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modLKinla.R
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modLKinla.R
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# fit standard LK model given data and relevant parameters
# obsCoords: spatial coordinates of the data
# obsValues: observations at the coordinates
# predCoords: places at which to make predictions
# nu: Matern smoothness parameter from "simple" LKrig model
# xObs: observation design matrix (intercept and covariates at obs locations)
# xPred: prediction design matrix (intercept and covariates at pred locations)
# nonlinearCovariateInds: indices in the designMatrix that are
# nonlinear covariates
# nonlinearModels: type of nonlinear covariate model (currently supported are
# rw1 and rw2, though others in theory can be used). Can
# either be a vector or a single value
# nKnotsNonlinear: a vector with the number of knots for the respective nonlinear effects
# rwPriors: list of priors for the nonlinear effect random walks
# rwKnots: list of vectors of knots, one vector for each nonlinear effect
# constrNonlinear: whether to add sum to zero constraints to the nonlinear effects
# NC: number of coarse lattice points over the longest dimension of the data
# int.strategy: "auto" or "eb" for empirical Bayes
# predClusterI: whether or not to include cluster effects for which predictions
# priorPar default was getPrior(.1, .1, 10, nLayer=nLayer)
# diagonal: A vector of "diagonal" values that are input to INLA in consecutive fits.
# Used when optimization is numerically unstable. Last value should be 0.0
# or else results will be less accurate
fitLKINLAStandard2 = function(obsCoords, obsValues, predCoords=obsCoords, nu=1.5, seed=1, nLayer=3, NC=5,
nBuffer=5, priorPar=NULL, dirichletConcentration=1.5,
xObs=cbind(1, obsCoords), xPred=cbind(1, predCoords), normalize=TRUE,
nonlinearCovariateInds=c(), nonlinearModels="rw1",
nKnotsNonlinear=30, rwPriors=NULL, rwKnots=NULL, constrNonlinear=NULL,
nonlinearCovariateInteractionInds=c(),
nrowInteraction=nKnotsNonlinear, ncolInteraction=nKnotsNonlinear,
rwIntPrior=NULL,
intStrategy="grid", strategy="gaussian", fastNormalize=TRUE,
predictionType=c("mean", "median"), significanceCI=0.8,
printVerboseTimings=FALSE, nPostSamples=1000, family=c("normal", "binomial", "betabinomial", "gamma"),
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,
useUrbanPrior=FALSE, savePrecomputationResults=FALSE, loadPrecomputationResults=FALSE,
precomputationFileNameRoot="precomputationResults", diagonal=0.0) {
startTime = proc.time()[3]
set.seed(seed)
# 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")
if(!(family %in% c("normal", "gamma")) && length(c(nonlinearCovariateInteractionInds, nonlinearCovariateInds)) > 0) {
warning("nonlinear covariates have not yet been tested for non-Gaussian responses")
}
# set up lattice ----
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
nLayer = length(latInfo)
}
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, useUrbanPrior=useUrbanPrior, dirichletConcentration=dirichletConcentration) # 1444.772/5
# set up nonlinear covariate effects ----
# check to make sure the intercept isn't included
nNonlinear = length(nonlinearCovariateInds)
nonlinearInteraction = length(nonlinearCovariateInteractionInds) > 0
xObsNonlinear = matrix(xObs[,nonlinearCovariateInds], ncol=length(nonlinearCovariateInds))
xPredNonlinear = matrix(xPred[,nonlinearCovariateInds], ncol=length(nonlinearCovariateInds))
if(nNonlinear > 0 && any(apply(xObsNonlinear, 2, function(x) {all(x == 1)}))) {
stop("the intercept cannot be set as a nonlinear covariate")
}
if(nNonlinear > length(nonlinearModels)) {
if(length(nonlinearModels) != 1) {
stop("number of nonlinear effects > length(nonlinearModels) != 1")
}
nonlinearModels = rep(nonlinearModels, nNonlinear)
}
if(nNonlinear > length(nKnotsNonlinear)) {
if(length(nKnotsNonlinear) != 1) {
stop("number of nonlinear effects > length(nKnotsNonlinear) != 1")
}
nKnotsNonlinear = rep(nKnotsNonlinear, nNonlinear)
}
if(!(family %in% c("normal", "gamma")) && nNonlinear > 0) {
stop("nonlinear effects are currently only implemented for gaussian data")
}
# set RW priors for nonlinear effects
if(is.null(rwPriors) && nNonlinear != 0) {
rwPriors = list()
for(i in 1:nNonlinear) {
rwPrior = getRandomWalkPriors(xObsNonlinear[,i], models=nonlinearModels[i], priorType="pc.prec", paramList=NULL, family=family, n=NULL)[1]
rwPriors = c(rwPriors, list(rwPrior))
}
}
if(is.null(rwIntPrior) && nonlinearInteraction) {
rwIntPrior = getRandomWalkPriors(c(xObs[,nonlinearCovariateInteractionInds]), models="rw1", priorType="pc.prec", paramList=NULL, family=family, n=NULL)[1]
}
# set knots if necessary
if(is.null(rwKnots) && nNonlinear != 0) {
rwKnots = list()
for(i in 1:nNonlinear) {
thisRWknots = make_knots(c(xObsNonlinear[,i], xPredNonlinear[,i]), n=nKnotsNonlinear[i])[[1]]
rwKnots = c(rwKnots, list(thisRWknots))
}
}
# must set each value of the covariates to the closest knot
rwEffects = NULL
rwEffectsNew = NULL
rwEffectsInds = NULL
rwEffectsIndsNew = NULL
if(nNonlinear != 0) {
rwEffects = list()
rwEffectsNew = list()
rwEffectsInds = list()
rwEffectsIndsNew = list()
for(i in 1:nNonlinear) {
thisrwEffects = match_with_knots(xObsNonlinear[,i], rwKnots[[i]])
thisrwEffectsNew = match_with_knots(xPredNonlinear[,i], rwKnots[[i]])
thisrwEffectsInds = match(thisrwEffects, rwKnots[[i]])
thisrwEffectsIndsNew = match(thisrwEffectsNew, rwKnots[[i]])
rwEffects = c(rwEffects, list(thisrwEffects))
rwEffectsNew = c(rwEffectsNew, list(thisrwEffectsNew))
rwEffectsInds = c(rwEffectsInds, list(thisrwEffectsInds))
rwEffectsIndsNew = c(rwEffectsIndsNew, list(thisrwEffectsIndsNew))
}
names(rwEffects) = paste("nonlinearEffect", 1:nNonlinear, sep="")
names(rwEffectsNew) = paste("nonlinearEffect", 1:nNonlinear, sep="")
}
# generate 2d random walk effects and indices
if(length(nonlinearCovariateInteractionInds) > 0) {
if(length(nonlinearCovariateInteractionInds) != 2) {
stop("length(nonlinearCovariateInteractionInds) != 2, but code implementation currently only supports a single 2d interaction effect")
}
covcoordsObs = xObs[,nonlinearCovariateInteractionInds]
covcoordsPred = xPred[,nonlinearCovariateInteractionInds]
rwIntIndsAll = matchWith2dKnots(covcoordsObs, nrow=nrowInteraction, ncol=ncolInteraction,
xlim=range(c(covcoordsObs[,1], covcoordsPred[,1])),
ylim=range(c(covcoordsObs[,2], covcoordsPred[,2])))
rwIntIndsNewAll = matchWith2dKnots(covcoordsPred, nrow=nrowInteraction, ncol=ncolInteraction,
xlim=range(c(covcoordsObs[,1], covcoordsPred[,1])),
ylim=range(c(covcoordsObs[,2], covcoordsPred[,2])))
rwIntInds = rwIntIndsAll$ind
rwIntIndsNew = rwIntIndsNewAll$ind
# generate a simple function for matching coordinates with associated 2d knots. Give it
# its own environment, since this environment is very large due to INLA model
rw2dMatchWithKnotsFun = function(covCoords) {
matchWith2dKnots(covCoords, nrow=nrowInteraction, ncol=ncolInteraction)
}
funEnv = new.env(parent=.GlobalEnv)
assign("nrowInteraction", nrowInteraction, envir=funEnv)
assign("ncolInteraction", ncolInteraction, envir=funEnv)
environment(rw2dMatchWithKnotsFun) = funEnv
rw2dKnotCoords = get2dKnotCoords(rbind(covcoordsObs, covcoordsPred))
rwIntA = list(1)
rwIntEffect = list(rw2d=rwIntInds)
rwIntANew = list(1)
rwIntEffectNew = list(rw2d=rwIntIndsNew)
} else {
rwIntA = NULL
rwIntEffect = NULL
rwIntANew = NULL
rwIntEffectNew = NULL
rw2dMatchWithKnotsFun = NULL
rw2dKnotCoords = NULL
}
# 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")
# The following code uses a PC prior for the beta overdose and perimeter that is
# a bit sketchy mathematically. We've therefore opted for a different prior
# lambda = getLambdapcBeta(U=1, logitU=TRUE, alpha=0.01, p=.5, normalize=TRUE)
# bbpcPriorTable = getpcBetaLogitTableForINLA(lambda, p=0.5, tailProb=1e-4, n=500)
# control.family = list(hyper = list(rho = list(prior = bbpcPriorTable)))
# 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()
}
# set up rgeneric ----
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, nu=nu, 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, nu=nu, datCoords=obsCoords, fastNormalize=fastNormalize,
printVerboseTimings=printVerboseTimings,
initialEffectiveRange=initialEffectiveRange, initialAlphas=initialAlphas,
precomputedNormalizationFun=precomputedNormalizationFun, ns=obsNs)
}
# browser()
# 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
# cmd = c("graph", "Q", "mu", "initial", "log.norm.const",
# "log.prior", "quit")
# thet = inla.rgeneric.lk.model.full("initial") # separate ranges
# test = inla.rgeneric.lk.model.full("Q", thet)
# thet = inla.rgeneric.lk.model.standard("initial") # non-separate ranges
# test = inla.rgeneric.lk.model.standard("Q", thet)
## set up the 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)
nonlinearA = NULL
if(nNonlinear != 0) {
nonlinearA = as.list(rep(1, nNonlinear))
}
if(family == "normal" || family == "gamma") {
if(!is.null(xObs)) {
stack.est = inla.stack(A =c(list(AEst, 1), nonlinearA, rwIntA),
effects =c(list(field=latticeInds, X=xObs), rwEffects, rwIntEffect),
data =list(y=obsValues, link=1),
tag ="est",
remove.unused=FALSE)
newEffectsList = c(list(field=latticeInds, X=matrix(xPred[1,], nrow=1)),
lapply(rwEffectsNew, function(x) {x[1]}))
if(nonlinearInteraction) {
newEffectsList = c(newEffectsList, list(rw2d=rwIntEffectNew[[1]][1]))
}
stack.pred = inla.stack(A =c(list(matrix(APred[1,], nrow=1), 1), nonlinearA, rwIntANew),
effects =newEffectsList,
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
#
allQuantiles = c(0.5, (1-significanceCI) / 2, 1 - (1-significanceCI) / 2)
startTimeFitModel = proc.time()[3]
endTimeFitModels = 1:length(diagonal)
for(i in 1:length(diagonal)) {
controls = list(strategy=strategy, int.strategy=intStrategy, diagonal=diagonal[i])
if(family == "normal" || family == "gamma") {
if(!is.null(xObs)) {
formulaText = "y ~ - 1 + X + f(field, model=rgen)"
if(nNonlinear != 0) {
for(i in 1:nNonlinear) {
formulaText = paste0(formulaText, " + f(nonlinearEffect", i, ", model=nonlinearModels[", i, "], ",
"values=rwKnots[[", i, "]], hyper=rwPriors[[", i, "]], scale.model=TRUE, constr=constrNonlinear)")
}
}
if(nonlinearInteraction) {
formulaText = paste0(formulaText,
" + f(rw2d, model='rw2d', nrow=nrowInteraction, ncol=ncolInteraction, ",
"hyper=rwIntPrior, scale.model=TRUE, constr=constrNonlinear)")
}
thisFormula = eval(as.formula(formulaText))
mod = inla(thisFormula,
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)
}
}
}
# if diagonal is a vector, update previous fit and restart at
# the previous maximum
previousFit = mod
if(!is.null(previousFit)) {
modeControl$result = previousFit
modeControl$theta = previousFit$mode$theta
modeControl$x = previousFit$mode$x
modeControl$restart = TRUE
}
endTimeFitModels[i] = proc.time()[3]
}
endTimeFitModel = proc.time()[3]
totalTimeFitModel = endTimeFitModel - startTimeFitModel
modelFitTimes = diff(c(startTimeFitModel, endTimeFitModels))
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]
# sample 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"))
# process posterior samples ----
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" || family == "gamma") {
rw2dInds = NULL
if(nonlinearInteraction) {
rw2dInds = nrow(hyperMat)
}
if(!separateRanges) {
if(nNonlinear == 0) {
mat = apply(hyperMat, 2, function(x) {c(totalVar=exp(x[3])+sum(1/x[c(1, rw2dInds)]), 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)]),
rw2dVar=1/x[rw2dInds], rw2dSD=sqrt(1/x[rw2dInds]))})
rw2dIndsMat = sort(c(grep("rw2dVar", rownames(mat)), grep("rw2dSD", rownames(mat))))
noRW2dIndsMat = -rw2dIndsMat
if(!nonlinearInteraction) {
noRW2dIndsMat = -(nrow(mat) + 1) # (to fix the behaviour of mat[-numeric(0),], we use this slightly sketchy work around)
}
mat = rbind(mat[noRW2dIndsMat,], alpha=1-colSums(matrix(mat[8:(7+nLayer-1),], nrow=length(8:(7+nLayer-1)))), mat[rw2dIndsMat,])
hyperNames = c("totalVar", "spatialVar", "clusterVar", "totalSD", "spatialSD", "clusterSD", "spatialRange",
paste0("alpha", 1:nLayer))
if(nonlinearInteraction) {
hyperNames = c(hyperNames, "rw2dVar", "rw2dSD")
}
}
else {
mat = apply(hyperMat, 2, function(x) {c(totalVar=exp(x[3])+1/x[1]+sum(1/x[(3 + nLayer):nrow(hyperMat)]), spatialVar=exp(x[3]), errorVar=1/x[1],
totalSD=sqrt(exp(x[3])+1/x[1]+sum(1/x[(3 + nLayer):(2 + nLayer + nNonlinear)])), spatialSD=sqrt(exp(x[3])), errorSD=sqrt(1/x[1]),
spatialRange=exp(x[2]), alpha=multivariateExpit(x[4:(3 + nLayer - 1)]),
rwVar=1/x[(3 + nLayer):(2 + nLayer + nNonlinear)], rwSD=1/sqrt(x[(3 + nLayer):(2 + nLayer + nNonlinear)]),
rw2dVar=1/x[rw2dInds], rw2dSD=sqrt(1/x[rw2dInds]))})
mat = rbind(mat[1:8,],
alpha=1-colSums(matrix(mat[8:(7+nLayer-1),], nrow=length(8:(7+nLayer-1)))),
mat[9:nrow(mat),])
# mat = mat[c(1:(7+nLayer-1), nrow(mat), (nrow(mat)-2):(nrow(mat)-1)),]
hyperNames = c("totalVar", "spatialVar", "clusterVar", "totalSD", "spatialSD", "clusterSD", "spatialRange",
paste0("alpha", 1:nLayer), paste0("rwVar", 1:nNonlinear), paste0("rwSD", 1:nNonlinear))
if(nonlinearInteraction) {
hyperNames = c(hyperNames, "rw2dVar", "rw2dSD")
}
}
} else {
if(nNonlinear == 0) {
mat = apply(hyperMat, 2, function(x) {c(totalVar=exp(x[2+nLayer])+sum(1/x[c(1, rw2dInds)]), 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[(2+nLayer):(2+2*nLayer-2)]),
rw2dVar=1/x[rw2dInds], rw2dSD=sqrt(1/x[rw2dInds]))})
rw2dIndsMat = sort(c(grep("rw2dVar", rownames(mat)), grep("rw2dSD", rownames(mat))))
noRW2dIndsMat = -rw2dIndsMat
if(!nonlinearInteraction) {
noRW2dIndsMat = -(nrow(mat) + 1) # (to fix the behaviour of mat[-numeric(0),], we use this slightly sketchy work around)
}
mat = rbind(mat[noRW2dIndsMat,], alpha=1-colSums(matrix(mat[(6+nLayer+1):(6+nLayer+1 + nLayer-2),], nrow=nLayer-1)), mat[rw2dIndsMat,])
hyperNames = c("totalVar", "spatialVar", "clusterVar", "totalSD", "spatialSD", "clusterSD", paste0("spatialRange", 1:nLayer),
paste0("alpha", 1:nLayer))
if(nonlinearInteraction) {
hyperNames = c(hyperNames, "rw2dVar", "rw2dSD")
}
} else {
hyperThetaI = which(grepl("Theta", rownames(hyperMat)))
hyperRangeI = hyperThetaI[1:nLayer]
hyperSpatialVarI = hyperThetaI[nLayer+1]
hyperAlphaI = hyperThetaI[(nLayer+2):(2*nLayer)]
hyperRWI = which(grepl("nonlinearEffect", rownames(hyperMat)))
hyperRW2DI = rw2dInds
mat = apply(hyperMat, 2, function(x) {c(totalVar=exp(x[hyperSpatialVarI])+1/x[1]+sum(1/x[c(hyperRWI, hyperRW2DI)]), spatialVar=exp(x[hyperSpatialVarI]), errorVar=1/x[1],
totalSD=sqrt(exp(x[hyperSpatialVarI])+1/x[1]+sum(1/x[c(hyperRWI, hyperRW2DI)])), spatialSD=sqrt(exp(x[hyperSpatialVarI])), errorSD=sqrt(1/x[1]),
spatialRange=exp(x[hyperRangeI]), alpha=multivariateExpit(x[hyperAlphaI]),
rwVar=1/x[hyperRWI], rwSD=1/sqrt(x[hyperRWI]),
rw2dVar=1/x[rw2dInds], rw2dSD=sqrt(1/x[rw2dInds]))})
matAlphaI = which(grepl("alpha", rownames(mat)))
mat = rbind(mat[1:max(matAlphaI),],
alpha=1-colSums(matrix(mat[matAlphaI,], nrow=nLayer-1)),
mat[(max(matAlphaI)+1):nrow(mat),])
# mat = mat[c(1:(6+nLayer+1 + nLayer-2), nrow(mat), (nrow(mat)-2):(nrow(mat)-1)),]
hyperNames = c("totalVar", "spatialVar", "clusterVar", "totalSD", "spatialSD", "clusterSD", paste0("spatialRange", 1:nLayer),
paste0("alpha", 1:nLayer), paste0("rwVar", 1:nNonlinear), paste0("rwSD", 1:nNonlinear))
if(nonlinearInteraction) {
hyperNames = c(hyperNames, "rw2dVar", "rw2dSD")
}
}
}
} 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(matrix(mat[8:(7+nLayer-1),], nrow=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))
nonlinearIndices = list()
for(i in 1:nNonlinear) {
nonlinearIndices = c(nonlinearIndices, list(which(grepl(paste0("nonlinearEffect", i), latentVarNames))))
}
rw2dInds = which(grepl("rw2d", latentVarNames))
# if(clusterEffect)
# clustIndices = grepl("clust", latentVarNames)
# generate predictions ----
# for prediction locations
# add in fixed effects
if(length(xPred) != 0)
fixedPart = xPred %*% latentMat[fixedIndices,]
else
fixedPart = 0
# add in random effects
predMat = fixedPart + APred %*% latentMat[fieldIndices,]
if(nNonlinear != 0) {
for(i in 1:nNonlinear) {
predMat = predMat + latentMat[nonlinearIndices[[i]],][rwEffectsIndsNew[[i]],]
}
}
if(nonlinearInteraction) {
predMat = predMat + latentMat[rw2dInds,][rwIntEffectNew[[1]],]
}
# for observation locations
# add in fixed part
if(length(xObs) != 0)
fixedPart = xObs %*% latentMat[fixedIndices,]
else
fixedPart = 0
# add in random part
obsMat = fixedPart + AObs %*% latentMat[fieldIndices,]
if(nNonlinear != 0) {
for(i in 1:nNonlinear) {
obsMat = obsMat + latentMat[nonlinearIndices[[i]],][rwEffectsInds[[i]],]
}
}
if(nonlinearInteraction) {
obsMat = obsMat + latentMat[rw2dInds,][rwIntEffect[[1]],]
}
# get draws from basis function coefficients
basisCoefMat = latentMat[fieldIndices,]
rwCoefMats = list()
if(nNonlinear > 0) {
for(i in 1:nNonlinear) {
rwCoefMats = c(rwCoefMats, list(latentMat[nonlinearIndices[[i]],]))
}
}
rw2dCoefMat = NULL
if(nonlinearInteraction) {
rw2dCoefMat = latentMat[rw2dInds,]
}
fixedMat = NULL
if(!is.null(xObs)) {
fixedMat = latentMat[fixedIndices,]
}
# add in cluster effect if necessary
if((family == "binomial" && clusterEffect) || family %in% c("normal", "gamma")) {
# get betabinomial overdispersion parameter
clusterVarI = which(grepl("clusterVar", hyperNames))
clusterVars = mat[clusterVarI,]
if(family != "gamma") {
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))
} else {
predMat = exp(as.matrix(predMat))
obsMat = exp(as.matrix(obsMat))
# see inla.doc("gamma") for INLA's weirdo parameterization of the gamma distribution:
# the "precision" is actually the precision of the gamma distribution divided by the
# square of the mean. The inverse of the "precision" is not the variance, but the
# dispersion parameter
dispersions = clusterVars
names(clusterVars) = rep("dispersion", length(clusterVars))
# the scale is the variance divided by the mean
# Work through the math to convert from dispersion to variance:
# scales = sweep(predMat, 2, dispersions, function(x, y) {(1/((1/y)/x^2))/x})
# scales = sweep(predMat, 2, dispersions, function(x, y) {(1/(1/(y*x^2)))/x})
# scales = sweep(predMat, 2, dispersions, function(x, y) {(y*x^2)/x})
# scales = sweep(predMat, 2, dispersions, function(x, y) {y*x})
scales = sweep(predMat, 2, dispersions, "*")
shapes = predMat / scales
predMatClustEffect = matrix(rgamma(length(predMat), shape=shapes, scale=scales), ncol=nPostSamples)
# scales = sweep(obsMat, 2, clusterVars, function(x, y) {y/x})
scales = sweep(obsMat, 2, dispersions, "*")
shapes = obsMat / scales
obsMatClustEffect = matrix(rgamma(length(obsMat), shape=shapes, scale=scales), ncol=nPostSamples)
}
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)
obsPreds = rowMeans(obsMat)
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)
predSDsNoNugget = predSDs
lowerPredsNoNugget = lowerPreds
medianPredsNoNugget = medianPreds
upperPredsNoNugget = upperPreds
obsPredsNoNugget = obsPreds
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)
obsSDsNoNugget = obsSDs
lowerObsNoNugget = lowerObs
medianObsNoNugget = medianObs
upperObsNoNugget = upperObs
} else {
if(family == "normal") {
preds = rowMeans(predMat)
obsPreds = rowMeans(obsMat)
} else {
preds = rowMeans(predMatClustEffect)
obsPreds = rowMeans(obsMatClustEffect)
}
medianPreds = apply(predMat, 1, median) # no nugget/cluster effect needed here
medianObs = apply(obsMat, 1, median)
medianPredsNoNugget = medianPreds
medianObsNoNugget = medianObs
predSDsNoNugget = apply(predMat, 1, sd)
lowerPredsNoNugget = apply(predMat, 1, quantile, probs=(1-significanceCI)/2)
upperPredsNoNugget = apply(predMat, 1, quantile, probs=1-(1-significanceCI)/2)
obsSDsNoNugget = apply(obsMat, 1, sd)
lowerObsNoNugget = apply(obsMat, 1, quantile, probs=(1-significanceCI)/2)
upperObsNoNugget = apply(obsMat, 1, quantile, probs=1-(1-significanceCI)/2)
if(family == "normal") {
# in this case, we can improve the SD and CI interval estimates using closed form due to Gaussian distribution
predSDs = rowMeans(outer(predSDsNoNugget^2, clusterVars, function(x, y) {sqrt(x + y)}))
lowerPreds = preds + qnorm(sd=predSDs, p=(1-significanceCI)/2)
upperPreds = preds + qnorm(sd=predSDs, p=1-(1-significanceCI)/2)
obsSDs = rowMeans(outer(obsSDsNoNugget^2, clusterVars, function(x, y) {sqrt(x + y)}))
lowerObs = obsPreds + qnorm(sd=obsSDs, p=(1-significanceCI)/2)
upperObs = obsPreds + qnorm(sd=obsSDs, p=1-(1-significanceCI)/2)
} else {
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
rwSummary = NULL
if(nNonlinear != 0) {
rwSummary = lapply(1:nNonlinear, function(i) {mod$summary.random[[paste0("nonlinearEffect", i)]][,c(1, 2, 4, 3, 5, 6)]})
names(rwSummary) = paste("nonlinearEffect", 1:nNonlinear, sep="")
}
rw2dSummary = NULL
if(nonlinearInteraction) {
rw2dSummary = mod$summary.random$rw2d[,c(1, 2, 4, 3, 5, 6)]
}
# compute basis function coefficient predictions and standard deviations
# startI = n+nrow(predCoords)+1
# endI = n+nrow(predCoords)+nx*ny
startI = 1
endI = nx*ny
thesePreds = rowMeans(basisCoefMat)
theseSDs = apply(basisCoefMat, 1, sd)
coefPreds = list(layer1 = thesePreds[startI:endI])
coefSDs = list(layer1 = theseSDs[startI:endI])
if(nLayer >= 2) {
for(i in 2:nLayer) {
startI = endI + 1
endI = startI + nrow(latInfo[[i]]$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
# process timings ----
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
# return results ----
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,
sigmasNoNugget=predSDsNoNugget, lowerNoNugget=lowerPredsNoNugget, medianNoNugget=medianPredsNoNugget, upperNoNugget=upperPredsNoNugget,
obsSigmasNoNugget=obsSDsNoNugget, obsLowerNoNugget=lowerObsNoNugget, obsMedianObsNoNugget=medianObsNoNugget, obsUpperNoNugget=upperObsNoNugget,
interceptSummary=interceptSummary, fixedEffectSummary=fixedEffectSummary, rangeSummary=rangeSummary,
sdSummary=sdSummary, varSummary=varSummary, overdispersionSummary=overdispersionSummary, parameterSummaryTable=parameterSummaryTable,
alphaSummary=alphaSummary, timings=timings, priorPar=priorPar, precomputedNormalizationFun=precomputedNormalizationFun,
rwSummary=rwSummary, rwKnots=rwKnots, rwMats=rwCoefMats, rwPriors=rwPriors,
rw2dSummary=rw2dSummary, rw2dMat=rw2dCoefMat, rw2dPrior=rwIntPrior,
rw2dMatchWithKnotsFun=rw2dMatchWithKnotsFun, rw2dKnotCoords=rw2dKnotCoords,
# the rest of the outputs are saved to be used for spatial aggregations later on
predMat=predMatClustEffect, obsMat=obsMatClustEffect, fixedMat=fixedMat,
hyperMat=hyperMat, basisMat=basisCoefMat, clusterVars=clusterVars, rhos=rhos,
modelFitTimes=modelFitTimes)
}
# construct priors for random walk effects
## Inputs:
# y: the observations, only used lim constructing the priors for the gaussian family, as
# recommended by INLA
# models: either a single string, or a list of them with the same length as the number of
# nonlinear effects in the model. The strings describe the order of random walk of the
# nonlinear effect.
# priorType: either a single string, or a list of them with the same length as the number
# of nonlinear effects in the model. The strings describe the type of model for
# the prior of each nonlinear effect
# paramList: a list of param vectors, which are inputs to the random walk models in inla.
# each param vector contains 2 values, which have different interpretations
# depending on the type of prior used. For the log gamma prior, the first element
# param is the shape parameter, and the second is the inverse scale. For the
# pc.prec prior, the first element is the standard deviation threshold, and
# the second is the probability the standard deviation is over that threshold.