vario.fit {synchrony}

vario.fit

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\left(\frac{SSE}{n}\right)+2p where n is the number of points in the variogram, SSE=\sum{(\hat{x}_{i}-x_{i}})^2, and p is the number of parameters

RMSE

Root Mean Square Error of the model fit: \sqrt{\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")