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modELK.R
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modELK.R
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# fit ELK model given data and relevant parameters
# obsCoords: matrix of spatial coordinates of the data
# obsValues: matrix of response at the observation coordinates
# predCoords: places at which to make predictions
# xObs: observation design matrix (intercept and covariates at obs locations)
# xPred: prediction design matrix (intercept and covariates at pred locations)
# NC: number of coarse lattice points over the longest dimension of the data
# nLayer: number of lattice layers
# seed: random seed set at beginning of function
# normalize: whether or not to normalize the process (highly recommended to set this to TRUE,
# since otherwise interpretation of correlation length and marginal variance priors
# will be highly suspect)
# intStrategy: see INLA:::control.inla()
# strategy: see INLA:::control.inla()
# predClusterI: whether or not to include cluster effects for which predictions
# priorPar default was getPrior(.1, .1, 10, nLayer=nLayer)
fitELK = function(obsCoords, obsValues, predCoords=obsCoords, seed=1, nLayer=3, NC=5,
nBuffer=5, priorPar=NULL,
xObs=cbind(1, obsCoords), xPred=cbind(1, predCoords), normalize=TRUE,
intStrategy="ccd", strategy="gaussian", fastNormalize=TRUE,
predictionType=c("mean", "median"), significanceCI=0.8,
printVerboseTimings=FALSE, nPostSamples=1000, family=c("normal", "binomial", "betabinomial"),
obsNs=rep(1, length(obsValues)), clusterEffect=TRUE, latInfo=NULL,
initialEffectiveRange=NULL, initialAlphas=rep(1/nLayer, nLayer-1),
effRangeRange=NULL, predClusterI=rep(TRUE, nrow(predCoords)),
plotNormalizationSplines=FALSE, verbose=TRUE, separateRanges=FALSE,
doValidation=FALSE, previousFit=NULL, precomputedNormalizationFun=NULL,
savePrecomputationResults=FALSE, loadPrecomputationResults=FALSE,
precomputationFileNameRoot="precomputationResults") {
startTime = proc.time()[3]
set.seed(seed)
if(!normalize)
warning("WARNING: normalize set to FALSE. Correlation length and marginal variance prior interpretation is suspect. It is highly recommended to set normalize to TRUE")
# get the type of prediction the user wants
predictionType = match.arg(predictionType)
family = match.arg(family)
# check to make sure inputs make sense
if(!clusterEffect && family == "normal")
stop("cluster effect must be included for the normal family")
# get lattice points, prediction points
if(is.null(latInfo)) {
xRangeDat = range(obsCoords[,1])
yRangeDat = range(obsCoords[,2])
latInfo = makeLatGrids(xRangeDat, yRangeDat, NC, nBuffer, nLayer)
} else {
xRangeDat = latInfo[[1]]$xRangeDat
yRangeDat = latInfo[[1]]$yRangeDat
}
nx = latInfo[[1]]$nx
ny = latInfo[[1]]$ny
if(is.null(priorPar))
priorPar = getPCPrior(1444.772/5, .01, 1, nLayer=nLayer, separateRanges=separateRanges, latticeInfo=latInfo) # 1444.772/5
# generate lattice basis matrix
AObs = makeA(obsCoords, latInfo)
## run precomputations
print("running precomputations...")
startTimePrecomputations = proc.time()[3]
# either run the precomputations or load them in
if(!loadPrecomputationResults) {
precomputedMatrices = precomputationsQ2(latInfo)
if(is.null(precomputedNormalizationFun)) {
precomputedNormalizationFun = precomputeNormalization(saveResults=FALSE, latticeInfo=latInfo, effRangeRange=effRangeRange,
plotNormalizationSplines=plotNormalizationSplines)
}
} else {
load(paste0("savedOutput/precomputations/", precomputationFileNameRoot, ".RData"))
}
# save the precomputations if necessary
if(savePrecomputationResults) {
save(precomputedMatrices, precomputedNormalizationFun,
file=paste0("savedOutput/precomputations/", precomputationFileNameRoot, ".RData"))
}
endTimePrecomputations = proc.time()[3]
precomputationTime = endTimePrecomputations - startTimePrecomputations
print(paste0("finished precomputations. Took ", round(precomputationTime / 60, 2), " minutes"))
# define the LK model
startTimeDefineModel = proc.time()[3]
# set beta binomial prior if necessary
if(family == "betabinomial") {
if(clusterEffect)
stop("cluster effect must not be set to TRUE for betabinomial model")
# set median at .04 and upper 97.5th pctile at 0.2
mu = logit(0.04)
prec = 1/((logit(.2)-logit(.04))/qnorm(.975))^2
control.family = list(hyper = list(rho = list(prior="logtnormal", param=c(mu, prec))))
} else {
control.family = list()
}
n = length(obsValues)
if(separateRanges) {
rgen = inla.rgeneric.define(model=inla.rgeneric.lk.model.full, latInfo=latInfo, ys=obsValues,
prior=priorPar, normalize=normalize, precomputedMatrices=precomputedMatrices,
X=xObs, datCoords=obsCoords, fastNormalize=fastNormalize,
printVerboseTimings=printVerboseTimings,
initialEffectiveRange=initialEffectiveRange, initialAlphas=initialAlphas,
precomputedNormalizationFun=precomputedNormalizationFun, ns=obsNs)
} else {
rgen = inla.rgeneric.define(model=inla.rgeneric.lk.model.standard, latInfo=latInfo, ys=obsValues,
prior=priorPar, normalize=normalize, precomputedMatrices=precomputedMatrices,
X=xObs, datCoords=obsCoords, fastNormalize=fastNormalize,
printVerboseTimings=printVerboseTimings,
initialEffectiveRange=initialEffectiveRange, initialAlphas=initialAlphas,
precomputedNormalizationFun=precomputedNormalizationFun, ns=obsNs)
}
# use these global variables for testing calls to inla.rgeneric.lk.model.simple
# latInfo<<-latInfo; ys<<-obsValues; ns<<-obsNs;
# prior<<-priorPar; normalize<<-normalize; precomputedMatrices<<-precomputedMatrices;
# X<<-xObs; nu<<-nu; datCoords<<-obsCoords; fastNormalize<<-fastNormalize;
# printVerboseTimings<<-printVerboseTimings; initialEffectiveRange<<-initialEffectiveRange;
# initialAlphas<<-initialAlphas; precomputedNormalizationFun<<-precomputedNormalizationFun
## generate inla stack:
# Stacked A matrix (A_s from notation of LR2015 Bayesian Spatial Modelling with R_INLA):
# (AEst 0 )
# ( 0 APred)
# eta_s = (c^T c^T)^T
# where c is the vector of lattice coefficients
AEst = makeA(obsCoords, latInfo)
APred = makeA(predCoords, latInfo)
latticeInds = 1:ncol(AEst)
clust = 1:length(obsValues)
if(family == "normal") {
if(!is.null(xObs)) {
stack.est = inla.stack(A =list(AEst, 1),
effects =list(field=latticeInds, X=xObs),
data =list(y=obsValues, link=1),
tag ="est",
remove.unused=FALSE)
stack.pred = inla.stack(A =list(APred, 1),
effects =list(field=latticeInds, X=xPred),
data =list(y=NA, link=1),
tag ="pred",
remove.unused=FALSE)
} else {
stack.est = inla.stack(A =list(AEst),
effects =list(field=latticeInds),
data =list(y=obsValues, link=1),
tag ="est",
remove.unused=FALSE)
stack.pred = inla.stack(A =list(APred),
effects =list(field=latticeInds),
data =list(y=NA, link=1),
tag ="pred",
remove.unused=FALSE)
}
}
else if(family == "binomial" || family == "betabinomial") {
if(clusterEffect) {
if(!is.null(xObs)) {
stack.est = inla.stack(A =list(AEst, 1, 1),
effects =list(field=latticeInds, clust=clust, X=xObs),
data =list(y=obsValues, link=1, Ntrials = obsNs),
tag ="est",
remove.unused=FALSE)
} else {
stack.est = inla.stack(A =list(AEst, 1),
effects =list(field=latticeInds, clust=clust),
data =list(y=obsValues, link=1, Ntrials = obsNs),
tag ="est",
remove.unused=FALSE)
}
} else {
if(!is.null(xObs)) {
stack.est = inla.stack(A =list(AEst, 1),
effects =list(field=latticeInds, X=xObs),
data =list(y=obsValues, link=1, Ntrials = obsNs),
tag ="est",
remove.unused=FALSE)
} else {
stack.est = inla.stack(A =list(AEst),
effects =list(field=latticeInds),
data =list(y=obsValues, link=1, Ntrials = obsNs),
tag ="est",
remove.unused=FALSE)
}
}
if(!is.null(xObs)) {
stack.pred = inla.stack(A =list(APred, 1),
effects =list(field=latticeInds, X=xPred),
data =list(y=NA, link=1, Ntrials=rep(1, nrow(APred)),
tag ="pred"),
remove.unused=FALSE)
} else {
stack.pred = inla.stack(A =list(APred),
effects =list(field=latticeInds),
data =list(y=NA, link=1, Ntrials=rep(1, nrow(APred)),
tag ="pred"),
remove.unused=FALSE)
}
}
stack.full = inla.stack(stack.est, stack.pred,
remove.unused=FALSE)
dat = inla.stack.data(stack.full, rgen=rgen, remove.unused=FALSE)
# initialize the fitting process based on a previous optimum if necessary
modeControl = inla.set.control.mode.default()
if(!is.null(previousFit)) {
# modeControl$result = previousFit
modeControl$theta = previousFit$mode$theta
modeControl$x = previousFit$mode$x
modeControl$restart = TRUE
}
endTimeDefineModel = proc.time()[3]
totalTimeDefineModel = endTimeDefineModel - startTimeDefineModel
# fit the model
# control.inla = list(cmin = 0, int.strategy=int.strategy)
# see: inla.doc("loggamma")
# shape=.1, scale=10 for unit mean, variance 100 prior
controls = list(strategy=strategy, int.strategy=intStrategy)
allQuantiles = c(0.5, (1-significanceCI) / 2, 1 - (1-significanceCI) / 2)
startTimeFitModel = proc.time()[3]
if(family == "normal") {
if(!is.null(xObs)) {
mod = inla(y ~ - 1 + X + f(field, model=rgen),
data=dat, quantiles=allQuantiles, family=family, verbose=verbose,
control.inla=controls,
control.mode=modeControl,
control.compute=list(config=TRUE, cpo=doValidation, dic=doValidation, waic=doValidation),
control.predictor=list(A=inla.stack.A(stack.full), compute=FALSE),
control.fixed=list(quantiles=allQuantiles),
control.family=list(hyper = list(prec = list(param=c(1, 0.05), prior="pc.prec"))))
} else {
mod = inla(y ~ - 1 + f(field, model=rgen),
data=dat, quantiles=allQuantiles, family=family, verbose=verbose,
control.inla=controls,
control.mode=modeControl,
control.compute=list(config=TRUE, cpo=doValidation, dic=doValidation, waic=doValidation),
control.predictor=list(A=inla.stack.A(stack.full), compute=FALSE),
control.fixed=list(quantiles=allQuantiles),
control.family=list(hyper = list(prec = list(param=c(1, 0.05), prior="pc.prec"))))
}
} else if(family == "binomial" || family == "betabinomial") {
if(clusterEffect) {
# clusterList = list(param=c(.15, 0.01), prior="pc.prec")
if(!is.null(xObs)) {
mod = inla(y ~ - 1 + X + f(field, model=rgen) +
f(clust, model="iid", hyper = list(prec = list(param=c(1, 0.01), prior="pc.prec"))),
data=dat, quantiles=allQuantiles, family=family, verbose=verbose,
control.inla=controls, Ntrials=dat$Ntrials,
control.mode=modeControl,
control.compute=list(config=TRUE, cpo=doValidation, dic=doValidation, waic=doValidation),
control.predictor=list(A=inla.stack.A(stack.full), compute=FALSE),
control.fixed=list(quantiles=allQuantiles), control.family = control.family)
} else {
mod = inla(y ~ - 1 + f(field, model=rgen) +
f(clust, model="iid", hyper = list(prec = list(param=c(1, 0.01), prior="pc.prec"))),
data=dat, quantiles=allQuantiles, family=family, verbose=verbose,
control.inla=controls, Ntrials=dat$Ntrials,
control.mode=modeControl,
control.compute=list(config=TRUE, cpo=doValidation, dic=doValidation, waic=doValidation),
control.predictor=list(A=inla.stack.A(stack.full), compute=FALSE),
control.fixed=list(quantiles=allQuantiles), control.family = control.family)
}
} else {
if(!is.null(xObs)) {
mod = inla(y ~ - 1 + X + f(field, model=rgen),
data=dat, quantiles=allQuantiles, family=family, verbose=verbose,
control.inla=controls, Ntrials=dat$Ntrials,
control.mode=modeControl,
control.compute=list(config=TRUE, cpo=doValidation, dic=doValidation, waic=doValidation),
control.predictor=list(A=inla.stack.A(stack.full), compute=FALSE),
control.fixed=list(quantiles=allQuantiles), control.family = control.family)
} else {
mod = inla(y ~ - 1 + f(field, model=rgen),
data=dat, quantiles=allQuantiles, family=family, verbose=verbose,
control.inla=controls, Ntrials=dat$Ntrials,
control.mode=modeControl,
control.compute=list(config=TRUE, cpo=doValidation, dic=doValidation, waic=doValidation),
control.predictor=list(A=inla.stack.A(stack.full), compute=FALSE, quantiles=allQuantiles),
control.fixed=list(quantiles=allQuantiles), control.family = control.family)
}
}
}
endTimeFitModel = proc.time()[3]
totalTimeFitModel = endTimeFitModel - startTimeFitModel
print(paste0("finished fitting model. Took ", round(totalTimeFitModel / 60, 2), " minutes"))
# # improve the approximation of the posterior if requested by the user
# if(improveHyperpar) {
# browser()
# mod = inla.hyperpar(mod)
# }
# browser()
# get predictive surface, SD, and data
index = inla.stack.index(stack.full, "pred")$data
obsInds = 1:n
predInds = (n+1):(n+nrow(predCoords))
if(predictionType == "mean") {
linpreds = mod[["summary.linear.predictor"]]$mean
# preds = linpreds[predInds]
# obsPreds = linpreds[obsInds]
} else {
linpreds = mod[["summary.linear.predictor"]]$`0.5quant`
# preds = linpreds[predInds]
# obsPreds = linpreds[obsInds]
}
linpred.sd = mod[["summary.linear.predictor"]]$sd
# predSDs = linpred.sd[predInds]
# obsSDs = linpred.sd[obsInds]
# generate samples from posterior
print("Sampling from posterior")
startTimePosteriorSampling = proc.time()[3]
postSamples = inla.posterior.sample(nPostSamples, mod)
endTimePosteriorSampling = proc.time()[3]
totalTimePosteriorSampling = endTimePosteriorSampling - startTimePosteriorSampling
print(paste0("finished sampling from the posterior. Took ", round(totalTimePosteriorSampling / 60, 2), " minutes"))
print("Processing posterior samples...")
startTimeSampleProcessing = proc.time()[3]
# get posterior hyperparameter samples and transform them as necessary
# interpretation of hyperparameters:
# 1: error precision
# 2: log effective range
# 3: log spatial variance
# 4-(3 + nLayer - 1): multivariateLogit alpha
hyperMat = sapply(postSamples, function(x) {x$hyperpar})
if(family == "normal") {
if(!separateRanges) {
mat = apply(hyperMat, 2, function(x) {c(totalVar=exp(x[3])+1/x[1], spatialVar=exp(x[3]), errorVar=1/x[1],
totalSD=sqrt(exp(x[3])+1/x[1]), spatialSD=sqrt(exp(x[3])), errorSD=sqrt(1/x[1]),
spatialRange=exp(x[2]), alpha=multivariateExpit(x[4:(3 + nLayer - 1)]))})
mat = rbind(mat, alpha=1-colSums(mat[8:(7+nLayer-1),]))
hyperNames = c("totalVar", "spatialVar", "clusterVar", "totalSD", "spatialSD", "clusterSD", "spatialRange",
paste0("alpha", 1:nLayer))
} else {
mat = apply(hyperMat, 2, function(x) {c(totalVar=exp(x[2+nLayer])+1/x[1], spatialVar=exp(x[2+nLayer]), errorVar=1/x[1],
totalSD=sqrt(exp(x[2+nLayer])+1/x[1]), spatialSD=sqrt(exp(x[2+nLayer])), errorSD=sqrt(1/x[1]),
spatialRange=exp(x[2:(1+nLayer)]), alpha=multivariateExpit(x[(3+nLayer):(3+2*nLayer-2)]))})
mat = rbind(mat, alpha=1-colSums(matrix(mat[(6+nLayer+1):(6+nLayer+1 + nLayer-2),], nrow=nLayer-1)))
hyperNames = c("totalVar", "spatialVar", "clusterVar", "totalSD", "spatialSD", "clusterSD", paste0("spatialRange", 1:nLayer),
paste0("alpha", 1:nLayer))
}
} else if(family == "binomial") {
if(clusterEffect) {
if(!separateRanges) {
logSpatialRangeI = 1
logSpatialVarI = 2
logitAlphaI = 3:(2 + nLayer - 1)
precisionI = 3 + nLayer - 1
mat = apply(hyperMat, 2, function(x) {c(totalVar=exp(x[logSpatialVarI])+1/x[precisionI], spatialVar=exp(x[logSpatialVarI]), clusterVar=1/x[precisionI],
totalSD=sqrt(exp(x[logSpatialVarI])+1/x[precisionI]), spatialSD=sqrt(exp(x[logSpatialVarI])), clusterSD=sqrt(1/x[precisionI]),
spatialRange=exp(x[logSpatialRangeI]), alpha=multivariateExpit(x[logitAlphaI]))})
mat = rbind(mat, alpha=1-colSums(mat[8:(7+nLayer-1),]))
hyperNames = c("totalVar", "spatialVar", "clusterVar", "totalSD", "spatialSD", "clusterSD", "spatialRange",
paste0("alpha", 1:nLayer))
} else {
logSpatialRangeI = 1:nLayer
logSpatialVarI = 1 + nLayer
logitAlphaI = (logSpatialVarI+1):(logSpatialVarI+1 + nLayer-2)
precisionI = max(logitAlphaI)+1
mat = apply(hyperMat, 2, function(x) {c(totalVar=exp(x[logSpatialVarI])+1/x[precisionI], spatialVar=exp(x[logSpatialVarI]), clusterVar=1/x[precisionI],
totalSD=sqrt(exp(x[logSpatialVarI])+1/x[precisionI]), spatialSD=sqrt(exp(x[logSpatialVarI])), clusterSD=sqrt(1/x[precisionI]),
spatialRange=exp(x[logSpatialRangeI]), alpha=multivariateExpit(x[logitAlphaI]))})
mat = rbind(mat, alpha=1-colSums(matrix(mat[(6+nLayer+1):(6+nLayer+1 + nLayer-2),], nrow=nLayer-1)))
hyperNames = c("totalVar", "spatialVar", "clusterVar", "totalSD", "spatialSD", "clusterSD", paste0("spatialRange", 1:nLayer),
paste0("alpha", 1:nLayer))
}
} else {
if(!separateRanges) {
logSpatialRangeI = 1
logSpatialVarI = 2
logitAlphaI = 3:(2 + nLayer - 1)
mat = apply(hyperMat, 2, function(x) {c(spatialVar=exp(x[logSpatialVarI]), spatialSD=sqrt(exp(x[logSpatialVarI])),
spatialRange=exp(x[logSpatialRangeI]), alpha=multivariateExpit(x[logitAlphaI]))})
mat = rbind(mat, alpha=1-colSums(matrix(mat[4:(3+nLayer-1),], nrow=nLayer-1)))
hyperNames = c("spatialVar", "spatialSD", "spatialRange", paste0("alpha", 1:nLayer))
} else {
logSpatialRangeI = 1:nLayer
logSpatialVarI = 1 + nLayer
logitAlphaI = (logSpatialVarI+1):(logSpatialVarI+1 + nLayer-2)
mat = apply(hyperMat, 2, function(x) {c(spatialVar=exp(x[logSpatialVarI]), spatialSD=sqrt(exp(x[logSpatialVarI])),
spatialRange=exp(x[logSpatialRangeI]), alpha=multivariateExpit(x[logitAlphaI]))})
# mat = rbind(mat, alpha=1-colSums(mat[4:(3+nLayer-1),]))
mat = rbind(mat, alpha=1-colSums(matrix(mat[(3+nLayer):(3+nLayer + nLayer-2),], nrow=nLayer-1)))
hyperNames = c("spatialVar", "spatialSD", paste0("spatialRange", 1:nLayer), paste0("alpha", 1:nLayer))
}
}
} else if(family == "betabinomial") {
overdispersionI = 1
if(!separateRanges) {
logSpatialRangeI = 2
logSpatialVarI = 3
logitAlphaI = 4:(3 + nLayer - 1)
mat = apply(hyperMat, 2, function(x) {c(spatialVar=exp(x[logSpatialVarI]), spatialSD=sqrt(exp(x[logSpatialVarI])),
spatialRange=exp(x[logSpatialRangeI]), alpha=multivariateExpit(x[logitAlphaI]),
overdispersion=x[overdispersionI])})
mat = rbind(mat[-nrow(mat),], alpha=1-colSums(matrix(mat[4:(3+nLayer-1),], nrow=nLayer-1)), mat[nrow(mat),])
hyperNames = c("spatialVar", "spatialSD", "spatialRange", paste0("alpha", 1:nLayer), "overdispersion")
} else {
logSpatialRangeI = 2:(1+nLayer)
logSpatialVarI = 2 + nLayer
logitAlphaI = (logSpatialVarI+1):(logSpatialVarI+1 + nLayer-2)
mat = apply(hyperMat, 2, function(x) {c(spatialVar=exp(x[logSpatialVarI]), spatialSD=sqrt(exp(x[logSpatialVarI])),
spatialRange=exp(x[logSpatialRangeI]), alpha=multivariateExpit(x[logitAlphaI]),
overdispersion=x[overdispersionI])})
# mat = rbind(mat, alpha=1-colSums(mat[4:(3+nLayer-1),]))
mat = rbind(mat[-nrow(mat),], alpha=1-colSums(matrix(mat[(3+nLayer):(3+nLayer + nLayer-2),], nrow=nLayer-1)), mat[nrow(mat),])
hyperNames = c("spatialVar", "spatialSD", paste0("spatialRange", 1:nLayer), paste0("alpha", 1:nLayer), "overdispersion")
}
}
rownames(mat) = hyperNames
getSummaryStatistics = function(draws) {
c(Est=mean(draws), SD=sd(draws),
Qlower=quantile(probs=(1 - significanceCI) / 2, draws),
Q50=quantile(probs=0.5, draws),
Qupper=quantile(probs=1 - (1 - significanceCI) / 2, draws))
}
summaryNames = c("Est", "SD", "Qlower", "Q50", "Qupper")
parameterSummaryTable = t(apply(mat, 1, getSummaryStatistics))
colnames(parameterSummaryTable) = summaryNames
# separate out default parameter summaries
varI = which(grepl("clusterVar", hyperNames))
rangeI = which(grepl("Range", hyperNames))
alphaI = which(grepl("alpha", hyperNames))
varSummary=parameterSummaryTable[varI,]
rangeSummary=parameterSummaryTable[rangeI,]
alphaSummary=parameterSummaryTable[alphaI,]
if(family == "normal" || clusterEffect) {
sdI = which(grepl("clusterSD", hyperNames))
sdSummary=parameterSummaryTable[sdI,]
} else {
sdSummary = matrix(rep(0, 5), nrow=1)
}
overdispersionSummary = matrix(rep(0, 5), nrow=1)
if(family == "betabinomial")
overdispersionSummary=parameterSummaryTable[nrow(parameterSummaryTable),]
# get samples of the latent field
latentMat = sapply(postSamples, function(x) {x$latent})
latentVarNames = rownames(postSamples[[1]]$latent)
fieldIndices = which(grepl("field", latentVarNames))
fixedIndices = which(grepl("X", latentVarNames))
# if(clusterEffect)
# clustIndices = grepl("clust", latentVarNames)
## generate logit predictions (first without cluster effect then add the cluster effect in)
# for prediction locations
if(length(xPred) != 0)
fixedPart = xPred %*% latentMat[fixedIndices,]
else
fixedPart = 0
predMat = fixedPart + APred %*% latentMat[fieldIndices,]
# for observation locations
if(length(xObs) != 0)
fixedPart = xObs %*% latentMat[fixedIndices,]
else
fixedPart = 0
obsMat = fixedPart + AObs %*% latentMat[fieldIndices,]
# get draws from basis function coefficients
basisCoefMat = latentMat[fieldIndices,]
# add in cluster effect if necessary
if((family == "binomial" && clusterEffect) || family == "normal") {
# get betabinomial overdispersion parameter
clusterVarI = which(grepl("clusterVar", hyperNames))
clusterVars = mat[clusterVarI,]
predMatClustEffect = predMat + sweep(matrix(rnorm(length(predMat), sd=rep(sqrt(clusterVars), each=nrow(predMat))), nrow=nrow(predMat)), 1, predClusterI, "*")
obsMatClustEffect = obsMat + matrix(rnorm(length(obsMat), sd=rep(sqrt(clusterVars), each=nrow(obsMat))), nrow=nrow(obsMat))
rhos = NULL
} else if(family == "betabinomial") {
# get cluster induced overdispersion
overdispersionI = which(grepl("overdispersion", hyperNames))
rhos = mat[overdispersionI,]
predMat = expit(predMat)
as = sweep(predMat, 2, 1/rhos-1, "*")
bs = sweep(1-predMat, 2, 1/rhos-1, "*")
predMatClustEffect = matrix(rbeta(length(predMat), c(as.matrix(as)), c(as.matrix(bs))), nrow=nrow(predMat))
obsMat = expit(obsMat)
as = sweep(obsMat, 2, 1/rhos-1, "*")
bs = sweep(1-obsMat, 2, 1/rhos-1, "*")
obsMatClustEffect = matrix(rbeta(length(obsMat), c(as.matrix(as)), c(as.matrix(bs))), nrow=nrow(obsMat))
clusterVars = NULL
} else {
clusterVars = NULL
rhos=NULL
predMatClustEffect = predMat
obsMatClustEffect = obsMat
}
# transform predictions from logit to probability scale
if(family == "binomial") {
predMat = expit(predMat)
predMatClustEffect = expit(predMatClustEffect)
obsMat = expit(obsMat)
obsMatClustEffect = expit(obsMatClustEffect)
}
# compute predictive credible intervals
if(is.null(predMatClustEffect)) {
preds = rowMeans(predMat)
predSDs = apply(predMat, 1, sd)
lowerPreds = apply(predMat, 1, quantile, probs=(1-significanceCI)/2)
medianPreds = apply(predMat, 1, median)
upperPreds = apply(predMat, 1, quantile, probs=1-(1-significanceCI)/2)
obsPreds = rowMeans(obsMat)
obsSDs = apply(obsMat, 1, sd)
lowerObs = apply(obsMat, 1, quantile, probs=(1-significanceCI)/2)
medianObs = apply(obsMat, 1, median)
upperObs = apply(obsMat, 1, quantile, probs=1-(1-significanceCI)/2)
} else {
if(family == "normal") {
preds = rowMeans(predMat)
medianPreds = apply(predMat, 1, median)
obsPreds = rowMeans(obsMat)
medianObs = apply(obsMat, 1, median)
} else {
preds = rowMeans(predMatClustEffect)
medianPreds = apply(predMatClustEffect, 1, median)
obsPreds = rowMeans(obsMatClustEffect)
medianObs = apply(obsMatClustEffect, 1, median)
}
predSDs = apply(predMatClustEffect, 1, sd)
lowerPreds = apply(predMatClustEffect, 1, quantile, probs=(1-significanceCI)/2)
upperPreds = apply(predMatClustEffect, 1, quantile, probs=1-(1-significanceCI)/2)
obsSDs = apply(obsMatClustEffect, 1, sd)
lowerObs = apply(obsMatClustEffect, 1, quantile, probs=(1-significanceCI)/2)
upperObs = apply(obsMatClustEffect, 1, quantile, probs=1-(1-significanceCI)/2)
}
if(!is.null(xObs) && all(xObs[,1]==1))
interceptSummary=mod$summary.fixed[1,c(1, 2, 4, 3, 5)]
else
interceptSummary = matrix(rep(0, 5), nrow=1)
if(!is.null(xObs))
fixedEffectSummary = mod$summary.fixed[,c(1, 2, 4, 3, 5)]
else
fixedEffectSummary = mod$summary.fixed
# compute basis function coefficient predictions and standard deviations
# startI = n+nrow(predCoords)+1
# endI = n+nrow(predCoords)+nx*ny
startI = 1
endI = nx*ny
thesePreds = rowMeans(basisCoefMat)
theseSDs = apply(basisCoefMat, 1, sd)
coefPreds = list(layer1 = thesePreds[startI:endI])
coefSDs = list(layer1 = theseSDs[startI:endI])
if(nLayer >= 2) {
for(i in 2:nLayer) {
startI = endI + 1
endI = startI + nrow(latInfo[[i]]$latCoords) - 1
# coefPreds = c(coefPreds, list(linpreds[startI:endI]))
# coefSDs = c(coefSDs, list(linpred.sd[startI:endI]))
coefPreds = c(coefPreds, list(thesePreds[startI:endI]))
coefSDs = c(coefSDs, list(theseSDs[startI:endI]))
}
}
endTime = proc.time()[3]
totalTimeSampleProcessing = endTime - startTimeSampleProcessing
print(paste0("finished processing samples. Took ", round(totalTimeSampleProcessing / 60, 2), " minutes"))
totalTime = endTime - startTime
timings = data.frame(totalTime=totalTime,
precomputationTime=precomputationTime,
modelDefineTime=totalTimeDefineModel,
modelFitTime=totalTimeFitModel,
posteriorSamplingTime=totalTimePosteriorSampling,
sampleProcessingTime=totalTimeSampleProcessing,
otherTime=totalTime-(precomputationTime + totalTimeDefineModel + totalTimeFitModel + totalTimePosteriorSampling + totalTimeSampleProcessing))
timings$precomputationTimePct = timings$precomputationTime / timings$totalTime
timings$modelDefinePct = timings$modelDefineTime / timings$totalTime
timings$modelFitTimePct = timings$modelFitTime / timings$totalTime
timings$posteriorSamplingTimePct = timings$posteriorSamplingTime / timings$totalTime
timings$sampleProcessingTimePct = timings$sampleProcessingTime / timings$totalTime
timings$otherTimePct = timings$otherTime / timings$totalTime
list(preds=preds, sigmas=predSDs, lower=lowerPreds, median=medianPreds, upper=upperPreds,
obsPreds=obsPreds, obsSDs=obsSDs, obsLower=lowerObs, obsMedian=medianObs, obsUpper=upperObs,
mod=mod, latInfo=latInfo, coefPreds=coefPreds, coefSDs=coefSDs,
interceptSummary=interceptSummary, fixedEffectSummary=fixedEffectSummary, rangeSummary=rangeSummary,
sdSummary=sdSummary, varSummary=varSummary, overdispersionSummary=overdispersionSummary, parameterSummaryTable=parameterSummaryTable,
alphaSummary=alphaSummary, timings=timings, priorPar=priorPar, precomputedNormalizationFun=precomputedNormalizationFun,
# the rest of the outputs are saved to be used for spatial aggregations later on
predMat=predMatClustEffect, obsMat=obsMatClustEffect, hyperMat=hyperMat, clusterVars=clusterVars, rhos=rhos
)
}
# fit ELK model given data and relevant parameters
# obsCoords: matrix of spatial coordinates of the data
# obsValues: matrix of response at the observation coordinates
# predCoords: places at which to make predictions
# xObs: observation design matrix (intercept and covariates at obs locations)
# xPred: prediction design matrix (intercept and covariates at pred locations)
# NC: number of coarse lattice points over the longest dimension of the data
# nLayer: number of lattice layers
# seed: random seed set at beginning of function
# normalize: whether or not to normalize the process (highly recommended to set this to TRUE,
# since otherwise interpretation of correlation length and marginal variance priors
# will be highly suspect)
# intStrategy: see INLA:::control.inla()
# strategy: see INLA:::control.inla()
# predClusterI: whether or not to include cluster effects for which predictions
# priorPar default was getPrior(.1, .1, 10, nLayer=nLayer)
fitELK2 = function(obsCoords, obsValues, predCoords=obsCoords, seed=1, nLayer=3, NC=5,
nBuffer=5, priorPar=NULL,
xObs=cbind(1, obsCoords), xPred=cbind(1, predCoords), normalize=TRUE,
intStrategy="ccd", strategy="gaussian", fastNormalize=TRUE,
predictionType=c("mean", "median"), significanceCI=0.8,
printVerboseTimings=FALSE, nPostSamples=1000, family=c("normal", "binomial", "betabinomial"),
obsNs=rep(1, length(obsValues)), clusterEffect=TRUE, latInfo=NULL,
initialEffectiveRange=NULL, initialAlphas=rep(1/nLayer, nLayer-1),
effRangeRange=NULL, predClusterI=rep(TRUE, nrow(predCoords)),
plotNormalizationSplines=FALSE, verbose=TRUE, separateRanges=FALSE,
doValidation=FALSE, previousFit=NULL, precomputedNormalizationFun=NULL,
savePrecomputationResults=FALSE, loadPrecomputationResults=FALSE,
precomputationFileNameRoot="precomputationResults") {
startTime = proc.time()[3]
set.seed(seed)
if(length(predCoords)< 1)
stop("must include prediction locations")
if(!normalize)
warning("WARNING: normalize set to FALSE. Correlation length and marginal variance prior interpretation is suspect. It is highly recommended to set normalize to TRUE")
# get the type of prediction the user wants
predictionType = match.arg(predictionType)
family = match.arg(family)
# check to make sure inputs make sense
if(!clusterEffect && family == "normal")
stop("cluster effect must be included for the normal family")
# get lattice points, prediction points
if(is.null(latInfo)) {
xRangeDat = range(obsCoords[,1])
yRangeDat = range(obsCoords[,2])
latInfo = makeLatGrids(xRangeDat, yRangeDat, NC, nBuffer, nLayer)
} else {
xRangeDat = latInfo[[1]]$xRangeDat
yRangeDat = latInfo[[1]]$yRangeDat
}
nx = latInfo[[1]]$nx
ny = latInfo[[1]]$ny
if(is.null(priorPar))
priorPar = getPCPrior(1444.772/5, .01, 1, nLayer=nLayer, separateRanges=separateRanges, latticeInfo=latInfo) # 1444.772/5
# generate lattice basis matrix
AObs = makeA(obsCoords, latInfo)
## run precomputations
print("running precomputations...")
startTimePrecomputations = proc.time()[3]
# either run the precomputations or load them in
if(!loadPrecomputationResults) {
precomputedMatrices = precomputationsQ2(latInfo)
if(is.null(precomputedNormalizationFun)) {
precomputedNormalizationFun = precomputeNormalization(saveResults=FALSE, latticeInfo=latInfo, effRangeRange=effRangeRange,
plotNormalizationSplines=plotNormalizationSplines)
}
} else {
load(paste0("savedOutput/precomputations/", precomputationFileNameRoot, ".RData"))
}
# save the precomputations if necessary
if(savePrecomputationResults) {
save(precomputedMatrices, precomputedNormalizationFun,
file=paste0("savedOutput/precomputations/", precomputationFileNameRoot, ".RData"))
}
endTimePrecomputations = proc.time()[3]
precomputationTime = endTimePrecomputations - startTimePrecomputations
print(paste0("finished precomputations. Took ", round(precomputationTime / 60, 2), " minutes"))
# define the LK model
startTimeDefineModel = proc.time()[3]
# set beta binomial prior if necessary
if(family == "betabinomial") {
if(clusterEffect)
stop("cluster effect must not be set to TRUE for betabinomial model")
# set median at .04 and upper 97.5th pctile at 0.2
mu = logit(0.04)
prec = 1/((logit(.2)-logit(.04))/qnorm(.975))^2
control.family = list(hyper = list(rho = list(prior="logtnormal", param=c(mu, prec))))
} else {
control.family = list()
}
n = length(obsValues)
if(separateRanges) {
rgen = inla.rgeneric.define(model=inla.rgeneric.lk.model.full, latInfo=latInfo, ys=obsValues,
prior=priorPar, normalize=normalize, precomputedMatrices=precomputedMatrices,
X=xObs, datCoords=obsCoords, fastNormalize=fastNormalize,
printVerboseTimings=printVerboseTimings,
initialEffectiveRange=initialEffectiveRange, initialAlphas=initialAlphas,
precomputedNormalizationFun=precomputedNormalizationFun, ns=obsNs)
} else {
rgen = inla.rgeneric.define(model=inla.rgeneric.lk.model.standard, latInfo=latInfo, ys=obsValues,
prior=priorPar, normalize=normalize, precomputedMatrices=precomputedMatrices,
X=xObs, datCoords=obsCoords, fastNormalize=fastNormalize,
printVerboseTimings=printVerboseTimings,
initialEffectiveRange=initialEffectiveRange, initialAlphas=initialAlphas,
precomputedNormalizationFun=precomputedNormalizationFun, ns=obsNs)
}
# use these global variables for testing calls to inla.rgeneric.lk.model.simple
# latInfo<<-latInfo; ys<<-obsValues; ns<<-obsNs;
# prior<<-priorPar; normalize<<-normalize; precomputedMatrices<<-precomputedMatrices;
# X<<-xObs; nu<<-nu; datCoords<<-obsCoords; fastNormalize<<-fastNormalize;
# printVerboseTimings<<-printVerboseTimings; initialEffectiveRange<<-initialEffectiveRange;
# initialAlphas<<-initialAlphas; precomputedNormalizationFun<<-precomputedNormalizationFun
## generate inla stack:
# Stacked A matrix (A_s from notation of LR2015 Bayesian Spatial Modelling with R_INLA):
# (AEst 0 )
# ( 0 APred)
# eta_s = (c^T c^T)^T
# where c is the vector of lattice coefficients
AEst = makeA(obsCoords, latInfo)
APred = makeA(predCoords, latInfo)
latticeInds = 1:ncol(AEst)
clust = 1:length(obsValues)
if(family == "normal") {
if(!is.null(xObs)) {
stack.est = inla.stack(A =list(AEst, 1),
effects =list(field=latticeInds, X=xObs),
data =list(y=obsValues, link=1),
tag ="est",
remove.unused=FALSE)
stack.pred = inla.stack(A =list(matrix(APred[1,], nrow=1), 1),
effects =list(field=latticeInds, X=matrix(xPred[1,], nrow=1)),
data =list(y=NA, link=1),
tag ="pred",
remove.unused=FALSE)
} else {
stack.est = inla.stack(A =list(AEst),
effects =list(field=latticeInds),
data =list(y=obsValues, link=1),
tag ="est",
remove.unused=FALSE)
stack.pred = inla.stack(A =list(matrix(APred[1,], nrow=1)),
effects =list(field=latticeInds),
data =list(y=NA, link=1),
tag ="pred",
remove.unused=FALSE)
}
}
else if(family == "binomial" || family == "betabinomial") {
if(clusterEffect) {
if(!is.null(xObs)) {
stack.est = inla.stack(A =list(AEst, 1, 1),
effects =list(field=latticeInds, clust=clust, X=xObs),
data =list(y=obsValues, link=1, Ntrials = obsNs),
tag ="est",
remove.unused=FALSE)
} else {
stack.est = inla.stack(A =list(AEst, 1),
effects =list(field=latticeInds, clust=clust),
data =list(y=obsValues, link=1, Ntrials = obsNs),
tag ="est",
remove.unused=FALSE)
}
} else {
if(!is.null(xObs)) {
stack.est = inla.stack(A =list(AEst, 1),
effects =list(field=latticeInds, X=xObs),
data =list(y=obsValues, link=1, Ntrials = obsNs),
tag ="est",
remove.unused=FALSE)
} else {
stack.est = inla.stack(A =list(AEst),
effects =list(field=latticeInds),
data =list(y=obsValues, link=1, Ntrials = obsNs),
tag ="est",
remove.unused=FALSE)
}
}
if(!is.null(xObs)) {
stack.pred = inla.stack(A =list(matrix(APred[1,], nrow=1), 1),
effects =list(field=latticeInds, X=matrix(xPred[1,], nrow=1)),
data =list(y=NA, link=1, Ntrials=1,
tag ="pred"),
remove.unused=FALSE)
} else {
stack.pred = inla.stack(A =list(matrix(APred[1,], nrow=1)),
effects =list(field=latticeInds),
data =list(y=NA, link=1, Ntrials=1,
tag ="pred"),
remove.unused=FALSE)
}
}
stack.full = inla.stack(stack.est, stack.pred,
remove.unused=FALSE)
dat = inla.stack.data(stack.full, rgen=rgen, remove.unused=FALSE)
# initialize the fitting process based on a previous optimum if necessary
modeControl = inla.set.control.mode.default()
if(!is.null(previousFit)) {
# modeControl$result = previousFit
modeControl$theta = previousFit$mode$theta
modeControl$x = previousFit$mode$x
modeControl$restart = TRUE
}
endTimeDefineModel = proc.time()[3]
totalTimeDefineModel = endTimeDefineModel - startTimeDefineModel
# fit the model
# control.inla = list(cmin = 0, int.strategy=int.strategy)
# see: inla.doc("loggamma")
# shape=.1, scale=10 for unit mean, variance 100 prior
controls = list(strategy=strategy, int.strategy=intStrategy)
allQuantiles = c(0.5, (1-significanceCI) / 2, 1 - (1-significanceCI) / 2)
startTimeFitModel = proc.time()[3]
if(family == "normal") {
if(!is.null(xObs)) {
mod = inla(y ~ - 1 + X + f(field, model=rgen),
data=dat, quantiles=allQuantiles, family=family, verbose=verbose,
control.inla=controls,
control.mode=modeControl,
control.compute=list(config=TRUE, cpo=doValidation, dic=doValidation, waic=doValidation),
control.predictor=list(A=inla.stack.A(stack.full), compute=FALSE),
control.fixed=list(quantiles=allQuantiles),
control.family=list(hyper = list(prec = list(param=c(1, 0.05), prior="pc.prec"))))
} else {
mod = inla(y ~ - 1 + f(field, model=rgen),
data=dat, quantiles=allQuantiles, family=family, verbose=verbose,
control.inla=controls,
control.mode=modeControl,
control.compute=list(config=TRUE, cpo=doValidation, dic=doValidation, waic=doValidation),
control.predictor=list(A=inla.stack.A(stack.full), compute=FALSE),
control.fixed=list(quantiles=allQuantiles),
control.family=list(hyper = list(prec = list(param=c(1, 0.05), prior="pc.prec"))))
}
} else if(family == "binomial" || family == "betabinomial") {
if(clusterEffect) {
# clusterList = list(param=c(.15, 0.01), prior="pc.prec")
if(!is.null(xObs)) {
mod = inla(y ~ - 1 + X + f(field, model=rgen) +
f(clust, model="iid", hyper = list(prec = list(param=c(1, 0.01), prior="pc.prec"))),
data=dat, quantiles=allQuantiles, family=family, verbose=verbose,
control.inla=controls, Ntrials=dat$Ntrials,
control.mode=modeControl,
control.compute=list(config=TRUE, cpo=doValidation, dic=doValidation, waic=doValidation),
control.predictor=list(A=inla.stack.A(stack.full), compute=FALSE),
control.fixed=list(quantiles=allQuantiles), control.family = control.family)
} else {
mod = inla(y ~ - 1 + f(field, model=rgen) +
f(clust, model="iid", hyper = list(prec = list(param=c(1, 0.01), prior="pc.prec"))),
data=dat, quantiles=allQuantiles, family=family, verbose=verbose,
control.inla=controls, Ntrials=dat$Ntrials,
control.mode=modeControl,
control.compute=list(config=TRUE, cpo=doValidation, dic=doValidation, waic=doValidation),
control.predictor=list(A=inla.stack.A(stack.full), compute=FALSE),
control.fixed=list(quantiles=allQuantiles), control.family = control.family)
}
} else {
if(!is.null(xObs)) {
mod = inla(y ~ - 1 + X + f(field, model=rgen),
data=dat, quantiles=allQuantiles, family=family, verbose=verbose,
control.inla=controls, Ntrials=dat$Ntrials,
control.mode=modeControl,
control.compute=list(config=TRUE, cpo=doValidation, dic=doValidation, waic=doValidation),
control.predictor=list(A=inla.stack.A(stack.full), compute=FALSE),
control.fixed=list(quantiles=allQuantiles), control.family = control.family)
} else {
mod = inla(y ~ - 1 + f(field, model=rgen),
data=dat, quantiles=allQuantiles, family=family, verbose=verbose,
control.inla=controls, Ntrials=dat$Ntrials,
control.mode=modeControl,
control.compute=list(config=TRUE, cpo=doValidation, dic=doValidation, waic=doValidation),
control.predictor=list(A=inla.stack.A(stack.full), compute=FALSE, quantiles=allQuantiles),
control.fixed=list(quantiles=allQuantiles), control.family = control.family)
}
}
}
endTimeFitModel = proc.time()[3]
totalTimeFitModel = endTimeFitModel - startTimeFitModel
print(paste0("finished fitting model. Took ", round(totalTimeFitModel / 60, 2), " minutes"))
# # improve the approximation of the posterior if requested by the user
# if(improveHyperpar) {
# browser()
# mod = inla.hyperpar(mod)
# }
# browser()
# get predictive surface, SD, and data
index = inla.stack.index(stack.full, "pred")$data
obsInds = 1:n
predInds = (n+1):(n+nrow(predCoords))
if(predictionType == "mean") {
linpreds = mod[["summary.linear.predictor"]]$mean
# preds = linpreds[predInds]
# obsPreds = linpreds[obsInds]
} else {
linpreds = mod[["summary.linear.predictor"]]$`0.5quant`
# preds = linpreds[predInds]
# obsPreds = linpreds[obsInds]
}
linpred.sd = mod[["summary.linear.predictor"]]$sd
# predSDs = linpred.sd[predInds]
# obsSDs = linpred.sd[obsInds]
# generate samples from posterior
print("Sampling from posterior")
startTimePosteriorSampling = proc.time()[3]
postSamples = inla.posterior.sample(nPostSamples, mod)
endTimePosteriorSampling = proc.time()[3]
totalTimePosteriorSampling = endTimePosteriorSampling - startTimePosteriorSampling
print(paste0("finished sampling from the posterior. Took ", round(totalTimePosteriorSampling / 60, 2), " minutes"))
print("Processing posterior samples...")
startTimeSampleProcessing = proc.time()[3]
# get posterior hyperparameter samples and transform them as necessary
# interpretation of hyperparameters:
# 1: error precision
# 2: log effective range
# 3: log spatial variance
# 4-(3 + nLayer - 1): multivariateLogit alpha
hyperMat = sapply(postSamples, function(x) {x$hyperpar})
if(family == "normal") {
if(!separateRanges) {
mat = apply(hyperMat, 2, function(x) {c(totalVar=exp(x[3])+1/x[1], spatialVar=exp(x[3]), errorVar=1/x[1],
totalSD=sqrt(exp(x[3])+1/x[1]), spatialSD=sqrt(exp(x[3])), errorSD=sqrt(1/x[1]),
spatialRange=exp(x[2]), alpha=multivariateExpit(x[4:(3 + nLayer - 1)]))})
mat = rbind(mat, alpha=1-colSums(mat[8:(7+nLayer-1),]))
hyperNames = c("totalVar", "spatialVar", "clusterVar", "totalSD", "spatialSD", "clusterSD", "spatialRange",
paste0("alpha", 1:nLayer))
} else {
mat = apply(hyperMat, 2, function(x) {c(totalVar=exp(x[2+nLayer])+1/x[1], spatialVar=exp(x[2+nLayer]), errorVar=1/x[1],
totalSD=sqrt(exp(x[2+nLayer])+1/x[1]), spatialSD=sqrt(exp(x[2+nLayer])), errorSD=sqrt(1/x[1]),
spatialRange=exp(x[2:(1+nLayer)]), alpha=multivariateExpit(x[(3+nLayer):(3+2*nLayer-2)]))})
mat = rbind(mat, alpha=1-colSums(matrix(mat[(6+nLayer+1):(6+nLayer+1 + nLayer-2),], nrow=nLayer-1)))
hyperNames = c("totalVar", "spatialVar", "clusterVar", "totalSD", "spatialSD", "clusterSD", paste0("spatialRange", 1:nLayer),
paste0("alpha", 1:nLayer))
}
} else if(family == "binomial") {
if(clusterEffect) {
if(!separateRanges) {
logSpatialRangeI = 1
logSpatialVarI = 2
logitAlphaI = 3:(2 + nLayer - 1)
precisionI = 3 + nLayer - 1
mat = apply(hyperMat, 2, function(x) {c(totalVar=exp(x[logSpatialVarI])+1/x[precisionI], spatialVar=exp(x[logSpatialVarI]), clusterVar=1/x[precisionI],
totalSD=sqrt(exp(x[logSpatialVarI])+1/x[precisionI]), spatialSD=sqrt(exp(x[logSpatialVarI])), clusterSD=sqrt(1/x[precisionI]),
spatialRange=exp(x[logSpatialRangeI]), alpha=multivariateExpit(x[logitAlphaI]))})
mat = rbind(mat, alpha=1-colSums(mat[8:(7+nLayer-1),]))
hyperNames = c("totalVar", "spatialVar", "clusterVar", "totalSD", "spatialSD", "clusterSD", "spatialRange",
paste0("alpha", 1:nLayer))
} else {
logSpatialRangeI = 1:nLayer
logSpatialVarI = 1 + nLayer
logitAlphaI = (logSpatialVarI+1):(logSpatialVarI+1 + nLayer-2)
precisionI = max(logitAlphaI)+1
mat = apply(hyperMat, 2, function(x) {c(totalVar=exp(x[logSpatialVarI])+1/x[precisionI], spatialVar=exp(x[logSpatialVarI]), clusterVar=1/x[precisionI],
totalSD=sqrt(exp(x[logSpatialVarI])+1/x[precisionI]), spatialSD=sqrt(exp(x[logSpatialVarI])), clusterSD=sqrt(1/x[precisionI]),
spatialRange=exp(x[logSpatialRangeI]), alpha=multivariateExpit(x[logitAlphaI]))})
mat = rbind(mat, alpha=1-colSums(matrix(mat[(6+nLayer+1):(6+nLayer+1 + nLayer-2),], nrow=nLayer-1)))
hyperNames = c("totalVar", "spatialVar", "clusterVar", "totalSD", "spatialSD", "clusterSD", paste0("spatialRange", 1:nLayer),
paste0("alpha", 1:nLayer))
}
} else {
if(!separateRanges) {
logSpatialRangeI = 1
logSpatialVarI = 2
logitAlphaI = 3:(2 + nLayer - 1)