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Simulation1_RandFX_SN.R
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Simulation1_RandFX_SN.R
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#--------------------------------------------------------------------------
#A Method of Correcting Estimation Failure in Latent Differential Equations with Comparisons to Kalman Filtering
#Pt. 2b: Random-Effects Simulation, Shot Noise Processes
#Author: Kevin McKee (mckeek@vcu.edu)
#Virginia Commonwealth University
#Virginia Institute of Psychiatric and Behavioral Genetics
#Last updated: 2/27/2019
#--------------------------------------------------------------------------
library(OpenMx)
library(signal)
library(deSolve)
library(DEoptim)
source("GLLAfunctions.R")
#Helper functions
smear<-function(x, t){
x.s<-matrix(NA, nrow=length(x), ncol=t)
x.s[,1]<-x
for(i in 2:t){
x.s[i:nrow(x.s),i]<-x[1:(length(x)-i+1)]
}
x.s.combine<-apply(x.s, 1, max, na.rm=T)
return(x.s.combine)
}
genDifs<-function(x, kern){
kern.mat<-matrix(kern, nrow=length(kern),ncol=1)
a<-gllaEmbed(x, embed=length(kern), tau=1, idColumn = F)
b<- a%*%kern.mat
return(as.matrix(b))
}
#Outlier detection and removal algorithm
PDA<-function(model, data, thres.sd=1,AR.order, max.iter=10, plot=F){
#Model variables
tData<-as.matrix(data)
D<-model$D$values[1]
data.cut<-tData
#include iteration count for max.iter stopping condition and minimum remaining rows of data.
i<-1
min.rows<-5
#Initial values for max range stopping condition.
iRange<-1
iRange.prior<-0
estEvent<-NULL
par(mfrow=c(1,1), mai=c(.5,.5,.5,.5))
while(iRange>iRange.prior & i<max.iter & nrow(tData)-length(estEvent) > min.rows) {
model<-mxModel(model, mxData(data.cut, type="raw"))
model<-mxRun(model, silent=T)
if(model$output$status$code!=0) model<-mxTryHard(model, silent=T, extraTries = 15)
m<-mahalanobis(tData[,1:D], center=model$fitfunction$info$expMean, cov=model$fitfunction$info$expCov)
m.ar<-ar(m, order.max=AR.order,aic=FALSE, method="ols")$ar
if(length(m.ar)==0) m.ar<-0
m.d<- genDifs(m, c(-m.ar,1))
m.d.thres<-as.numeric(mean(m.d)+thres.sd*sd(m.d))
m.d.s<-matrix(c(smear(m.d, t=(D-1))))
data.cut<-tData[m.d.s<m.d.thres, ]
estEvent<- which(m.d.s>m.d.thres)
iRange.prior<-iRange
iRange<-range(m.d.s)[2]-range(m.d.s)[1]
i<-i+1
if(plot){
plot(m.d.s, type="l")
abline(h=m.d.thres)
abline(v=estEvent, lty=3, col="blue")
}
}
# Output ------------------------------------------------------------------
return(list("fit"=model, "exclusions"=estEvent))
}
# Generate shot noise process ---------------------------------------------
DLOsim <- function(t, prevState, parms) {
x <- prevState[1]
y <- prevState[2]
with(as.list(parms),
{
dx <- y
dy <- parms[[1]]*x + parms[[2]]*y
res<-c(dx, dy)
list(res)
}
)
}
genSN<-function(pars, eventFreq=.1, eventType="level", iv=c(1,0)){
# Generate events ---------------------------------------------------------
eta<- pars[4]#-(2*pi/pars[[4]])^2
zeta<-pars[5]#log(pars[[5]])*sqrt(-eta)/pi
pars.conv<-c(eta, zeta)
t<-1:pars[[1]]
shocks<-list()
shocks<-rbinom(pars[[1]],1,eventFreq)*rnorm(pars[[1]]) #sample(c(-1, 1), 100, replace=T)#
# shocks<-rbinom(pars[[1]],1,eventFreq)*sample(c(-1, 1), pars[[1]], replace=T)#
shocks.m<-NULL
if(eventType=="slope"){
shocks.m<-c(shocks.m, rep(0,pars[[1]]), shocks)
}else{
shocks.m<-c(shocks.m, shocks, rep(0,pars[[1]]))
}
eventdat <- data.frame(var = c(rep("x",pars[[1]]),rep("y",pars[[1]])),
time = rep(t, 2),
value = shocks.m,
method = rep("add", 2))
eventdat<-eventdat[eventdat$value!=0,]
names(iv)<-c("x","y")
dat<-lsoda(y=iv, times=t, DLOsim, pars.conv, events = list(data=eventdat))
x<-cbind(t, dat[,2]+rnorm(pars[[1]])*pars[[2]])
plot(x, type="l", col='darkgrey')
lines(dat[,1:2])
lines(eventdat[,2:3], type="h", col="red", lwd=2)
return(x)
}
nIter<-200000
#---------------------------------------------------------------------------
# Simulation 2--------------------------------------------------------------
#---------------------------------------------------------------------------
randEffects<-data.frame(
"N"=sample(80:400, nIter, replace=T),
"measErr"=runif(nIter, 1/32, 1/2),
"dynErr"=.3,#runif(nIter, 1/32, 1/2),
"Period"= -(2*pi/sample(8:40, nIter, replace=T))^2,
"Damping"=0,
"p"=runif(nIter, 0, 1),
"type"=1#sample(c(1,2),nIter, replace=T)
)
randEffects$Damping<-log(runif(nIter, 0.05, .95))*sqrt(-randEffects$Period)/pi
cl<-makeCluster(2)
library(foreach)
library(doSNOW)
registerDoSNOW(cl)
#####
continue<-F #If false, create new data set. If true, append existing set.
#####
foreach(i=1:nIter,
.combine = rbind,
.packages = c("OpenMx","deSolve"),
.export=c("DLOsim","genSN","gllaEmbed","PDA","smear","randEffects", "genDifs"))%dopar%{
parSet<-randEffects[i,]
y<-data.frame("obs"=matrix(0,parSet$N,1), tim=1:parSet$N)
dataGen<-readRDS("SSM_model.RDS")
dataGen<-mxModel(dataGen, mxData(y, type="raw"))
dataGen<-omxSetParameters(dataGen, labels=names(coef(dataGen)), values=unlist(c(parSet[4:5], parSet$dynErr, parSet$measErr^2, 1, 0)))
dat<-mxGenerateData(dataGen)$obs
#Embed data for the LDE
D<-floor(round(2*pi/sqrt(-parSet$Period))/2)
tEmbedded <- gllaEmbed(dat, embed=D, tau=1, idColumn=FALSE)
colnames(tEmbedded)<-paste0("x1_",0:(D-1))
tEmbedded<-cbind(tEmbedded, "Occasion"=1:nrow(tEmbedded))
Lmat<-matrix((1:D)-mean(1:D),nrow=D, ncol=3)
for(k in 1:3) Lmat[,k]<-Lmat[,k]^(k-1)/factorial(k-1)
# LDE ---------------------------------------------------------------------
LDE<-readRDS("LDE_model.RDS")
LDE<-mxModel(LDE,
mxMatrix("Full", nrow=D, 3, values=Lmat, name="L", dimnames=list(colnames(tEmbedded)[1:D], rownames(LDE$S$values))),
mxMatrix("Diag", nrow=D, ncol=D, values=.1, free=T, labels="e_x1", lbound=1e-10, name="U", dimnames=list(colnames(tEmbedded)[1:D],colnames(tEmbedded)[1:D])),
mxMatrix("Full", nrow=1, ncol=D, values=.001, free=T, labels="mu_x1", name="M", dimnames=list(NULL,colnames(tEmbedded)[1:D])),
mxExpectationNormal("R","M"))
dimnames(LDE$R)<-list(colnames(tEmbedded)[1:D],colnames(tEmbedded)[1:D])
LDE$D$values<-D
LDE.EA<-LDE
LDE<-mxModel(LDE, mxData(tEmbedded, type="raw"))
LDE$compute<-omxDefaultComputePlan()
LDE$compute$steps$GD<-mxComputeNelderMead(maxIter = 500000)
LDE<-mxRun(LDE)
if(LDE$output$status$code!=0) LDE<-mxTryHard(LDE, silent=T, extraTries = 15)
# LDE EA ------------------------------------------------------------------
LDE.EA<-omxSetParameters(LDE.EA, "d2x1ts1", values=0,free=F,lbound=NA)
LDE.EA$compute<-omxDefaultComputePlan()
LDE.EA$compute$steps$GD<-mxComputeNelderMead(maxIter = 500000)
phi<- -0.152344 +0.004885*D +0.002200*length(dat) #NEW: VARIANCE AND BIAS (QUICK CALIBRATION): Obj value 0.317456
AR<-D
LDEPDA.fit<-PDA(LDE.EA, tEmbedded, thres.sd=phi,AR.order=AR, max.iter=25, plot=F)
# SSM ---------------------------------------------------------------------
ssm<-readRDS("SSM_model.RDS")
ssm<-mxModel(ssm, mxData(data.frame("obs"=dat, "tim"=1:parSet$N), type="raw"))
ssm$compute<-omxDefaultComputePlan()
ssm$compute$steps$GD<-mxComputeNelderMead(maxIter = 500000)
ssm<-mxRun(ssm, silent=T)
if(ssm$output$status$code!=0) ssm<-mxTryHard(ssm, silent=T, extraTries = 15)
# Output ------------------------------------------------------------------
out<-unlist(c(parSet, "LDE"=coef(LDE)[1:2], "LDE.EA"=coef(LDEPDA.fit$fit)[1:2], "SSM"=coef(ssm)[1:2],
"SC.LDE"=LDE$output$status$code, "SC.LDE.OR"=LDEPDA.fit$fit$output$status$code, "SC.SSM"=ssm$output$status$code,
"SE.LDE"=LDE$output$standardErrors[1:2,1], "SE.LDE.OR"=LDEPDA.fit$fit$output$standardErrors[1:2,1], "SE.SSM"=ssm$output$standardErrors[1:2,1]))
write.table(t(out), sep=",", file="outputDiffProc_Rand.csv",append=ifelse(i==1, continue, T), col.names=ifelse(i==1, !continue, F), row.names=F)
}
stopCluster(cl)