ceSimErrorsUnequalHWI {assocInd}

Simulate HWI under combined group and individual location errors with unequal observation probabilities

Description

Generate an estimated half weight index under conditions where both group and individual location errors are present, but where individual location errors are not equal for all individuals

Usage

ceSimErrorsUnequalHWI(aAB, w, psi, Emean, Esd, n)

Arguments

aAB

The real association rate between individuals A and B

w

The group location error term

psi

The relative importance of the group location error to the individual location error

Emean

The mean probability of missing one individual given that it is not with the other

Esd

The standard deviation of the individual location error distribution

n

The number of sampling periods

Details

A simple function that simulates data for a given probability of missing groups and real association strength. The w term represents the likelihood of failing to observe a group containing a and b compared to failing to observe both groups containing a and b if the two individuals are apart. E (Epsilon) is probability of missing one individual given that it is not with the other. psi represents the relative importance of the group location error to the individual identification error. The function allows a distribution of individual location error probabilities to be given using Emean and Esd. The function returns the simulated half weight index and whether the value lies within the 95 percent confidence intervals of the half weight index given the number of samples and under the assumption of no error.

Value

Returns two values: the simulated half weight index and whether or not it falls within the 95 percent confidence intervals (1 = yes, 0 = no)

Author(s)

William Hoppitt <[e-mail]> Damien Farine <[e-mail]>

References

Hoppitt, W. & Farine, D.R. (in prep) Association indices for quantifying social relationships: how to deal with missing observations of individuals or groups.

Examples

	# Set a real association index
	aAB <- 0.5
	
	# Set w range
	w <- seq(-1,1,0.1)

	# Set errors parameters
	psi <- 0.5
	Emean <- 0.5
	Esd <- 0.05
	
	# Replicate N times
	replicates <- 100  # small number used to save computation time
	
	# Create a blank storage matrices
	assocStrength <- matrix(NA,nrow=replicates,ncol=length(w))
	inCIs <- matrix(NA,nrow=replicates,ncol=length(w))
	
	# Loop through repeating N times for each error value
	for (i in 1:length(w)) { 
		for (j in 1:replicates) {
			out <- ceSimErrorsUnequalHWI(aAB,w[i],psi,Emean,Esd,20)
			assocStrength[j,i] <- out[1]
			inCIs[j,i] <- out[2]
		}
	}
	
	# Plot the results
	par(mfrow=c(1,2))
	plot(w,colMeans(assocStrength, na.rm=TRUE), pch=20, ylim=c(0,1), ylab="Simulated HWI")
	CIs <- apply(assocStrength,2,quantile,c(0.025,0.975),na.rm=TRUE)
	arrows(w,CIs[1,],w,CIs[2,],len=0.1,code=3,angle=90)
	abline(h=0.5,col="red")
	
	plot(w,colMeans(inCIs, na.rm=TRUE), pch=20, ylim=c(0,1), ylab="Percent of times in CIs")
	abline(h=0.95, col="red")