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# Compute chi-square gof test for io.fi models
#
# model ddf model object
# breaks distance cut points
# nc number of distance classes
#
# return list with chi-square value, df and p-value
# documented in ?ddf.gof
gof.io.fi <- function(model,breaks=NULL,nc=NULL){
width <- model$meta.data$width
left <- model$meta.data$left
xmat <- model$mr$data
n <- dim(xmat)[1]/2
# Set up omega index
# 1 - detected by primary only
# 2 - detected by secondary only
# 3 - detected by both
xmat <- xmat[xmat$observer==1,]
xmat$omega <- rep(1,dim(xmat)[1])
xmat$omega[xmat$timesdetected==2] <- 3
xmat$omega[xmat$timesdetected==1&xmat$detected==0] <- 2
# If number of classes for histogram intervals was not set
# compute a reasonable default
if(is.null(nc)){
nc <- round(sqrt(min(length(xmat$distance[xmat$observer==1 &
xmat$detected==1]),
length(xmat$distance[xmat$observer==1 &
xmat$timesdetected==2]))), 0)
}
# Set up default break points - need to allow user-defined values
if(is.null(breaks)){
breaks <- left + ((width-left)/nc)*(0:nc)
}else{
nc <- length(breaks)-1
}
# Get predicted values for mr component
predict.list <- predict(model)
p1 <- predict.list$p1
p2 <- predict.list$p2
p.omega <- data.frame(object=rep(1:n,3),
omega=c(rep(1,n),rep(2,n),rep(3,n)),
distance=rep(xmat$distance,3),
prob=rep(0,3*n))
p.omega$prob[p.omega$omega==1] <- p1*(1-p2)/(p1+p2-p1*p2)
p.omega$prob[p.omega$omega==2] <- p2*(1-p1)/(p1+p2-p1*p2)
p.omega$prob[p.omega$omega==3] <- p1*p2/(p1+p2-p1*p2)
expected.2 <- by(p.omega$prob,list(as.factor(p.omega$omega),
cut(p.omega$distance,breaks,
include.lowest=TRUE)),
sum,na.rm=TRUE)
# Get predicted values for ds component
expected.1 <- rep(0,nc)
for(j in 1:nc){
expected.1[j] <- sum(predict(model,integrate=TRUE,compute=TRUE,
int.range=breaks[j+1])$fitted/model$fitted)
}
n <- expected.1[nc]
expected.1[2:nc] <- expected.1[2:nc]- expected.1[1:(nc-1)]
expected.1 <- n*expected.1/sum(expected.1)
# Compute observed values of distance bins
observed.count.1 <- table(cut(xmat$distance,breaks,include.lowest=TRUE))
observed.count.2 <- table(as.factor(xmat$omega),
cut(xmat$distance,breaks,include.lowest=TRUE))
chisq.1 <- sum((observed.count.1-expected.1)^2/expected.1,na.rm=TRUE)
chisq.2 <- sum((observed.count.2-expected.2)^2/expected.2,na.rm=TRUE)
df.1 <- NA
p.1 <- NA
df.2 <- NA
p.2 <- NA
return(list(chi1=list(observed=observed.count.1,
expected=expected.1,
chisq=chisq.1,
p=p.1,
df=df.1),
chi2=list(observed=observed.count.2,
expected=expected.2[1:3,],
chisq=chisq.2,
p=p.2,
df=df.2),
pooled.chi=list(chisq=chisq.1+chisq.2,
df=3*nc-length(model$par)-1,
p=1-pchisq(chisq.1+chisq.2,
3*nc-length(model$par)-1))))
}
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