Approach for Known Fate/Staggered Entry/Age Transition

[bacollier]

All,
I guess this is a follow up question to the thread 'known fate model and age' posted 14 July 2004 on this forum at the below address, (http://www.phidot.org/forum/viewtopic.p ... hlight=age). But, I had some additional questions so I thought I would repost.

Situation: I have a known fate dataset (30 encounter occassions-months over 2.5 years) where individuals were captured every January (2001, 2002, 2003) as either juveniles (~6 months old) and adults (~1.5 years old). Juveniles transition to adults on 1 June based on the structure shown in the above thread with 2 encounter histories for each individual, captured adults stay adults throughout. The 'at-risk' period for juveniles is between 1 and 6 months (when they transition to adults at the median of the breeding season).

I want to estimate survival based on age and I was a little unclear on how known fate in MARK estimates the beta and real parameters for juveniles. So, trying out a simple model (B_0 + B_1*Age), and using user-defined individual covariates I get a constant estimate for all 30 encounter occasions, which I suppose would make sense if there were juveniles at-risk in all occasions, but, from July-December of each year, all individuals are classified as adults as all juveniles were censored at the end of May.

So, I went and build a time-dependent age model (Age on the diagonal following the MARKBOOK individual covariate chapter) and set user-defined individual covariates to 1 (Adult) and I get age-specific estimates of survival for each encounter occasion. When I do the same for juveniles, I get beta and real estimates for all 30 encounter occasions, even though there were only 18 months where juveniles were at-risk as juveniles?

So, I went to the Age and Cohort Cp. in the MARKBOOK and had no luck figuring this out? I guess I am unclear on how known fate in MARK estimates juvenile survival for periods when the at-risk set has zero individuals in it?

Am I looking at this the wrong way? Does anyone have an suggestions/comments/direction?


A small piece of my encounter history follows with individual covariates of Sex, Age, Site, Region.

/*2299-1.035-A*/ 101010101010101100000000000000000000000000000000000000000000 1 0 1 1 1;
/*2293-0.024-A*/ 101010101010101010101010101010101010101010101010101010101010 1 0 1 1 1;
/*2291-1.135-J*/ 101010000000000000000000000000000000000000000000000000000000 1 0 0 1 1;
/*2291-1.135-A*/ 000000101011000000000000000000000000000000000000000000000000 1 0 1 1 1;
/*2297-1.916-A*/ 101011000000000000000000000000000000000000000000000000000000 1 0 1 1 1;
/*2298-1.844-A*/ 101010101010101010101010101010101010110000000000000000000000 1 0 1 1 1;
/*2284-0.594-A*/ 100000000000000000000000000000000000000000000000000000000000 1 0 1 1 1;
/*2288-0.784-J*/ 101010000000000000000000000000000000000000000000000000000000 1 0 0 1 1;
/*2288-0.784-A*/ 000000101010101010101010101010101010101010000000000000000000 1 0 1 1 1;

[ganghis]

Typically one would want to enter the different age classes as different groups rather than as covariates. Then you can use the PIM structure to specify when juveniles turn into adults.

Paul Conn

[bacollier]

Paul,
Thanks, I have some other individual covariates (continuous data) that I was interested in working into the analysis that won't work with the group data format. I did not include them above to reduce the amount of info thrown out, sorry.

Bret

[bacollier]

All,
A little followup. Using suggestions from Paul and from offlist, using a test dataset, I worked up a PIM for juvies (e.g., 30 encounter occasions, juvies for the
first 3, so 1, 2, 3, 4, 4, ..., 4; then adult PIM is all 4's) in the grouped data format.

With this structure, I get 4 S_hat estimates:
1:S--1.00
2:S--1.00
3:S--0.90
4:S--0.96

All of which make sense as no juveniles died in the first 2 intervals, 1 died in the 3rd (from a 'at risk' set of 10 thus 9/10), and the 0.96 coincides with a additive "age' when I use a DM column with age and set the covariate=Adult for a dataset using encounter histories.

When I run the same model (using encounter history data) with age=juvenile, I get estimates of S_hat for juveniles of 0.96, when the estimate (I thought) should be 0.90 (1 died out of 10 during the 3 intervals that had juveniles), anyone know why this would happen?

So, tinkering with the DM yesterday, I managed to get 'close', but I have no faith in these estimates. Using the below DM


1 0 0 0
1 2 0 0
1 0 2 0
1 0 0 Age
1 0 0 Age
. .
. .
. .
1 0 0 Age

I get the below estimates (note that the Age column (4:S) in these results would go down to 30 encounter occasions with the same numbers).

Parameter Estimate
1:S 0.9772728
2:S 1.0000000
3:S 0.9000000
4:S 0.9679359



So, 2:S and 3:S in theory are OK, 4:S is off a bit (0.0016), but 1:S should be 1.00 (no juvenile deaths in that interval). However, I do not think that the estimates for 1:S-3:S are correct, as they are not specific to Age=Juvenile, but to the time period and thus probably include adults.

Then, I tried to force Age=Juvenile (=0) for the 1st 3 parameters using product(0, Age), and then estimate Age=Adult (setting the individual covariate=1) for the full 30 periods in a different column, but then I get a >200 in AIC and estimates for the 1st 3 periods of 0.50?


So, to date, I have not been able to figure out how to make this work. If anyone has any suggestions let me know. I am also somewhat interested in why I get the same estimates when I set the individual covariate=Adult, but not for Juvenile in the DM?