        quiet = TRUE, resamp = 0)
## Not run: plot(fit2)

Mantel Test

Description

A simple function to do a permutation-based Mantel test. The data can either be two distance/similarity matrices or (x, y, z) data.

Usage

mantel.test(
  M1 = NULL,
  M2 = NULL,
  x = NULL,
  y = NULL,
  z = NULL,
  resamp = 999,
  latlon = FALSE,
  quiet = FALSE
)

Arguments

Details

Typical usages are

mantel.test(M1, M2, x = NULL, y = NULL, z = NULL, resamp = 999, 
            latlon = FALSE, quiet = FALSE)

mantel.test(x, y, z, M1 = NULL, M2 = NULL, resamp = 999, latlon = FALSE, 
            quiet = FALSE)

Missing values are treated through pairwise deletion.

Value

An object of class "Mantel" is returned, consisting of a list with two components:

Author(s)

Ottar N. Bjornstad onb1@psu.edu

Examples

# first generate some sample data
x <- expand.grid(1:20, 1:5)[, 1]
y <- expand.grid(1:20, 1:5)[, 2]
# z data from an exponential random field
z <- cbind(
  rmvn.spa(x = x, y = y, p = 2, method = "exp"), 
  rmvn.spa(x = x, y = y, p = 2, method = "exp")
  )

# the Mantel test
mantel.test(x = x, y = y, z = z[, 1], resamp = 999)

Partial Mantel test

Description

A simple function to calculate permutation-based partial mantel tests for three matrices, the partial mantel test is calculated to test for relationships between M1 and M2 (M3) controlling for M3 (M2). syntax and logic follows Legendre and Legendre (1998) pp 557-558.

Usage

partial.mantel.test(
  M1,
  M2,
  M3,
  resamp = 999,
  method = "pearson",
  quiet = FALSE
)

Arguments

Details

Missing values are treated through pairwise deletion.

The method must be one of "pearson" (default), "spearman" or "kendall".

Value

An object of class "partial.Mantel" is returned, consisting of a list with two components:

Author(s)

Ottar N. Bjornstad onb1@psu.edu

References

Legendre, P., and L. Legendre. 1998. Numerical Ecology, 2nd edition. Elsevier, Amsterdam

See Also

mantel.test

Examples

# first generate some sample data and dissimilarity matrices
x <- rnorm(10)
y <- rnorm(10)
z <- rnorm(10)
M1 <- sqrt(outer(x, x, "-")^2)
M2 <- sqrt(outer(y, y, "-")^2)
M3 <- sqrt(outer(z, z, "-")^2)

partial.mantel.test(M1 = M1, M2 = M2, M3 = M3, resamp = 999)

Plots nonparametric spatial correlation-functions

Description

'plot' method for class "Sncf".

Usage

## S3 method for class 'Sncf'
plot(x, ylim = c(-1, 1), add = FALSE, ...)

Arguments

Value

A plot of the nonparametric spatial covariance function (with CI's if bootstraps are available)

See Also

Sncf, Sncf.srf

Plots nonparametric spatial covariance-functions

Description

'plot' method for class "Sncf.cov".

Usage

## S3 method for class 'Sncf.cov'
plot(x, ...)

Arguments

Value

A plot of the nonparametric spatial covariance function (with CI's if bootstrapps are available)

See Also

Sncf.srf, plot.Sncf

Plots anisotropic spatial correlation-functions

Description

plot method for class "Sncf2D".

Usage

## S3 method for class 'Sncf2D'
plot(x, xmax = 0, ylim = c(-1, 1), detail = FALSE, ...)

Arguments

Value

A plot or panel-plot results. These represents the xy-plot of distance against spatial (cross-)correlation for each cardinal direction.

See Also

Sncf2D, plot.Sncf

Plots the cc.offset summary of the anisotropic spatial correlation-functions

Description

plot method for class "cc.offset".

Usage

## S3 method for class 'cc.offset'
plot(x, dmax = NULL, inches = NULL, ...)

Arguments

Value

A radial symbol plot results. The radius represents the distance to peak correlation (the mode) of the correlation function (in the positive direction). The size of the symbol represents the magnitude of the correlation at the mode for the given cardinal direction.

See Also

cc.offset, Sncf2D, plot.Sncf2D

Plots spatial correlograms

Description

‘plot’ method for class "correlog".

Usage

## S3 method for class 'correlog'
plot(x, ...)

Arguments

Value

A spatial or Mantel (cross-correlogram) is plotted.

If a permutation test was performed, values significant at a nominal (two-sided) 5%-level will be represented by filled circles and non-significant values by open circles.

See Also

correlog, correlog.nc

Plots local indicators of spatial association

Description

‘plot’ method for class "lisa".

Usage

## S3 method for class 'lisa'
plot(x, neigh.mean = FALSE, add = FALSE, inches = 0.2, ...)

Arguments

Value

A bubble-plot of observations against spatial coordinates is produced. Above mean values are signified by red circles. Below mean values are signified by black squares.

If a permutation test was performed, observations for which the associated LISA statistic is significant at a nominal (two-sided) 5%-level will be represented by filled symbols and non-significant values by open symbols. Thus spatial hot-spots are represented by red filled circles and cold-spots by black filled squares.

See Also

lisa, lisa.nc

Plots a spline correlogram

Description

‘plot’ method for class "spline.correlog".

Usage

## S3 method for class 'spline.correlog'
plot(x, ylim = c(-1, 1), ...)

Arguments

Value

A plot of the spline correlogram function against distance is produced. 95% pointwise confidence (or null) envelopes are superimposed (if available).

See Also

spline.correlog, summary.spline.correlog

Print function for Sncf objects

Description

'print' method for class "Sncf".

Usage

## S3 method for class 'Sncf'
print(x, ...)

Arguments

Value

The function-call is printed to screen.

See Also

Sncf

Print function for Sncf2D objects

Description

‘print’ method for class "Sncf2D".

Usage

## S3 method for class 'Sncf2D'
print(x, ...)

Arguments

Value

The function-call is printed to screen.

See Also

Sncf2D

Print function for mSynch objects

Description

‘print’ method for class "mSynch".

Usage

## S3 method for class 'mSynch'
print(x, verbose = FALSE, ...)

Arguments

Value

If verbose is FALSE, a list summarizing the regional correlation is produced:

See Also

mSynch

Print function for spline.correlog objects

Description

‘print’ method for class "spline.correlog".

Usage

## S3 method for class 'spline.correlog'
print(x, ...)

Arguments

Value

The function-call is printed to screen.

See Also

spline.correlog

Simulate spatially correlated data

Description

Function to generate spatially autocorrelated random normal variates using the eigendecomposition method. Spatial covariance can follow either and exponential or Gaussian model.

Usage

rmvn.spa(x, y, p, method = "exp", nugget = 1)

Arguments

Details

A target covariance matrix A between the n units is generated by calculating the distances between the locations and thereafter evaluating the covariance function in each pairwise distance. A vector, Z, of spatially correlated normal data with the target covariance is subsequently generated using the eigendecomposition method (Ripley, 1987).

Value

A vector of spatially correlated random normal variates with zero mean and unit variance is returned

Author(s)

Ottar N. Bjornstad onb1@psu.edu

References

Ripley, B.D. (1987). Stochastic Simulation. Wiley.

See Also

mSynch

Simple wrapper around symbols to visualize spatial data

Description

spatial.plot is a quick function to visualize spatial data using bubble plots

Usage

spatial.plot(x, y, z, ctr = TRUE, add = FALSE, inches = 0.2, ...)

Arguments

Details

This is a simple function to visualize spatial data. Positive (or above average) observations are shown by red circles, Negative (or below average) observations are shown as black squares. For hot/coldspot analysis using Local indicators of spatial association use lisa.

Value

A bubble-plot of the spatial data is produced.

Author(s)

Ottar N. Bjornstad onb1@psu.edu

References

Ripley, B.D. (1987). Stochastic Simulation. Wiley.

See Also

lisa

Examples

# first generate some sample data
x <- expand.grid(1:20, 1:5)[, 1]
y <- expand.grid(1:20, 1:5)[, 2]

# z data from an exponential random field
z <- rmvn.spa(x = x, y = y, p = 2, method = "gaus")

# plot data
## Not run: spatial.plot(x = x, y = y, z = z, ctr = FALSE)

Uni- and multivariate spline correlograms

Description

spline.correlog is the function to estimate the spline (cross-)correlogram from spatial data. Either univariate or multivariate (time seres) for each site can be used.

Usage

spline.correlog(
  x,
  y,
  z,
  w = NULL,
  df = NULL,
  type = "boot",
  resamp = 1000,
  npoints = 300,
  save = FALSE,
  filter = FALSE,
  fw = 0,
  max.it = 25,
  xmax = FALSE,
  latlon = FALSE,
  na.rm = FALSE,
  quiet = FALSE
)

Arguments

Details

If observations are univariate the spline (cross-)correlogram represents the generalization of the spatial (cross-)correlogram; if observations are multivariate the spline (cross-)correlogram represents the generalization of the Mantel (cross-)correlogram.

The spline (cross-)correlogram differs from the spatial correlogram (and Mantel correlogram) in that it estimated spatial dependence as a continuous functions of distance (rather than binning into distance classes). The spline correlogram differs from the nonparametric (cross-)correlation function in that the zero-correlation reference line in the former corresponds to the region-wide correlation reference line in the latter. The x-intercept in the spline correlogram is the distance at which object are no more similar than that expected by-chance-alone across the region.

Missing values are allowed – values are assumed missing at random.

Value

An object of class "spline.correlog" is returned, consisting of the following components:

Author(s)

Ottar N. Bjornstad onb1@psu.edu

References

Bjornstad, O.N. & Falck, W. (2001) Nonparametric spatial covariance functions: estimation and testing. Environmental and Ecological Statistics, 8:53-70. <doi:10.1023/A:1009601932481>

See Also

summary.spline.correlog, plot.spline.correlog, Sncf, spline.correlog2D, correlog

Examples

# first generate some sample data
x <- expand.grid(1:20, 1:5)[, 1]
y <- expand.grid(1:20, 1:5)[, 2]

# z data from an exponential random field
z <- cbind(
  rmvn.spa(x = x, y = y, p = 2, method = "exp"), 
  rmvn.spa(x = x, y = y, p = 2, method = "exp")
  )

# w data from a gaussian random field
w <- cbind(
  rmvn.spa(x = x, y = y, p = 2, method = "gaus"), 
  rmvn.spa(x = x, y = y, p = 2, method = "gaus")
  )

# univariate spline correlogram
fit1 <- spline.correlog(x = x, y = y, z = z[, 1], resamp = 100)
## Not run: plot.spline.correlog(fit1)
summary(fit1)

# multivariate spline correlogram
fit2 <- spline.correlog(x = x, y = y, z = z, resamp = 100)
## Not run: plot.spline.correlog(fit2)
summary(fit2)

# multivariate spline cross-correlogram
fit3 <- spline.correlog(x = x, y = y, z = z, w = w, resamp = 100)
## Not run: plot.spline.correlog(fit3)
summary(fit3)

Anisotropic nonparametric (cross-)correlation function for univariate spatial data

Description

spline.correlog2D is the function to estimate the anisotropic nonparametric correlation function in 8 (or arbitrary) directions (North - Southeast) for univariate data. Correlation functions are calculated for each different bearing. The function assumes univariate observations at each location. (use Sncf2D otherwise).

Usage

spline.correlog2D(
  x,
  y,
  z,
  w = NULL,
  df = NULL,
  type = "boot",
  resamp = 1000,
  npoints = 300,
  save = FALSE,
  max.it = 25,
  xmax = FALSE,
  na.rm = FALSE,
  jitter = FALSE,
  quiet = FALSE,
  angle = c(0, 22.5, 45, 67.5, 90, 112.5, 135, 157.5)
)

Arguments

Details

see Sncf2D

Value

An object of class "Sncf2D" is returned. See Sncf2D for details.

Note

The function to estimate the UNIvariate anisotropic nonparametric (cross-)correlation function in arbitrary directions. In particular it was developed to calculate the univariate lagged cross-correlation function used in (Humston et al. 2005). Note that this 2D spline correlogram does the anisotropic analysis NOT by doing the angle-with-tolerance-wedge-style of Oden and Sokal (1986) but by projecting the the spatial coordinates of all locations on a sequence of cardinal angles (a la Sncf2D). Hence, all data points are used every time, it is only their relative distances that are changed. For example {0, 0} and {0, 10} are distance zero in the zero-degree direction but at distance 10 in the 90-degree direction.

References

Oden, N.L. and Sokal, R.R. 1986. Directional autocorrelation: an extension of spatial correlograms to two dimensions. Systematic Zoology 35: 608-617. <doi:10.2307/2413120> @references Humston, R., Mortensen, D. and Bjornstad, O.N. 2005. Anthropogenic forcing on the spatial dynamics of an agricultural weed: the case of the common sunflower. Journal of Applied Ecology 42: 863-872. <doi:10.1111/j.1365-2664.2005.01066.x>

See Also

Sncf2D

Summarizing nonparametric spatial correlation-functions

Description

'summary' method for class "Sncf".

Usage

## S3 method for class 'Sncf'
summary(object, ...)

Arguments

Value

A list summarizing the nonparametric (cross-)covariance function is returned.

See Also

Sncf, plot.Sncf

Summarizing anisotropic spatial correlation-functions

Description

Summary method for class "Sncf2D".

Usage

## S3 method for class 'Sncf2D'
summary(object, ...)

Arguments

Value

A list summarizing the nonparametric covariance function in each cardinal direction results, each with the entires as in summary.Sncf.

See Also

Sncf2D, cc.offset, summary.Sncf

Summarizing spline correlograms

Description

‘summary’ method for class "spline.correlog".

Usage

## S3 method for class 'spline.correlog'
summary(object, ...)

Arguments

Value

A list summarizing the spline correlogram is returned.

See Also

spline.correlog, plot.spline.correlog