geostatsp (version 2.0.6)

likfitLgm: Likelihood Based Parameter Estimation for Gaussian Random Fields

Description

Maximum likelihood (ML) or restricted maximum likelihood (REML) parameter estimation for (transformed) Gaussian random fields.

Usage

likfitLgm(formula, data, 
		paramToEstimate = c("range","nugget"),
		reml=TRUE,
		coordinates=data,
		param=NULL,
		upper=NULL,lower=NULL, parscale=NULL,
		verbose=FALSE)
		
loglikLgm(param, 
		data, formula, coordinates=data,
		reml=TRUE, 
		minustwotimes=TRUE,
		moreParams=NULL)

Value

likfitLgm produces list with elements

parameters

Maximum Likelihood Estimates of model parameters

varBetaHat

Variance matrix of the estimated regression parameters

optim

results from optim

trend

Either formula for the fixed effects or names of the columns of the model matrix, depending on trend supplied.

summary

a table of parameter estimates, standard errors, confidence intervals, p values, and a logical value indicating whether each parameter was estimated as opposed to fixed.

resid

residuals, being the observations minus the fixed effects, on the transformed scale.

loglikLgm returns a scalar value, either the log likelihood or -2 times the log likelihood. Attributes of this result include the vector of parameters (including the MLE's computed for the variance and coefficients), and the variance matrix of the coefficient MLE's.

Arguments

formula

A formula for the fixed effects portion of the model, specifying a response and covariates. Alternately, data can be a vector of observations and formula can be a model matrix.

data

An object of class SpatVect, a vector of observations, or a data frame containing observations and covariates.

coordinates

A SpatVect object containing the locations of each observation, which defaults to data. Alternately, coordinates can be a symmetricMatrix-class or dist object reflecting the distance matrix of these coordinates (though this is only permitted if the model is isotropic).

param

A vector of model parameters, with named elements being amongst range, nugget, boxcox, shape, anisoAngleDegrees, anisoAngleRadians, anisoRatio, and possibly variance (see matern). When calling likfitLgm this vector is a combination of starting values for parameters to be estiamated and fixed values of parameters which will not be estimated. For loglikLgm, it is the covariance parameters for which the likelihood will be evaluated.

reml

Whether to use Restricted Likelihood rather than Likelihood, defaults to TRUE.

paramToEstimate

Vector of names of model parameters to estimate, with parameters excluded from this list being fixed. The variance parameter and regression coefficients are always estimated even if not listed.

lower

Named vector of lower bounds for model parameters passed to optim, defaults are used for parameters not specified.

upper

Upper bounds, as above.

parscale

Named vector of scaling of parameters passed as control=list(parscale=parscale) to optim.

minustwotimes

Return -2 times the log likelihood rather than the likelihood

moreParams

Vector of additional parameters, combined with param. Used for passing fixed parameters to loglikLgm from within optim.

verbose

if TRUE information is printed by optim.

See Also

lgm

Examples

n=40
mydat = vect(
	cbind(runif(n), seq(0,1,len=n)), 
	atts=data.frame(cov1 = rnorm(n), cov2 = rpois(n, 0.5))
	)

# simulate a random field
trueParam = c(variance=2^2, range=0.35, shape=2, nugget=0.5^2)
set.seed(1)

oneSim = RFsimulate(model=trueParam,x=mydat)

values(mydat) = cbind(values(mydat) , values(oneSim))

# add fixed effects
mydat$Y = -3 + 0.5*mydat$cov1 + 0.2*mydat$cov2 + 
	mydat$sim + rnorm(length(mydat), 0, sd=sqrt(trueParam["nugget"]))

plot(mydat, "sim", col=rainbow(10), main="U")
plot(mydat, "Y", col=rainbow(10), main="Y")


myres = likfitLgm(
	formula=Y ~ cov1 + cov2, 
	data=mydat, 
	param=c(range=0.1,nugget=0.1,shape=2), 
	paramToEstimate = c("range","nugget")
	)

myres$summary[,1:4]


# plot variograms of data, true model, and estimated model
myv = variog(mydat, formula=Y ~ cov1 + cov2,option="bin", max.dist=0.5)
# myv will be NULL if geoR isn't installed
if(!is.null(myv)){
plot(myv, ylim=c(0, max(c(1.2*sum(trueParam[c("variance", "nugget")]),myv$v))),
	main="variograms")
distseq = seq(0, 0.5, len=50)
lines(distseq, 
	sum(myres$param[c("variance", "nugget")]) - matern(distseq, param=myres$param),
	col='blue', lwd=3)
lines(distseq, 
	sum(trueParam[c("variance", "nugget")]) - matern(distseq, param=trueParam),
	col='red')	

legend("bottomright", fill=c("black","red","blue"), 
	legend=c("data","true","MLE"))
}

# without a nugget
myresNoN = likfitLgm(
	formula=Y ~ cov1 + cov2, 
	data=mydat, 
	param=c(range=0.1,nugget=0,shape=1), 
	paramToEstimate = c("range")
	)

myresNoN$summary[,1:4]


# plot variograms of data, true model, and estimated model
myv = variog(mydat, formula=Y ~ cov1 + cov2,option="bin", max.dist=0.5)

if(!is.null(myv)){
plot(myv, ylim=c(0, max(c(1.2*sum(trueParam[c("variance", "nugget")]),myv$v))),
	main="variograms")
	
distseq = seq(0, 0.5, len=50)
lines(distseq, 
	sum(myres$param[c("variance", "nugget")]) - matern(distseq, param=myres$param),
	col='blue', lwd=3)
lines(distseq, 
	sum(trueParam[c("variance", "nugget")]) - matern(distseq, param=trueParam),
	col='red')	

lines(distseq, 
	sum(myresNoN$param[c("variance", "nugget")]) - 
			matern(distseq, param=myresNoN$param),
	col='green', lty=2, lwd=3)	
legend("bottomright", fill=c("black","red","blue","green"), 
	legend=c("data","true","MLE","no N"))
}


# calculate likelihood
temp=loglikLgm(param=myres$param, 
		data=mydat, 
		formula = Y ~ cov1 + cov2,
		reml=FALSE, minustwotimes=FALSE)



# an anisotropic example


trueParamAniso = param=c(variance=2^2, range=0.2, shape=2,
	 nugget=0,anisoRatio=4,anisoAngleDegrees=10, nugget=0)

mydat$U = geostatsp::RFsimulate(trueParamAniso,mydat)$sim

mydat$Y = -3 + 0.5*mydat$cov1 + 0.2*mydat$cov2 + 
	mydat$U + rnorm(length(mydat), 0, sd=sqrt(trueParamAniso["nugget"]))

oldpar = par(no.readonly = TRUE)

par(mfrow=c(1,2), mar=rep(0.1, 4))

plot(mydat, col=as.character(cut(mydat$U, breaks=50, labels=heat.colors(50))),
	pch=16, main="aniso")
 
plot(mydat, col=as.character(cut(mydat$Y, breaks=50, labels=heat.colors(50))),
	pch=16,main="iso")



myres = likfitLgm( 
	formula=Y ~ cov1 + cov2, 
	data=mydat,
	param=c(range=0.1,nugget=0,shape=2, anisoAngleDegrees=0, anisoRatio=2), 
	paramToEstimate = c("range","nugget","anisoRatio","anisoAngleDegrees") 
	)

myres$summary

par(oldpar)
par(mfrow=c(1,2))

myraster = rast(nrows=30,ncols=30,xmin=0,xmax=1,ymin=0,ymax=1)
covEst = matern(myraster, y=c(0.5, 0.5), par=myres$param)
covTrue = matern(myraster, y=c(0.5, 0.5), par=trueParamAniso)

plot(covEst, main="estimate")
plot(covTrue, main="true")

par(oldpar)