Nest survival encounter history matrix with variability in nest period

[Stephanie Augustine]

Hello,

I'm running a straightforward nest survival model, generally using the code from the IPM book pg 164 as a framework. Age of the nest is also a covariate of interest. So the JAGS model code would be:

model {
# Priors and linear models
for (i in 1:n.nest){
    for (t in f[i]:(k[i]-1)){
        phi[i,t] <- phia[age[i] + t - f[i]]
    } #t
} #i
for (a in 1:T){
    phia[a] <- ilogit(alpha + beta * a)
}
alpha ~ dnorm(0, 0.001)
beta ~ dnorm(0, 0.001)
# Likelihood
for (i in 1:n.nest){
    for (t in (f[i]+1):k[i]){
        y[i,t] ~ dbern(phi[i,t-1] * y[i,t-1])
    } #t
} #i
# Derived parameter: nest success
nu <- prod(phia[1:T])
}

where f = day first monitored, k = day last checked, age = age of the nest at time t.

 My questions relate to real world data with variable nesting periods. In the text, the T in nu <- prod(phia[1:T]) is specified to be assumed constant. 

In my real data, the average nesting period from lay to fledge is 23, but there are nests that fledge early or late for any number of reasons (i.e., larger or smaller clutch size adding or reducing # days laying, weather delaying or accelerating development and therefore hatching or fledging, just individual variation). If I assume I want to use the average nesting period of 23 days, then in an age-specific model, any nests that fledged after 23 days of age don't cooperate with a nicely preset T = 23 because the age covariate at fledge ends up being out of bounds of the T vector. 

If I set T to the longest possible fledge period (in my data, age = 26 at fledge), is DSR for age > 23 just based off those cases where it fledged late? And what about where it fledges early, and age = 20 in a successful nest? Is that biasing the DSR for T 20-23 lower because it fledges prior to reaching that age? 

One way to avoid the issue would be to change the date of k (last checked) from the real day to coerce it to = 23 in a successful nest, but I haven't been able to find evidence of that as standard practice and I am wary of coercing the data to my will. 

Any insight into how to handle variation in nest period in an age specific model, and whether or not that variation introduces bias, would be very helpful, thanks in advance!

Stephanie Augustine (she/her)

Avian Program Manager

Ecostudies Institute 

610-360-502