#'Compute and plot pseudoresiduals
#'
#'This function, modified from Zuchinni and MacDonald (2009), plots the ordinary
#'normal pseudoresiduals. Three plots are produced-a qq-plot, normal pseudoresiduals
#'plotted through time, and an ACF plot. Pseudoresiduals for integer valued
#'distributions need to be fixed.
#'
#'@param move.HSMM A move.HSMM object containing a fitted HSMM model.
#'@param plots A logical indicating whether or not to produce plots
#'@param returnresids A logical indicating whether or not to return the pseudo-residuals
#'@include Distributions.R
#'@include move.HSMM.state_probs.R
#'@return A list of normal pseudoresiduals of length ndist.
#'@export
#'
move.HSMM.psresid=function(move.HSMM,plots=T,returnresids=F){
params=move.HSMM$params
nstates=move.HSMM$nstates
dists=move.HSMM$dists
obs=move.HSMM$obs
m=move.HSMM$m1
ndist=length(dists)-1
out=Distributions(dists,nstates)
PDFs=out[[3]]
CDFs=out[[4]]
Gamma <- gen.Gamma(m,params,PDFs,CDFs)
delta <- solve(t(diag(sum(m))-Gamma+1),rep(1,sum(m)))
delta[delta<0]=1e19
n <- nrow(obs)
fb <- move.HSMM.lalphabeta(move.HSMM)
if(nstates>2){
params[[1]]=NULL
}
la <- t(fb$la)
lb <- t(fb$lb)
la <- cbind(log(delta),la)
lafact <- apply(la ,2,max)
lbfact <- apply(lb ,2,max)
w <- matrix(NA ,ncol=n,nrow=sum(m))
for (i in 1:n){
foo <- (exp(la[,i]-lafact[i])%*% Gamma)*exp(lb[,i]-lbfact[i])
w[,i] <- foo/sum(foo)
}
resids=vector("list",ndist-1)
for(i in 1:ndist){
resids[[i]]=numeric(n)
}
mstart=c(1,cumsum(m)+1)
mstart=mstart[-length(mstart)]
mstop=cumsum(m)
for(k in 1:n){
#for each distribution
for(j in 1:nstates){
for(i in 1:(ndist)){
nparam=max(1,ncol(params[[i+1]]))
if(nparam==2){
resids[[i]][k]=resids[[i]][k]+sum(CDFs[[i+1]](obs[k,i],params[[i+1]][j,1],params[[i+1]][j,2])*w[mstart[j]:mstop[j],k])
}else if(nparam==1){
resids[[i]][k]=resids[[i]][k]+sum(CDFs[[i+1]](obs[k,i],params[[i+1]][j,1])*w[mstart[j]:mstop[j],k])
}else if(nparam==3){
resids[[i]][k]=resids[[i]][k]+sum(CDFs[[i+1]](obs[k,i],params[[i+1]][j,1],params[[i+1]][j,2],params[[i+1]][j,3])*w[mstart[j]:mstop[j],k])
}
}
}
}
#remove NA resids
for(i in 1:ndist){
rem=which(is.na(obs[,i]))
if(length(rem)>0){
resids[[i]]=resids[[i]][-rem]
}
}
#Plots
if(plots==TRUE){
label=names(CDFs)[2:length(CDFs)]
par(mfrow=c(ndist,1))
#QQ plots
for(i in 1:ndist){
qqnorm(qnorm(resids[[i]]),main=paste(label[i],"Q-Q plot"),xlab="",ylab="",xlim=c(-3,3),ylim=c(-3,3))
abline(a=0,b=1)
}
par(ask = TRUE)
#resids through time
for(i in 1:ndist){
plot(qnorm(resids[[i]]),pch=1,main=paste(label[i],"Residuals through time"), ylab="residual")
abline(h=0)
lines(loess.smooth(seq(1:length(resids[[i]])),qnorm(resids[[i]])),col="red",lwd=2)
}
#acf
for(i in 1:ndist){
a=acf(qnorm(resids[[i]]),na.action=na.pass,plot=F)
plot(a,pch=1,main=paste(label[i],"ACF"))
}
par(mfrow=c(1,1))
par(ask = F)
}
if(returnresids==T){
names(resids)=dists
resids
}
}
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