vario.fit: vario.fit

In synchrony: Methods for Computing Spatial, Temporal, and Spatiotemporal Statistics

Description

Fit model to the empirical variogram

Usage

vario.fit (vario, bins, weights = rep(1, length(vario)),
                       type = c("spherical", "gaussian", "nugget", "linear", 
                       "exponential", "sill", "periodic", "hole"),
                       start.vals = list(c0 = 0, c1 = max(vario), 
                                          a = max(bins)/4, b=0.1, c=0.1),
                       control = list(maxit=10000)) 

Arguments

vario	Empirical variogram from emp.vario function
bins	Bins or lag distances from emp.vario function
weights	Vector of weights of the same length as vario. If weights is a vector containing the number of points in each distance bin, the model will be fit via weighted least squares with the weights corresponding to the proportion of points within each bin (i.e., weights sum to 1). Default is a vector of weights equal to 1
type	Type of variogram model to fit to the data. Default is spherical. Other options are gaussian, nugget, linear, exponential, sill, periodic, and hole
start.vals	Named list containing the start values for the variogram model: c0: nugget, c1: sill, a: spatial range; b: slope; c: frequency
control	optional parameter for the optim function. See ?optim for details

Value

Return a named list containing the following variables:

vario	Empirical variogram values
bins	Empirical variogram bins/lag distances
AIC	AIC score of the model fit: AIC=nlog≤ft(\frac{SSE}{n}\right)+2p where n is the number of points in the variogram, SSE=∑{(\hat{x}_{i}-x_{i}})^2, and p is the number of parameters
RMSE	Root Mean Square Error of the model fit: √{\frac{SSE}{n}}
params	Named list containing the best model parameter estimates
fit	Predicted variogram values from the model fit
nls.success	did nls succeed?
convergence	did nls or optim converge?

Note

Selecting proper initial values is critical for fitting a reasonable model to the empirical variogram. If these values are off, nls will fail and fall-back functions will be used to determine the best parameter values that minimize the Root Mean Square Error (RMSE).

Author(s)

Tarik C. Gouhier ([e-mail])

See Also

vario, vario.func

Examples

# Load data
data(pisco.data)
# Environmental variogram
d=subset(pisco.data, subset=year==2000, select=c("latitude", "longitude", "upwelling"))
semiv=vario(data=d)
plot(semiv, xlab="Lag distance (km)")
mod.sph=vario.fit(semiv$vario, semiv$mean.bin.dist)
# Weighted least squares fit based on the number of points
mod.exp=vario.fit(semiv$vario, semiv$mean.bin.dist, 
                  weights=semiv$npoints/sum(semiv$npoints), 
                  type="expo")
mod.gau=vario.fit(semiv$vario, semiv$mean.bin.dist, type="gauss")
mod.lin=vario.fit(semiv$vario, semiv$mean.bin.dist, type="lin")
lines(semiv$mean.bin.dist, mod.sph$fit, col="red")
lines(semiv$mean.bin.dist, mod.exp$fit, col="black")
lines(semiv$mean.bin.dist, mod.gau$fit, col="blue")
lines(semiv$mean.bin.dist, mod.lin$fit, col="green")
legend(x="topleft", legend=paste(c("Spherical AIC:", "Exponential AIC:", 
                                   "Gaussian AIC:", "Linear AIC:"), 
                                   c(format(mod.sph$AIC, dig=2), 
                                   format(mod.exp$AIC, dig=2), 
                                   format(mod.gau$AIC, dig=2), 
       format(mod.lin$AIC, dig=2))), lty=1, col=c("red", "black", "blue", "green"), 
       bty="n")

# Correlogram
cover=subset(pisco.data, subset=year==2000, 
             select=c("latitude", "longitude", "mussel_abund"))
moran=vario(data=cover, type="moran")
mod.hol=vario.fit(moran$vario, moran$mean.bin.dist, 
                  type="hole", start.vals=list(c0=0.6, a=25, c1=0.01))
mod.per=vario.fit(moran$vario, moran$mean.bin.dist, type="period",
                  start.vals=list(a=1, b=3, c=0))
mod.lin=vario.fit(moran$vario, moran$mean.bin.dist, type="linear")
plot(moran, xlab="Lag distance (km)", ylim=c(-0.6, 0.8))
lines(moran$mean.bin.dist, mod.per$fit, col="red")
lines(moran$mean.bin.dist, mod.hol$fit, col="black")
lines(moran$mean.bin.dist, mod.lin$fit, col="blue")
legend(x="topleft", legend=paste(c("Periodic AIC:", "Hole AIC:", 
                                   "Linear AIC:"), 
                                   c(format(mod.per$AIC, dig=2), 
                                   format(mod.hol$AIC, dig=2), 
                                   format(mod.lin$AIC, dig=2))), 
                                   lty=1, col=c("red", "black", "blue"), bty="n")

synchrony documentation built on March 26, 2020, 7:14 p.m.