piFuns: Compute multinomial cell probabilities
In ianfiske/unmarked: Models for Data from Unmarked Animals

Description Usage Arguments Details Value Examples

Compute the cell probabilities used in the multinomial-Poisson model multinomPois.

1 2	removalPiFun(p) doublePiFun(p)

`p`	matrix of detection probabilities at each site for each observation

These two functions are provided as examples of possible functions to calculate multinomial cell probabilities. Users may write their own functions for specific sampling designs and use them in multinomPois. See the example for a user-defined function.

For removalPiFun, a matrix of cell probabilties for each site and sampling period.

For doublePiFun, a matrix of cell probabilities for each site and observer combination. Column one is probability observer 1 but not observer 2 detects the object, column two is probability that observer 2 but not observer 1 detects the object, and column 3 is probability of both detecting.

(pRem <- matrix(0.5, nrow=3, ncol=3))	# Capture probabilities
removalPiFun(pRem)			# Cell probs

(pDouble <- matrix(0.5, 3, 2))		# Observer detection probs
doublePiFun(pDouble)			# Cell probs

# A user-defined piFun calculating removal probs when time intervals differ.
# Here 10-minute counts were divided into 2, 3, and 5 minute intervals.
# This function could be supplied to unmarkedFrameMPois along with the obsToY
# argument shown below.

instRemPiFun <- function(p) {
	M <- nrow(p)
	J <- ncol(p)
	pi <- matrix(NA, M, J)
	p[,1] <- pi[,1] <- 1 - (1 - p[,1])^2
	p[,2] <- 1 - (1 - p[,2])^3
	p[,3] <- 1 - (1 - p[,3])^5
	for(i in 2:J) {
		pi[,i] <- pi[, i - 1]/p[, i - 1] * (1 - p[, i - 1]) * p[, i]
		}
	return(pi)
	} 
	
instRemPiFun(pRem)

# Associated obsToY matrix required by unmarkedFrameMPois
o2y <- diag(3)
o2y[upper.tri(o2y)] <- 1
o2y