age-specific/cohort CJS model

[williamMO]

HellO All,

I just got registered here. I wonder if someone can help me with questions listed below regarding age-cohort CJS model (addressed in Chapter
7 in Mark manual book). Any help is greatly appreciated.

Suppose I have three age groups, say age-0, age-1 and age-2. In each year certain number of animals were released from each age group and was recaptured for three occasions (an increment of 1 year between occasions). Now I want to use Mark program and estimate age-specific survival rate (i.e. survival rate for age-0, age-1, and age-2 groups). Here age-2 groups includes animals of 2-years old or older. The hypothesized encounter history is given as below:
encounter_hist age_group count
1111 0 20
1110 0 30
1100 0 10
1101 0 15
1000 0 5
1001 0 12
1010 0 16
1011 0 23
0111 0 30
0011 0 50
1111 1 40
1110 1 60
1100 1 70
1101 1 35
1000 1 25
1001 1 52
1010 1 66
1011 1 73
0111 1 40
0011 1 60
1111 2 90
1110 2 80
1100 2 70
1101 2 51
1000 2 53
1001 2 71
1010 2 37
1011 2 21
0111 2 50
0011 2 70


1. What should be the be input data format for me to age-cohort model? I assume I need 4 columns in the input data file like below:
encounter_hist age-0 age-1 age-2

1111 20 40 90
1110 30 60 80
1100 10 70 70
1101 15 35 51
1000 5 25 53
1001 12 52 71
1010 16 66 37
1011 23 73 21
0111 30 40 50
0011 50 60 70
The first column is the encounter history, the last three columns being the count for that particular history for each age-group! Am I correct?


2. Assume phi[1], phi[2] and phi[3] are the survival rates for age-0, age-1 and age-2 groups. Also,
For my PIM for survival rates, is it like the following?
Survival rate for age-0 group
--- j=1 j=2 j=3
i=1 1 2 3
i=2 - 1 2
i=3 - - 1

survival rate for age-1 group
--- j=1 j=2 j=3
i=1 2 3 3
i=2 - 2 3
i=3 - - 2

survival rate for age-1 group
---- j=1 j=2 j=3
i=1 3 3 3
i=2 - 3 3
i=3 - - 3
3. After I input the data in Mark, I can get the output summary, i.e. the commonly known m-array for each age-group? Are those summary data
Mark used when running the analysis?
The summary data for age-0 is given below
----------------- j=1 j=2 j=3 total
i=1 (Ri=131) ----- 75 39 0 114
i=2 (Ri=30+75=105) - 80 0 80
i=3 (Ri=50+119=169) - - 150 150

I see this output summary problem is not correct. Since if we look at i=2, Ri=30+75, where 30 is newly released animal at occasion i=2, while 75(at age-1 now) is the total number of animal released at occasion i=1 but re-captured at j=1. But, those 105 animal are of different ages. If this is the data Mark uses for analysis, how can we distinguish the age-difference among 105 animals. Do I misunderstand anything here?


Thanks for your help!

[cooch]

Don't have time at the moment for a lengthy answer, but some cautionary advice: age, cohort and time are linear functions of each other. Meaning, you can only build an estimable model with 2 out of 3 (a full age x time x cohort model would be massively non-identifiable).

Having said that, an age x cohort model is potentially problematic since you wouldn't be able to differentiate age and (possible) time effects. In other words, you won't know if the 'effects' you see are due to age, or time, or both. This is likely the reason that I'd have to think really hard of a single example of an age x cohort model being published anywhere )there are in fact precious few studies that have considered cohort effects at all -- in most cases, cohort effects are ascribed to things like 'early growth conditions', which often means 'marked as juveniles', which means...confounding of age and time effects. There are a few ways around some of the problems, but not many. And, as a result, relatively few uses of 'cohort models'). While an age x cohort model would be identifiable (by and large), it might not be particularly informative, since age and time effects might be confounded.

Just something to think about...