I am seeking to develop a CJS model from capture-recapture data for which individual "spawn year" is known. I am interested in estimating parameters of annual survival and encounter probability for these cohorts. My method and data are represented in spirit in this code chunk:
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# capture events represent annual detection results spanning 1993 - 2022
ch_df <- data.frame(ch = c(000000001100000000000000000000, 000000000000000000010011000000, 000000000000000000000000001010), spawn_year = c(1998, 2008, 2015), init.age = c(4, 5, 5))
Here is my first point of uncertainty: in general, what are the differences to be expected when generating parameter estimates by using a grouping variable such as spawn_year vs translating spawn_year into a measure of age-at-encounters, as I understand can be accomplished within the "initial.ages" argument in process.data. I should clarify that I am interpretting the "initial.ages" to be "the age when the individual was first encountered", which corresponds to the first "1" in my capture histories. Correct me if this is incorrect, here.
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I have been proceeding to calculate the age-at-initial-encounter from the data above when processing data, as below:
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dat.pr <- process.data(ch_df, initial_ages = c(4 , 5))
dat.ddl <- make.design.data(dat.pr)
# Define parameters
Phi.age <- list(formula = ~ age)
p.dot <- list(formula = ~ 1)
# Construct models
results <- mark.wrapper(create.model.list("CJS", data = ch_df, ddl = dat.ddl)
# output in question
results$Phi.age.p.dot$results$real
My largest question is relating to the interpretation of this output. It appears as though I am not generating parameter estimates for age-structured survival, as the output looks something like this, where x-variables represent unique annual estimates:
Phi g1 c1 a0 t1 x1
Phi g1 c1 a1 t2 x2
...
Phi g1 c1 a28 t29 x29
p g1 c1 a1 t2 x30
This doesn't appear to be generating estimates of survival-at-age, so much as it resembles a model of time-structured survival estimates. I will note that the annual estimates do vary from those generated from a corresponding Phi ~ time model, although I am not certain why. Am I making some error in my code to indicate the variable use for assigning known age-at-encounters? Or am I making an error in my interpretation of parameter estimates?