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fitModelTMB.R
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fitModelTMB.R
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library(TMB)
library(alabama)
# source("setup.R")
# fits the combined model with normalized taper using TMB jointly with the variance inflation
# parameters as well as the gamma spline parameters
fitModelTMB = function(modelInfo=NULL, paramInit=NULL, gpsDat=slipDatCSZ, gpsDepthThreshold=21000,
G=NULL, subDat=dr1, fault=csz, nKnots=5,
dStar=25000, maxit=500, latRange=c(40, 50),
diffGPSTaper=TRUE, nKnotsGPS=nKnots, reltol=1e-8,
nKnotsVar=5, includeGammaSpline=TRUE, nKnotsGamma=7,
dStarGPS=40000, seed=123, debug=FALSE, doVarSpline=TRUE,
fixInflation=FALSE, maxCount=1, fixedPenalty=TRUE,
logPenaltyPar=log(10), sharedPenalty=FALSE, doMeanSpline=TRUE,
nKnotsMean=ifelse(doMeanSpline, 5, 1), nKnotsMeanGPS=ifelse(doMeanSpline, 7, 1),
doSmoothnessPenalty=FALSE, doDiffPenalty=FALSE, logDiffPenaltyPar=log(1),
fixedDiffPenalty=FALSE, debugPlotting=TRUE, saveResults=TRUE,
diffLow=log(1), diffHigh=log(100), penLow=log(1), penHigh=log(100),
diffMean=FALSE, constrainMean=TRUE, muBarrier=1e-04, useAlabama=TRUE,
useHyperpriors=FALSE, sharedSpatialProcess=FALSE, jointShared=FALSE,
inflateVarLocking=FALSE, diffVar=FALSE, nKnotsVarGPS=1, estimateGpsShared=FALSE,
conditionalGamma=FALSE, calcHess=FALSE, recompile=FALSE, varSmoothnessPenalty=FALSE,
varLogLambda=NULL, reparameterizeVar=FALSE) {
if(is.null(modelInfo)) {
# get all input values
allInputs = as.list(environment())
# threshold the gps data and multiplied standard deviations by three as in the literature
threshSlipDat = gpsDat[gpsDat$Depth<gpsDepthThreshold,]
if(!inflateVarLocking)
threshSlipDat$slipErr = threshSlipDat$slipErr*3
# get input parameters and separate them
initParams = getInitialParameters(nKnots, nKnotsVar, nKnotsGamma, logScale=TRUE, diffGPSTaper=diffGPSTaper)
out = getInputPar(initParams, fault, threshSlipDat, nKnots, diffGPSTaper=diffGPSTaper, nKnotsGPS, taperedGPSDat=TRUE,
anisotropic=TRUE, normalModel=TRUE, nKnotsVar, doVarSpline=TRUE,
includeGammaSpline=TRUE, nKnotsGamma=nKnotsGamma, includeInflation=TRUE)
logmu = out$muZeta
betaMean = rep(0, nKnotsMean - 1)
logMeanGPS = 0
betaMeanGPS = rep(0, nKnotsMeanGPS - 1)
betaTaper = out$taperPar
betaTaperIntercept = betaTaper[1]
betaTaper = betaTaper[-1]
betaTaperGPS = out$taperParGPS
if(is.null(betaTaperGPS))
betaTaperGPS = rep(0, nKnotsGPS)
# taperParGPS = out$taperParGPS
logphi = out$phiZeta
# lambda0 = out$lambda0
logalpha = out$alpha
betasd = out$varPar
betasdIntercept = betasd[1]
betasd = betasd[-1]
if(!reparameterizeVar)
betasdInterceptGPS = 0
else
betasdInterceptGPS = betasdIntercept
betasdGPS = rep(0, nKnotsVarGPS - 1)
betaGamma = out$gammaPar
betaGammaIntercept = betaGamma[1]
betaGamma = betaGamma[-1]
loglowInflate = out$lowInflation
loghighInflate = out$highInflation
parscale = out$parscale
parNames = out$parNames
parNamesTMB = out$parNamesTMB
logitOmega = logit(0.25) # initially, assume most of the variation is taken up by iid spatial processes rather than shared
logitOmega2 = logitOmega
logLockInflate = log(3^2)
# determine which of the input parameters will be optimized
includeI = c(TRUE, TRUE, rep(doVarSpline, nKnotsVar - 1), rep(TRUE, nKnots), rep(TRUE, nKnotsGPS * diffGPSTaper), !conditionalGamma,
rep(as.numeric(includeGammaSpline)*as.numeric(!conditionalGamma), nKnotsGamma - 1), rep(!fixInflation, 2), TRUE, TRUE)
parscale = parscale[includeI]
parNames = parNames[includeI]
parNamesTMBShort = parNamesTMB[includeI]
# PARAMETER(logmu);
# PARAMETER_VECTOR(betaTaperIntercept);
# PARAMETER_VECTOR(betaTaper);
# PARAMETER_VECTOR(betasdIntercept);
# PARAMETER_VECTOR(betasd);
# PARAMETER_VECTOR(betaGammaIntercept);
# PARAMETER_VECTOR(betaGamma);
# PARAMETER(logphi);
# PARAMETER(logalpha);
# PARAMETER(loglowInflate);
# PARAMETER(loghighInflate);
##### calculate correlation matrices for Zeta in km (for CSZ grid and the GPS data)
# get Okada linear transformation matrix
if(is.null(G)) {
nx = 300
ny= 900
lonGrid = seq(lonRange[1], lonRange[2], l=nx)
latGrid = seq(latRange[1], latRange[2], l=ny)
G = okadaAll(fault, lonGrid, latGrid, cbind(subDat$Lon, subDat$Lat), slip=1, poisson=0.25)
}
##### calculate depths of the centers of the CSZ subfaults
cszDepths = getFaultCenters(fault)[,3]
### Rather than training the fault, we redefine an axis to be the strike access in Euclidean space
### using a Lambert projection and PCA
out = straightenFaultLambert()
faultGeomStraight = out$fault
scale = out$scale
parameters = out$projPar
transformation = out$transformation
##### compute distance matrices for straightened fault and for straightened gps data
cszStraight = divideFault2(faultGeomStraight)
centers = getFaultCenters(csz)[,1:2]
newCenters = transformation(centers)
cszStraight$centerX = newCenters[,2]
cszStraight$centerY = newCenters[,1]
straightenedGpsCoords = transformation(cbind(threshSlipDat$lon, threshSlipDat$lat))
# calculate along strike and along dip squared distances in kilometers
strikeCoordsCSZ = cbind(0, cszStraight$centerY)
dipCoordsCSZ = cbind(cszStraight$centerX, 0)
squareStrikeDistCsz = rdist(strikeCoordsCSZ)^2
squareDipDistCsz = rdist(dipCoordsCSZ)^2
# do the same for the gps data
strikeCoords = cbind(0, straightenedGpsCoords[,1])
dipCoords = cbind(straightenedGpsCoords[,2], 0)
squareStrikeDistGps = rdist(strikeCoords)^2
squareDipDistGps = rdist(dipCoords)^2
# calculate the cross distance matrix (GPS, CSZ)
squareStrikeDistCross = rdist(strikeCoords, strikeCoordsCSZ)^2
squareDipDistCross = rdist(dipCoords, dipCoordsCSZ)^2
# squareStrikeDistJoint = rbind(cbind(squareStrikeDistGps, squareStrikeDistCross),
# cbind(t(squareStrikeDistCross), squareStrikeDistCsz))
# squareDipDistJoint = rbind(cbind(squareDipDistGps, squareDipDistCross),
# cbind(t(squareDipDistCross), squareDipDistCsz))
# compute all required inputs for the TMB cpp code
lambdaBasisY = getSplineBasis(fault, nKnots=nKnots, latRange=latRange)[,-1]
lambdaBasisX = getSplineBasis(data.frame(list(latitude=threshSlipDat$lat)), nKnots=nKnots, latRange=latRange)[,-1]
lambdaBasisXGPS = getSplineBasis(data.frame(list(latitude=threshSlipDat$lat)), nKnots=nKnotsGPS, latRange=latRange)
meanBasisY = getSplineBasis(fault, nKnots=nKnotsMean, latRange=latRange)[,-1]
meanBasisX = getSplineBasis(data.frame(list(latitude=threshSlipDat$lat)), nKnots=nKnotsMean, latRange=latRange)[,-1]
meanBasisXGPS = getSplineBasis(data.frame(list(latitude=threshSlipDat$lat)), nKnots=nKnotsMeanGPS, latRange=latRange)[,-1]
DSStrikeCSZ = squareStrikeDistCsz
DSDipCSZ = squareDipDistCsz
DSStrikeGPS = squareStrikeDistGps
DSDipGPS = squareDipDistGps
zeroMask = eventsEqMask(subDat)
lowI = as.numeric(as.numeric(subDat$quality) != 1)
y = -subDat$subsidence
ysd = subDat$Uncertainty
x = threshSlipDat$slip
xsd = threshSlipDat$slipErr
xDepths = threshSlipDat$Depth
faultDepths = cszDepths
dStar = dStar
dStarGPS = dStarGPS
sdBasisX = getSplineBasis(data.frame(list(latitude=threshSlipDat$lat)), nKnots=nKnotsVar, latRange=latRange)[,-1]
sdBasisXGPS = getSplineBasis(data.frame(list(latitude=threshSlipDat$lat)), nKnots=nKnotsVarGPS, latRange=latRange)[,-1]
sdBasisY = getSplineBasis(fault, nKnots=nKnotsVar, latRange=latRange)[,-1]
if(!conditionalGamma) {
gammaBasis = getSplineBasis(data.frame(list(latitude=threshSlipDat$lat)), nKnots=nKnotsGamma, latRange=latRange)[,-1]
}
else {
gammaBasis = getSplineBasis(data.frame(list(latitude=threshSlipDat$lat)), nKnots=nKnotsGamma, latRange=latRange)
}
latSeq = seq(latRange[1], latRange[2], l=500)
deltaPenalty = latSeq[2] - latSeq[1]
meanBasisPenalty = getSplineBasis(fault=fault, nKnots=nKnotsMean, lats=latSeq, latRange=latRange)[,-1]
meanBasisGPSPenalty = getSplineBasis(fault=fault, nKnots=nKnotsMeanGPS, lats=latSeq, latRange=latRange)[,-1]
sdBasisPenalty = getSplineBasis(fault=fault, nKnots=nKnotsVar, lats=latSeq, latRange=latRange)[,-1]
sdBasisGPSPenalty = getSplineBasis(fault=fault, nKnots=nKnotsVarGPS, lats=latSeq, latRange=latRange)[,-1]
taperBasisPenalty = getSplineBasis(fault=fault, nKnots=nKnots, lats=latSeq, latRange=latRange)[,-1]
taperBasisGPSPenalty = getSplineBasis(fault=fault, nKnots=nKnotsGPS, lats=latSeq, latRange=latRange)
gammaBasisPenalty = getSplineBasis(fault=fault, nKnots=nKnotsGamma, lats=latSeq, latRange=latRange)[,-1]
# should choose penalty parameter (kappa) so that
# kappa * deltaPenalty * sum((diff(latSeq / 10) / deltaPenalty)^2) = kappa * 0.1
# is 90% chance between .1, and 10. implying that the penalty factors should be between 1 and 100
penaltyMean = mean(c(penLow, penHigh))
penaltySD = (penHigh-penaltyMean)/qnorm(.95)
# should choose penalty parameter (kappa) so that
# kappa * integrate(function(x) {1}, 40, 50) = kappa * 10
# is 90% chance between .1, and 1. implying that the penalty factors should be between 1/100 and 1/10
diffPenaltyMean = mean(c(diffLow, diffHigh))
diffPenaltySD = (diffHigh-diffPenaltyMean)/qnorm(.95)
# compile the function and its gradient
if(!conditionalGamma) {
if(!debug)
compile("fitModelTMB.cpp")
else
compile("fitModelTMB.cpp","-O0 -g")
dyn.load(dynlib("fitModelTMB"))
}
else {
if(!debug)
compile("fitModelTMBconditionalGamma.cpp")
else
compile("fitModelTMBconditionalGamma.cpp","-O0 -g")
dyn.load(dynlib("fitModelTMBconditionalGamma"))
}
set.seed(seed)
data <- list(y=y, x=x, lambdaBasisY=lambdaBasisY, lambdaBasisX=lambdaBasisX, lambdaBasisXGPS=lambdaBasisXGPS, DSStrikeCSZ=DSStrikeCSZ,
DSDipCSZ=DSDipCSZ, DSStrikeGPS=DSStrikeGPS, DSDipGPS=DSDipGPS, zeroMask=zeroMask, lowI=lowI,
ysd=ysd, xsd=xsd, xDepths=xDepths, faultDepths=faultDepths, dStar=dStar, sdBasisX=sdBasisX,
sdBasisY=sdBasisY, gammaBasis=gammaBasis, G=G, dStarGPS=dStarGPS, deltaPenalty=deltaPenalty,
sdBasisPenalty=sdBasisPenalty, sdBasisGPSPenalty=sdBasisGPSPenalty, taperBasisPenalty=taperBasisPenalty, taperBasisGPSPenalty=taperBasisGPSPenalty,
gammaBasisPenalty=gammaBasisPenalty, penaltyMean=penaltyMean, penaltySD=penaltySD,
sharedPenalty=as.numeric(sharedPenalty), meanBasisX=meanBasisX, meanBasisXGPS=meanBasisXGPS, meanBasisY=meanBasisY,
meanBasisPenalty=meanBasisPenalty, meanBasisGPSPenalty=meanBasisGPSPenalty, doDiffPenalty=as.numeric(doDiffPenalty),
diffPenaltyMean=diffPenaltyMean, diffPenaltySD=diffPenaltySD, diffMean=as.numeric(diffMean),
useHyperpriors=as.numeric(useHyperpriors), sharedSpatialProcess=as.numeric(sharedSpatialProcess),
jointShared=as.numeric(jointShared), DSStrikeCross=squareStrikeDistCross,
DSDipCross=squareDipDistCross, diffGPSTaper=as.numeric(diffGPSTaper), sdBasisXGPS=sdBasisXGPS,
diffVar=as.numeric(diffVar), doSmoothnessPenalty=as.numeric(doSmoothnessPenalty),
estimateGpsShared=as.numeric(estimateGpsShared), varSmoothnessPenalty=as.numeric(varSmoothnessPenalty),
reparameterizeVar=as.numeric(reparameterizeVar))
parameters = list(logmu=logmu, betasdIntercept=betasdIntercept, betasd=betasd, betasdInterceptGPS=betasdInterceptGPS,
betasdGPS=betasdGPS, betaMean=betaMean, logMeanGPS=logMeanGPS, betaMeanGPS=betaMeanGPS,
betaTaperIntercept=betaTaperIntercept, betaTaper=betaTaper, betaTaperGPS=betaTaperGPS,
betaGammaIntercept=betaGammaIntercept, betaGamma=betaGamma,
loglowInflate=loglowInflate, loghighInflate=loghighInflate,
logphi=logphi, logalpha=logalpha,
betasdPenaltyLogLambda=0, betasdGPSPenaltyLogLambda=0,
betaTaperPenaltyLogLambda=0, betaTaperGPSPenaltyLogLambda=0,
betaGammaPenaltyLogLambda=0, betaMeanPenaltyLogLambda=0,
taperDiffPenaltyLogLambda=0, betaMeanGPSPenaltyLogLambda=0,
meanDiffPenaltyLogLambda=0, sdDiffPenaltyLogLambda=0,
logitOmega=logitOmega, logitOmega2=logitOmega2, logLockInflate=logLockInflate)
if(fixedPenalty) {
parameters$betasdPenaltyLogLambda = logPenaltyPar
parameters$betasdGPSPenaltyLogLambda = logPenaltyPar
parameters$betaTaperPenaltyLogLambda = logPenaltyPar
parameters$betaTaperGPSPenaltyLogLambda = logPenaltyPar
parameters$betaGammaPenaltyLogLambda = logPenaltyPar
parameters$betaMeanPenaltyLogLambda = logPenaltyPar
parameters$betaMeanGPSPenaltyLogLambda = logPenaltyPar
}
if(!is.null(varLogLambda)) {
parameters$betasdPenaltyLogLambda = varLogLambda
parameters$betasdGPSPenaltyLogLambda = varLogLambda
}
if(fixedDiffPenalty) {
taperDiffPenaltyLogLambda = logDiffPenaltyPar
meanDiffPenaltyLogLambda = logDiffPenaltyPar
sdDiffPenaltyLogLambda = logDiffPenaltyPar
}
if(conditionalGamma) {
parameters$betaGammaIntercept = NULL
parameters$betaGamma = NULL
parameters$betaGammaPenaltyLogLambda = NULL
}
# pick which parameters will be fixed
includeTaperDiffPar = !fixedDiffPenalty && doDiffPenalty
map = list()
if(!includeGammaSpline) {
if(!conditionalGamma)
map = c(map, list(betaGamma=rep(factor(NA), length(betaGamma))))
}
if(!doVarSpline)
map = c(map, list(betasd=rep(factor(NA), length(betasd))))
if(!doMeanSpline)
map = c(map, list(betaMean=rep(factor(NA), length(betaMean))))
if(!diffMean)
map = c(map, list(logMeanGPS=factor(NA), betaMeanGPS=rep(factor(NA), length(betaMeanGPS))))
if(!diffVar)
map = c(map, list(betasdInterceptGPS=factor(NA), betasdGPS=rep(factor(NA), length(betasdGPS))))
if(fixInflation)
map = c(map, list(loghighInflate=factor(NA), loglowInflate=factor(NA)))
if(!diffGPSTaper)
map = c(map, list(betaTaperGPS=rep(factor(NA), length(betaTaperGPS))))
if(fixedPenalty || !doSmoothnessPenalty) {
map = c(map, list(betasdPenaltyLogLambda=factor(NA),
betasdGPSPenaltyLogLambda=factor(NA),
betaTaperPenaltyLogLambda=factor(NA),
betaTaperGPSPenaltyLogLambda=factor(NA),
betaMeanPenaltyLogLambda=factor(NA),
betaMeanGPSPenaltyLogLambda=factor(NA)))
if(!conditionalGamma)
map = c(map, list(betaGammaPenaltyLogLambda=factor(NA)))
}
else if(sharedPenalty) {
map = c(map, list(betasdGPSPenaltyLogLambda=factor(NA),
betaTaperPenaltyLogLambda=factor(NA),
betaTaperGPSPenaltyLogLambda=factor(NA),
betaMeanPenaltyLogLambda=factor(NA),
betaMeanGPSPenaltyLogLambda=factor(NA)))
if(!conditionalGamma)
map = c(map, list(betaGammaPenaltyLogLambda=factor(NA)))
}
if(!includeTaperDiffPar) {
map = c(map, list(taperDiffPenaltyLogLambda=factor(NA)))
map = c(map, list(meanDiffPenaltyLogLambda=factor(NA)))
map = c(map, list(sdDiffPenaltyLogLambda=factor(NA)))
}
if(!sharedSpatialProcess) {
map = c(map, list(logitOmega=factor(NA), logitOmega2=factor(NA)))
}
if(!jointShared || !estimateGpsShared) {
map = c(map, list(logitOmega2=factor(NA)))
}
if(!inflateVarLocking) {
map = c(map, list(logLockInflate=factor(NA)))
}
if(!conditionalGamma)
obj <- MakeADFun(data, parameters, DLL="fitModelTMB", map=map)
else
obj <- MakeADFun(data, parameters, DLL="fitModelTMBconditionalGamma", map=map)
obj$hessian <- FALSE
# reparameterize inputs from optim to constrOptim
obj$f = obj$fn
obj$grad = obj$gr
obj$theta = obj$par
obj$mu=muBarrier
# set optimization control parameters (adding in penalty parameters)
nPenaltyPar = ifelse(sharedPenalty, 1, 5 - as.numeric(conditionalGamma))
controls = list(parscale=c(parscale[1:2], rep(1, (nKnotsMean - 1) * as.numeric(doMeanSpline) + as.numeric(diffMean) * nKnotsMeanGPS + as.numeric(diffVar) * nKnotsVarGPS), parscale[3:length(parscale)],
rep(1, nPenaltyPar * as.numeric(!fixedPenalty) + 2 * as.numeric(includeTaperDiffPar) + as.numeric(sharedSpatialProcess) +
as.numeric(sharedSpatialProcess && jointShared && estimateGpsShared) + as.numeric(inflateVarLocking))))
obj$control = controls
}
else {
set.seed(seed)
data = modelInfo$data
parameters = modelInfo$parameters
map = modelInfo$map
ui = modelInfo$obj$ui
ci = modelInfo$obj$ci
controls = modelInfo$obj$control
# compile the function and its gradient
if(recompile) {
if(!conditionalGamma) {
if(!debug)
compile("fitModelTMB.cpp")
else
compile("fitModelTMB.cpp","-O0 -g")
dyn.load(dynlib("fitModelTMB"))
}
else {
if(!debug)
compile("fitModelTMBconditionalGamma.cpp")
else
compile("fitModelTMBconditionalGamma.cpp","-O0 -g")
dyn.load(dynlib("fitModelTMBconditionalGamma"))
}
if(fixedPenalty) {
parameters$betasdPenaltyLogLambda = logPenaltyPar
parameters$betasdGPSPenaltyLogLambda = logPenaltyPar
parameters$betaTaperPenaltyLogLambda = logPenaltyPar
parameters$betaTaperGPSPenaltyLogLambda = logPenaltyPar
parameters$betaGammaPenaltyLogLambda = logPenaltyPar
parameters$betaMeanPenaltyLogLambda = logPenaltyPar
parameters$betaMeanGPSPenaltyLogLambda = logPenaltyPar
}
if(fixedDiffPenalty) {
parameters$taperDiffPenaltyLogLambda = logDiffPenaltyPar
parameters$meanDiffPenaltyLogLambda = logDiffPenaltyPar
parameters$sdDiffPenaltyLogLambda = logDiffPenaltyPar
}
if(!is.null(varLogLambda)) {
parameters$betasdPenaltyLogLambda = varLogLambda
parameters$betasdGPSPenaltyLogLambda = varLogLambda
}
if(!conditionalGamma)
obj <- MakeADFun(data, parameters, DLL="fitModelTMB", map=map)
else
obj <- MakeADFun(data, parameters, DLL="fitModelTMBconditionalGamma", map=map)
obj$hessian <- FALSE
# reparameterize inputs from optim to constrOptim
obj$f = obj$fn
obj$grad = obj$gr
obj$theta = obj$par
obj$mu=muBarrier
}
else {
obj = modelInfo$obj
}
doDiffPenalty = data$doDiffPenalty
doSmoothnessPenalty = data$doSmoothnessPenalty
includeTaperDiffPar = !fixedDiffPenalty && doDiffPenalty
xDepths = data$xDepths
faultDepths = data$faultDepths
lambdaBasisX = data$lambdaBasisX
lambdaBasisY = data$lambdaBasisY
sdBasisX = data$sdBasisX
sdBasisXGPS = data$sdBasisXGPS
sdBasisY = data$sdBasisY
dStar = data$dStar
dStarGPS = data$dStarGPS
gammaBasis = data$gammaBasis
deltaPenalty = data$deltaPenalty
sdBasisPenalty = data$sdBasisPenalty
sdBasisGPSPenalty = data$sdBasisGPSPenalty
taperBasisPenalty = data$taperBasisPenalty
taperBasisGPSPenalty = data$taperBasisGPSPenalty
gammaBasisPenalty = data$gammaBasisPenalty
meanBasisX = data$meanBasisX
meanBasisY = data$meanBasisY
meanBasisXGPS = data$meanBasisXGPS
meanBasisPenalty = data$meanBasisPenalty
meanBasisGPSPenalty = data$meanBasisGPSPenalty
diffGPSTaper = data$diffGPSTaper
sharedPenalty = data$sharedPenalty
fixInflation = modelInfo$allInputs$fixInflation
inflateVarLocking = modelInfo$allInputs$inflateVarLocking
squareStrikeDistGps = data$DSStrikeGPS^2
squareDipDistGps = data$DSDipGPS^2
squareStrikeDistCsz = data$DSStrikeCSZ^2
squareDipDistCsz = data$DSDipCSZ^2
squareStrikeDistCross = data$strikeDistCross^2
squareDipDistCross = data$dipDistCross^2
transformation = modelInfo$transformation
diffMean = modelInfo$diffMean
diffVar = modelInfo$diffVar
diffHigh = modelInfo$diffHigh
penHigh = modelInfo$penHigh
gpsDepthThreshold = modelInfo$gpsDepthThreshold
allInputs = modelInfo$allInputs
}
# set constraints on the parameters
# !lambdaInRange || any(sigmaZeta <= 0) || (muZeta <= 0) || (phiZeta <= 0) || (alpha <= 0.05) || (alpha >= 20))
# feasible region given by: ui %*% theta - ci >= 0
# for now, only restrict alpha, which is the last parameter, for numerical stability
# logalpha - log(0.05) >= 0
# -logalpha + log(20) >= 0 ==> logalpha <= log(20)
nPenaltyPar = ifelse(sharedPenalty, 1, 5)
ui = rbind(c(rep(0, length(obj$par)-1 - (2 * as.numeric(!fixInflation) + nPenaltyPar * as.numeric(!fixedPenalty) + 2 * as.numeric(includeTaperDiffPar) + as.numeric(inflateVarLocking))),
1, rep(0, 2 * as.numeric(!fixInflation) + nPenaltyPar * as.numeric(!fixedPenalty) + 2 * as.numeric(includeTaperDiffPar) + as.numeric(inflateVarLocking))),
c(rep(0, length(obj$par)-1 - (2 * as.numeric(!fixInflation) + nPenaltyPar * as.numeric(!fixedPenalty) + 2 * as.numeric(includeTaperDiffPar) + as.numeric(inflateVarLocking))),
-1, rep(0, 2 * as.numeric(!fixInflation) + nPenaltyPar * as.numeric(!fixedPenalty) + 2 * as.numeric(includeTaperDiffPar) + as.numeric(inflateVarLocking))))
ci = c(log(0.05), -log(20))
if(constrainMean) {
# feasible region given by: ui %*% theta - ci >= 0
# we need meanBasisPenalty %*% betaMean - sdBasisPenalty %*% betas >= 0
# (ensure that mean is larger than standard deviation at all latitudes)
parNames = names(obj$par)
# get indices of the parameters corresponding to the mean
logMuI = 1
meanParI = which(grepl("betaMean", parNames))
logMeanParGPSI = which(grepl("logMeanGPS", parNames))
meanParGPSI = which(grepl("betaMeanGPS", parNames))
meanParI = meanParI[!(meanParI %in% meanParGPSI)]
# get indices of the parameters corresponding to the sd
sdParI = which(grepl("betasd", parNames))
sdParInterceptI = which(grepl("betasdIntercept", parNames))
sdParI = sdParI[!(sdParI == sdParInterceptI)]
sdParInterceptGPSI = which(grepl("betasdInterceptGPS", parNames))
sdParInterceptI = sdParInterceptI[!(sdParInterceptI == sdParInterceptGPSI)]
sdParGPSI = which(grepl("betasdGPS", parNames))
sdParI = sdParI[!(sdParI %in% sdParGPSI)]
# add in the linear constraints
if(!(diffMean || diffVar)) {
newui = matrix(0, nrow=nrow(meanBasisPenalty), ncol=ncol(ui))
newui[,logMuI] = 1
newui[,meanParI] = rbind(meanBasisPenalty)
newui[,sdParInterceptI] = -1
newui[,sdParI] = rbind(-sdBasisPenalty)
ui = rbind(ui, newui)
} else {
newui = matrix(0, nrow=2 * nrow(meanBasisPenalty), ncol=ncol(ui))
# add in constraint for the fault (and part of the constraint for the locking rate data)
newui[, logMuI] = 1
newui[, meanParI] = rbind(meanBasisPenalty, meanBasisPenalty)
newui[, sdParInterceptI] = -1
newui[, sdParI] = rbind(-sdBasisPenalty, -sdBasisPenalty)
# add in constraint for the locking rate data
if(diffMean) {
newui[(nrow(meanBasisPenalty) + 1):nrow(newui), logMeanParGPSI] = rep(1, nrow(meanBasisGPSPenalty))
newui[(nrow(meanBasisPenalty) + 1):nrow(newui), meanParGPSI] = meanBasisGPSPenalty
}
if(diffVar) {
newui[(nrow(meanBasisPenalty) + 1):nrow(newui), sdParInterceptGPSI] = -1
newui[(nrow(meanBasisPenalty) + 1):nrow(newui), sdParGPSI] = -sdBasisGPSPenalty
}
ui = rbind(ui, newui)
}
ci = c(ci, rep(0, nrow(newui)))
}
obj$ui = ui
obj$ci = ci
# initialize optimization at the given parameters if necessary
if(!is.null(paramInit)) {
obj$par = paramInit
obj$theta = paramInit
}
finalFitControls = controls
finalFitControls$parscale = finalFitControls$parscale / 25
keepCalling = TRUE
lastPar = obj$theta
count = 0
allPar = matrix(NA, nrow=maxCount, ncol=length(obj$par))
objectiveValues = rep(NA, maxCount)
while(keepCalling) {
count = count + 1
print("Beginning optimization at: ")
print(obj$theta)
if(useAlabama) {
obj$hin = function(x) {c(ui %*% x-ci)}
obj$hin.jac = function(x) {ui}
opt = constrOptim.nl(obj$par, obj$fn, obj$gr, obj$hin, obj$hin.jac, control.optim=obj$control)
} else {
# opt <- do.call("optim", obj)
opt <- do.call("constrOptim", obj)
# opt <- do.call("myConstrOptim", obj)
}
grad = obj$gr()
if(abs(max(grad, na.rm=TRUE)) < 0.01 || count >= maxCount)
keepCalling = FALSE
else {
obj$par = opt$par* jitter(rep(1, length(opt$par)), amount = 0.05 * 0.5^count)
obj$theta = obj$par
obj$control = finalFitControls
lastPar = opt$par
obj$control$parscale = finalFitControls$parscale*2^(-count)
}
allPar[count,] = opt$par
objectiveValues[count] = opt$value
# reorder output parameters
minPar = opt$par
optParNames = names(opt$par)
logmuEst = minPar[which(optParNames == "logmu")]
betaMeanEst = c(logmuEst, minPar[which(optParNames == "betaMean")])
logMeanGPSEst = minPar[which(optParNames == "logMeanGPS")]
betaMeanGPSEst = c(logMeanGPSEst, minPar[which(optParNames == "betaMeanGPS")])
if(!diffMean)
logMeanGPSEst = 0
betasdInterceptEst = minPar[which(optParNames == "betasdIntercept")]
betasdEst = c(betasdInterceptEst, minPar[which(optParNames == "betasd")])
betasdInterceptGPSEst = minPar[which(optParNames == "betasdInterceptGPS")]
betasdGPSEst = c(betasdInterceptGPSEst, minPar[which(optParNames == "betasdGPS")])
betaTaperInterceptEst = minPar[which(optParNames == "betaTaperIntercept")]
betaTaperEst = c(betaTaperInterceptEst, minPar[which(optParNames == "betaTaper")])
betaTaperGPSEst = c(minPar[which(optParNames == "betaTaperGPS")])
betaGammaInterceptEst = minPar[which(optParNames == "betaGammaIntercept")]
betaGammaEst = c(betaGammaInterceptEst, minPar[which(optParNames == "betaGamma")])
if(conditionalGamma) {
## use log-transformed OLS estimate
# calculate the mean
meanBasisX = getSplineBasis(data.frame(list(latitude=threshSlipDat$lat)), nKnots=ifelse(doMeanSpline, nKnotsMean, 1), latRange=latRange)
meanBasisXGPS = getSplineBasis(data.frame(list(latitude=threshSlipDat$lat)), nKnots=nKnotsMeanGPS, latRange=latRange)
if(diffMean)
meanVecX = exp(meanBasisX %*% betaMeanEst + as.numeric(diffMean) * (meanBasisXGPS %*% betaMeanGPSEst))
else
meanVecX = exp(meanBasisX %*% betaMeanEst)
# calculate the taper
lambdaBasisX = getSplineBasis(data.frame(list(latitude=threshSlipDat$lat)), nKnots=nKnots, latRange=latRange)
lambdaBasisXGPS = getSplineBasis(data.frame(list(latitude=threshSlipDat$lat)), nKnots=nKnotsGPS, latRange=latRange)
if(!diffGPSTaper)
taperVecX = taper(xDepths, exp(lambdaBasisX %*% betaTaperEst), dStar = dStarGPS)
else
taperVecX = taper(xDepths, exp(lambdaBasisX %*% betaTaperEst + lambdaBasisXGPS %*% betaTaperGPSEst), dStar = dStarGPS)
# now perform the regression
logX = log(data$x)
newVarx = (data$xsd / data$x)^2
offset = log(meanVecX) + log(taperVecX)
gammaBasis = getSplineBasis(data.frame(list(latitude=threshSlipDat$lat)), nKnots=nKnotsGamma, latRange=latRange)
if(!includeGammaSpline)
gammaBasis = matrix(1, nrow=nrow(threshSlipDat))
mod = lm(logX~gammaBasis - 1, offset=offset, weights=1 / newVarx)
betaGammaEst = coef(mod)
}
logphiEst = minPar[which(optParNames == "logphi")]
logalphaEst = minPar[which(optParNames == "logalpha")]
loglowInflateEst = minPar[which(optParNames == "loglowInflate")]
loghighInflateEst = minPar[which(optParNames == "loghighInflate")]
if(!fixedPenalty && doSmoothnessPenalty) {
betasdPenaltyLogLambdaEst = minPar[which(optParNames == "betasdPenaltyLogLambda")]
if(!sharedPenalty) {
betaTaperPenaltyLogLambdaEst = minPar[which(optParNames == "betaTaperPenaltyLogLambda")]
betaTaperGPSPenaltyLogLambdaEst = minPar[which(optParNames == "betaTaperGPSPenaltyLogLambda")]
betaGammaPenaltyLogLambdaEst = minPar[which(optParNames == "betaGammaPenaltyLogLambda")]
betaMeanPenaltyLogLambdaEst = minPar[which(optParNames == "betaMeanPenaltyLogLambdaEst")]
betasdGPSPenaltyLogLambdaEst = minPar[which(optParNames == "betasdGPSPenaltyLogLambda")]
betaMeanGPSPenaltyLogLambdaEst = minPar[which(optParNames == "betaMeanGPSPenaltyLogLambda")]
}
else {
betaTaperPenaltyLogLambdaEst = betasdPenaltyLogLambdaEst
betaTaperGPSPenaltyLogLambdaEst = betasdPenaltyLogLambdaEst
betaGammaPenaltyLogLambdaEst = betasdPenaltyLogLambdaEst
betaMeanPenaltyLogLambdaEst = betasdPenaltyLogLambdaEst
betaMeanGPSPenaltyLogLambdaEst = betasdPenaltyLogLambdaEst
betasdGPSPenaltyLogLambdaEst = betasdPenaltyLogLambdaEst
}
} else {
betasdPenaltyLogLambdaEst = logPenaltyPar
betaTaperPenaltyLogLambdaEst = logPenaltyPar
betaTaperGPSPenaltyLogLambdaEst = logPenaltyPar
betaGammaPenaltyLogLambdaEst = logPenaltyPar
betaMeanPenaltyLogLambdaEst = logPenaltyPar
betaMeanGPSPenaltyLogLambdaEst = logPenaltyPar
betasdGPSPenaltyLogLambdaEst = logPenaltyPar
}
if(!is.null(varLogLambda)) {
betasdPenaltyLogLambdaEst = varLogLambda
betasdGPSPenaltyLogLambdaEst = varLogLambda
}
if(includeTaperDiffPar) {
taperDiffPenaltyLogLambdaEst = minPar[which(optParNames == "taperDiffPenaltyLogLambdaEst")]
meanDiffPenaltyLogLambdaEst = minPar[which(optParNames == "meanDiffPenaltyLogLambda")]
sdDiffPenaltyLogLambdaEst = minPar[which(optParNames == "sdDiffPenaltyLogLambda")]
}
else if(fixedDiffPenalty) {
taperDiffPenaltyLogLambdaEst = logDiffPenaltyPar
meanDiffPenaltyLogLambdaEst = logDiffPenaltyPar
sdDiffPenaltyLogLambdaEst = logDiffPenaltyPar
}
else {
taperDiffPenaltyLogLambdaEst = NULL
meanDiffPenaltyLogLambdaEst = NULL
sdDiffPenaltyLogLambdaEst = NULL
}
if(sharedSpatialProcess) {
logitOmegaEst = minPar[which(optParNames == "logitOmega")]
omegaEst = expit(logitOmegaEst)
if(estimateGpsShared) {
logitOmega2Est = minPar[which(optParNames == "logitOmega2")]
omega2Est = expit(logitOmega2Est)
}
else {
logitOmega2Est = logitOmegaEst
omega2Est = omegaEst
}
} else {
omegaEst = 0
logitOmegaEst = -Inf
omega2Est = 0
logitOmega2Est = -Inf
}
if(inflateVarLocking) {
logLockInflateEst = minPar[which(optParNames == "logLockInflate")]
lockInflateEst = exp(logLockInflateEst)
} else {
logLockInflateEst = log(3^2)
lockInflateEst = exp(logLockInflateEst)
}
finalPar = c(logmuEst=logmuEst, betaMeanEst=betaMeanEst, logMeanGPSEst=logMeanGPSEst, betaMeanGPSEst=betaMeanGPSEst,
betasdEst=betasdEst, betasdGPSEst = betasdGPSEst, betaTaperEst=betaTaperEst, betaTaperGPSEst=betaTaperGPSEst,
betaGammaEst=betaGammaEst, logphiEst=logphiEst, logalphaEst=logalphaEst,
loglowInflateEst=loglowInflateEst, loghighInflateEst=loghighInflateEst,
betasdPenaltyLogLambdaEst=betasdPenaltyLogLambdaEst,
betasdGPSPenaltyLogLambdaEst=betasdGPSPenaltyLogLambdaEst,
betaTaperPenaltyLogLambdaEst=betaTaperPenaltyLogLambdaEst,
betaTaperGPSPenaltyLogLambdaEst=betaTaperGPSPenaltyLogLambdaEst,
betaGammaPenaltyLogLambdaEst=betaGammaPenaltyLogLambdaEst,
betaMeanPenaltyLogLambdaEst=betaMeanPenaltyLogLambdaEst,
betaMeanGPSPenaltyLogLambdaEst=betaMeanGPSPenaltyLogLambdaEst,
taperDiffPenaltyLogLambdaEst=taperDiffPenaltyLogLambdaEst,
meanDiffPenaltyLogLambdaEst=meanDiffPenaltyLogLambdaEst,
sdDiffPenaltyLogLambdaEst = sdDiffPenaltyLogLambdaEst,
omegaEst=omegaEst, logitOmegaEst=logitOmegaEst, omega2Est=omega2Est, logitOmega2Est=logitOmega2Est,
logLockInflateEst=logLockInflateEst,
lockInflateEst=lockInflateEst)
lambdaBasisY = getSplineBasis(fault, nKnots=nKnots, latRange=latRange)
lambdaBasisX = getSplineBasis(data.frame(list(latitude=threshSlipDat$lat)), nKnots=nKnots, latRange=latRange)
lambdaBasisXGPS = getSplineBasis(data.frame(list(latitude=threshSlipDat$lat)), nKnots=nKnotsGPS, latRange=latRange)
sdBasisX = getSplineBasis(data.frame(list(latitude=threshSlipDat$lat)), nKnots=nKnotsVar, latRange=latRange)
sdBasisY = getSplineBasis(fault, nKnots=nKnotsVar, latRange=latRange)
sdBasisXGPS = getSplineBasis(data.frame(list(latitude=threshSlipDat$lat)), nKnots=nKnotsVarGPS, latRange=latRange)
meanBasisX = getSplineBasis(data.frame(list(latitude=threshSlipDat$lat)), nKnots=nKnotsMean, latRange=latRange)
meanBasisXGPS = getSplineBasis(data.frame(list(latitude=threshSlipDat$lat)), nKnots=nKnotsMeanGPS, latRange=latRange)
meanBasisY = getSplineBasis(fault, nKnots=nKnotsMean, latRange=latRange)
gammaBasis = getSplineBasis(data.frame(list(latitude=threshSlipDat$lat)), nKnots=nKnotsGamma, latRange=latRange)
if(!includeGammaSpline)
gammaBasis = matrix(1, nrow=nrow(threshSlipDat))
if(!doMeanSpline) {
meanBasisX = matrix(1, nrow=nrow(threshSlipDat))
meanBasisXGPS = matrix(1, nrow=nrow(threshSlipDat))
meanBasisY = matrix(1, nrow=nrow(threshSlipDat))
}
if(!diffGPSTaper)
taperVecX = taper(xDepths, exp(lambdaBasisX %*% betaTaperEst), dStar = dStarGPS)
else
taperVecX = taper(xDepths, exp(lambdaBasisX %*% betaTaperEst + lambdaBasisXGPS %*% betaTaperGPSEst), dStar = dStarGPS)
taperVecY = taper(faultDepths, exp(lambdaBasisY %*% betaTaperEst), dStar = dStar)
if(doVarSpline) {
if(diffVar) {
if(!reparameterizeVar)
sdVecX = exp(sdBasisX %*% betasdEst + sdBasisXGPS %*% betasdGPSEst)
else
sdVecX = exp(sdBasisXGPS %*% betasdGPSEst)
}
else
sdVecX = exp(sdBasisX %*% betasdEst)
sdVecY = exp(sdBasisY %*% betasdEst)
}
else {
if(diffVar) {
if(!reparameterizeVar)
sdVecX = rep(exp(betasdEst + betasdGPSEst), length(xDepths))
else
sdVecX = rep(exp(betasdGPSEst), length(xDepths))
}
else
sdVecX = rep(exp(betasdEst ), length(xDepths))
sdVecY = rep(exp(betasdEst), length(faultDepths))
}
if(diffMean)
meanVecX = exp(meanBasisX %*% betaMeanEst + diffMean * (meanBasisXGPS %*% betaMeanGPSEst))
else
meanVecX = exp(meanBasisX %*% betaMeanEst)
meanVecY = exp(meanBasisY %*% betaMeanEst)
gammaVec = exp(gammaBasis %*% betaGammaEst)
if(count == 1) {
if(debugPlotting)
browser()
}
# preview results with plot
# plot lambda and taper
latSeq = seq(latRange[1], latRange[2], l=500)
splineMat = getSplineBasis(fault=fault, nKnots=nKnots, lats=latSeq, latRange=latRange)
splineMatGPS = getSplineBasis(fault=fault, nKnots=nKnotsGPS, lats=latSeq, latRange=latRange)
lambdaSeq = exp(splineMat %*% betaTaperEst)
if(diffGPSTaper)
lambdaSeqGPS = exp(splineMat %*% betaTaperEst + splineMatGPS %*% betaTaperGPSEst)
else
lambdaSeqGPS = lambdaSeq
par(mfrow=c(1,2))
plot(latSeq, lambdaSeq, type="l", ylim=range(c(lambdaSeq, 0, lambdaSeqGPS)))
lines(latSeq, lambdaSeqGPS, col="blue")
tmp = getTaperSpline(betaTaperEst, nKnots=nKnots, dStar=dStar, latRange=latRange, fault=fault, normalize=TRUE, logScale = TRUE)
plotFault(fault, tmp, varRange=c(0, 1))
# plot taper (on original scale and GPS scale) and standard deviation
taperSeq = taper(10000, lambdaSeq, dStar = dStar)
taperSeqGPS = taper(10000, lambdaSeqGPS, dStar = dStarGPS)
par(mfrow=c(1,2))
plot(latSeq, taperSeq, type="l", ylim=range(c(taperSeq, 0, taperSeqGPS)))
lines(latSeq, taperSeqGPS, col="blue")
legend("bottomright", c("Fault taper", "Locking rate taper"), col=c("black", "blue"), lty=1)
sdMat = getSplineBasis(data.frame(list(latitude=threshSlipDat$lat)), nKnots=nKnotsVar, lats=latSeq, latRange=latRange)
sdMatGPS = getSplineBasis(data.frame(list(latitude=threshSlipDat$lat)), nKnots=nKnotsVarGPS, lats=latSeq, latRange=latRange)
if(doVarSpline) {
sdSeq = exp(sdMat %*% betasdEst)
if(diffVar) {
if(!reparameterizeVar)
sdSeqGPS = exp(sdMat %*% betasdEst + sdMatGPS %*% betasdGPSEst)
else
sdSeqGPS = exp(sdMatGPS %*% betasdGPSEst)
}
else
sdSeqGPS = exp(sdMat %*% betasdEst)
}
else {
sdSeq = rep(exp(betasdEst), length(latSeq))
if(diffVar) {
if(!reparameterizeVar)
sdSeqGPS = rep(exp(betasdEst + betasdGPSEst), length(latSeq))
else
sdSeqGPS = rep(exp(betasdGPSEst), length(latSeq))
}
else
sdSeqGPS = rep(exp(betasdEst), length(latSeq))
}
plot(latSeq, sdSeq, type="l", ylim=range(c(0, sdSeq, sdSeqGPS)))
sdSharedSeq = sdSeq * sqrt(omegaEst)
lines(latSeq, sdSharedSeq, lty=2)
lines(latSeq, sdSeqGPS, col="blue")
lines(latSeq, sdSeqGPS * sqrt(omegaEst), col="blue", lty=2)
# plot gamma and mean vectors
latSeq = seq(latRange[1], latRange[2], l=500)
gammaMat = getSplineBasis(fault=fault, nKnots=nKnotsGamma, lats=latSeq, latRange=latRange)
if(!includeGammaSpline)
gammaMat = matrix(1, nrow=length(latSeq))
gammaSeq = exp(gammaMat %*% betaGammaEst)
meanMat = getSplineBasis(fault=fault, nKnots=nKnotsMean, lats=latSeq, latRange=latRange)
meanMatGPS = getSplineBasis(fault=fault, nKnots=nKnotsMeanGPS, lats=latSeq, latRange=latRange)
if(!doMeanSpline) {
meanMat = matrix(1, nrow=length(latSeq))
meanMatGPS = matrix(1, nrow=length(latSeq))
}
meanSeq = exp(meanMat %*% betaMeanEst)
if(diffMean)
meanSeqGPS = exp(meanMat %*% betaMeanEst + as.numeric(diffMean) * (meanMatGPS %*% betaMeanGPSEst))
else
meanSeqGPS = exp(meanMat %*% betaMeanEst)
plot(latSeq, gammaSeq, type="l", ylim=range(c(gammaSeq, 0)))
plot(latSeq, meanSeq, type="l", ylim=range(c(meanSeq, 0, meanSeqGPS)))
lines(latSeq, meanSeqGPS, col="blue")
par(mfrow=c(1,1))
meanBasisX = getSplineBasis(data.frame(list(latitude=threshSlipDat$lat)), nKnots=nKnotsMean, latRange=latRange)
meanBasisXGPS = getSplineBasis(data.frame(list(latitude=threshSlipDat$lat)), nKnots=nKnotsMeanGPS, latRange=latRange)
if(!doMeanSpline) {
meanBasisX = matrix(1, nrow=length(threshSlipDat$lat))
meanBasisXGPS = matrix(1, nrow=length(threshSlipDat$lat))
}
if(diffMean)
meanVecX = exp(meanBasisX %*% betaMeanEst + as.numeric(diffMean) * (meanBasisXGPS %*% betaMeanGPSEst))
else
meanVecX = exp(meanBasisX %*% betaMeanEst)
sortI = sort(threshSlipDat$lat, index.return=TRUE)$ix
plot(threshSlipDat$lat, 1000 * meanVecX * taperVecX / threshSlipDat$slip, pch=19, cex=.1,
ylab="Time (Years)", xlab="Latitude", main="Estimated time between earthquakes",
ylim = range(c(1000 * meanVecX * taperVecX / threshSlipDat$slip, 1000 / gammaVec[sortI])))
lines(threshSlipDat$lat[sortI], 1000 / gammaVec[sortI], col="blue")
plot(threshSlipDat$lat, threshSlipDat$slip / taperVecX, pch=19, cex=.1,
ylim=range(c(threshSlipDat$slip / taperVecX, meanSeqGPS * gammaSeq)),
main="Estimated untapered locking rate")
lines(latSeq, meanSeqGPS * gammaSeq, col="blue")
report = obj$report()
par(mfrow=c(1,2))
plot(report$xResiduals, threshSlipDat$lat)
plot(report$yResiduals, subDat$Lat)
if(count == 1) {
if(debugPlotting)
browser()
}
}
minI = which(objectiveValues == min(objectiveValues, na.rm = TRUE))[1]
minPar = allPar[minI,]
# opt$hessian ## <-- FD hessian from optim
grad = obj$gr(minPar)
if(calcHess) {
hess = obj$he(minPar) ## <-- Analytical hessian
sdReport = sdreport(obj)
}
else {
# calculate this stuff later
hess = NULL
sdReport = NULL
}
report = obj$report()
print("optimum parameters for each iteration:")
print(t(allPar[,1:count]))
print("optimum parameters for best iteration:")
print(minPar)
print("optimum gradient for best iteration")
print(grad)
print("sdreport")
print(report)
optParNames = names(opt$par)
logmuEst = minPar[which(optParNames == "logmu")]
betaMeanEst = c(logmuEst, minPar[which(optParNames == "betaMean")])
logMeanGPSEst = minPar[which(optParNames == "logMeanGPS")]
betaMeanGPSEst = c(logMeanGPSEst, minPar[which(optParNames == "betaMeanGPS")])
if(!diffMean)
logMeanGPSEst = 0
betasdInterceptEst = minPar[which(optParNames == "betasdIntercept")]
betasdEst = c(betasdInterceptEst, minPar[which(optParNames == "betasd")])
betasdInterceptGPSEst = minPar[which(optParNames == "betasdInterceptGPS")]
betasdGPSEst = c(betasdInterceptGPSEst, minPar[which(optParNames == "betasdGPS")])
betaTaperInterceptEst = minPar[which(optParNames == "betaTaperIntercept")]
betaTaperEst = c(betaTaperInterceptEst, minPar[which(optParNames == "betaTaper")])
betaTaperGPSEst = c(minPar[which(optParNames == "betaTaperGPS")])
betaGammaInterceptEst = minPar[which(optParNames == "betaGammaIntercept")]
betaGammaEst = c(betaGammaInterceptEst, minPar[which(optParNames == "betaGamma")])
if(conditionalGamma) {
## use log-transformed OLS estimate
# calculate the mean
meanBasisX = getSplineBasis(data.frame(list(latitude=threshSlipDat$lat)), nKnots=nKnotsMean, latRange=latRange)
meanBasisXGPS = getSplineBasis(data.frame(list(latitude=threshSlipDat$lat)), nKnots=nKnotsMeanGPS, latRange=latRange)
if(diffMean)
meanVecX = exp(meanBasisX %*% betaMeanEst + as.numeric(diffMean) * (meanBasisXGPS %*% betaMeanGPSEst))
else
meanVecX = exp(meanBasisX %*% betaMeanEst)
# calculate the taper
lambdaBasisX = getSplineBasis(data.frame(list(latitude=threshSlipDat$lat)), nKnots=nKnots, latRange=latRange)
lambdaBasisXGPS = getSplineBasis(data.frame(list(latitude=threshSlipDat$lat)), nKnots=nKnotsGPS, latRange=latRange)
if(!diffGPSTaper)
taperVecX = taper(xDepths, exp(lambdaBasisX %*% betaTaperEst), dStar = dStarGPS)
else
taperVecX = taper(xDepths, exp(lambdaBasisX %*% betaTaperEst + lambdaBasisXGPS %*% betaTaperGPSEst), dStar = dStarGPS)
# now perform the regression
logX = log(data$x)
newVarx = (data$xsd / data$x)^2
offset = log(meanVecX) + log(taperVecX)
gammaBasis = getSplineBasis(data.frame(list(latitude=threshSlipDat$lat)), nKnots=nKnotsGamma, latRange=latRange)
if(!includeGammaSpline)
gammaBasis = matrix(1, nrow=nrow(threshSlipDat))
mod = lm(logX~gammaBasis - 1, offset=offset, weights=1 / newVarx)
betaGammaEst = coef(mod)
}
logphiEst = minPar[which(optParNames == "logphi")]
logalphaEst = minPar[which(optParNames == "logalpha")]
loglowInflateEst = minPar[which(optParNames == "loglowInflate")]
loghighInflateEst = minPar[which(optParNames == "loghighInflate")]
if(!fixedPenalty && doSmoothnessPenalty) {
betasdPenaltyLogLambdaEst = minPar[which(optParNames == "betasdPenaltyLogLambda")]
if(!sharedPenalty) {
betaTaperPenaltyLogLambdaEst = minPar[which(optParNames == "betaTaperPenaltyLogLambda")]
betaTaperGPSPenaltyLogLambdaEst = minPar[which(optParNames == "betaTaperGPSPenaltyLogLambda")]
betaGammaPenaltyLogLambdaEst = minPar[which(optParNames == "betaGammaPenaltyLogLambda")]
betaMeanPenaltyLogLambdaEst = minPar[which(optParNames == "betaMeanPenaltyLogLambdaEst")]
betasdGPSPenaltyLogLambdaEst = minPar[which(optParNames == "betasdGPSPenaltyLogLambda")]
betaMeanGPSPenaltyLogLambdaEst = minPar[which(optParNames == "betaMeanGPSPenaltyLogLambda")]
}
else {
betaTaperPenaltyLogLambdaEst = betasdPenaltyLogLambdaEst
betaTaperGPSPenaltyLogLambdaEst = betasdPenaltyLogLambdaEst
betaGammaPenaltyLogLambdaEst = betasdPenaltyLogLambdaEst
betaMeanPenaltyLogLambdaEst = betasdPenaltyLogLambdaEst
betaMeanGPSPenaltyLogLambdaEst = betasdPenaltyLogLambdaEst
betasdGPSPenaltyLogLambdaEst = betasdPenaltyLogLambdaEst
}
} else {
betasdPenaltyLogLambdaEst = logPenaltyPar
betaTaperPenaltyLogLambdaEst = logPenaltyPar
betaTaperGPSPenaltyLogLambdaEst = logPenaltyPar
betaGammaPenaltyLogLambdaEst = logPenaltyPar
betaMeanPenaltyLogLambdaEst = logPenaltyPar
betaMeanGPSPenaltyLogLambdaEst = logPenaltyPar
betasdGPSPenaltyLogLambdaEst = logPenaltyPar
}
if(!is.null(varLogLambda)) {
betasdPenaltyLogLambdaEst = varLogLambda
betasdGPSPenaltyLogLambdaEst = varLogLambda
}
if(includeTaperDiffPar) {
taperDiffPenaltyLogLambdaEst = minPar[which(optParNames == "taperDiffPenaltyLogLambdaEst")]
meanDiffPenaltyLogLambdaEst = minPar[which(optParNames == "meanDiffPenaltyLogLambda")]
sdDiffPenaltyLogLambdaEst = minPar[which(optParNames == "sdDiffPenaltyLogLambda")]
}
else if(fixedDiffPenalty) {
taperDiffPenaltyLogLambdaEst = logDiffPenaltyPar
meanDiffPenaltyLogLambdaEst = logDiffPenaltyPar
sdDiffPenaltyLogLambdaEst = logDiffPenaltyPar
}
else {
taperDiffPenaltyLogLambdaEst = NULL
meanDiffPenaltyLogLambdaEst = NULL
sdDiffPenaltyLogLambdaEst = NULL
}
if(sharedSpatialProcess) {
logitOmegaEst = minPar[which(optParNames == "logitOmega")]
omegaEst = expit(logitOmegaEst)
if(estimateGpsShared) {
logitOmega2Est = minPar[which(optParNames == "logitOmega2")]
omega2Est = expit(logitOmega2Est)
}
else {
logitOmega2Est = logitOmegaEst
omega2Est = omegaEst
}