Multi-state and missing occasion COVID conundrum

[X33277]

Hello there, I am sure I am not the only one trying to reconcile a missing occasion from COVID. I am working with a multi-state model with 3 geographic states and 2 harvest states from 2017-2023. I have read "the bible" religiously, especially chapter 10, however I am still unclear of the best approach. No sampling occurred in 2020 but we still obtained harvest data. As such, I added a 0 to the capture history for 2020 for each geographic state and fixed p=0. The parameter of interest is psi, particularly time varying in relation to an environment covariate. The top model without time variation in psi is S(G)P(G*t)psi(G). Detection is fairly high with p ranging between .4 and .8 between states. When I build a psi(G*t) model things seem to fall of the rails and the parameter estimates don’t make any sense. Obviously, all psi parameter estimates from 2019-2020 and 2020-2021 don’t have any data and assume is the root of the problem. If I constrain the psi transitions from 2019-2020 and 2020-2021 to the estimates from the psi(G) model I get estimates that make sense psi for 2017-2018, 2018-2019, 2021-2022 and 2022-2023. This also becomes the top model with a delta AICc of 23 for the second top model. This seems slightly unfair since I am essentially getting parameter estimates for free. To account for this, I adjusted the number of parameters in the model upwards accounting for the number of fixed parameters that were “borrowed” from the psi(G) model. The top model remained the same however the second top model now had a delta AICc of 4, so a seemingly more even playing field. Just wondering if there is anything inherently wrong with this approach or if anyone has an alternative approach to a similar problem.
Any thoughts or suggestions are greatly appreciated.

[jhines]

Since you're missing data from 2020, you should set S(2019)=1 for all strata, which means the estimates of S for S(2020) will actually be the probabilities of of surviving from 2019 to 2021. Similarly, fix psi(2019)=0 (ie., individuals remain in strata) for 2019, causing the estimates for 2020 to be the probabilities of transition to other states during the 2-year interval.

One other recommendation is to try multiple starting values in multi-state models, especially if estimates are "whacky".

[X33277]

Voila! Thanks Jim, that is perfect and does the trick nicely and works way better than what I was trying to do. Now I get the all important psi for 2020-2021 although with the caveat of it representing the 2 year interval.
Greatly appreciate the advice!
Thanks very much.

[cooch]

Voila! Thanks Jim, that is perfect and does the trick nicely and works way better than what I was trying to do. Now I get the all important psi for 2020-2021 although with the caveat of it representing the 2 year interval.
Greatly appreciate the advice!
Thanks very much.

It is worth thinking hard about what psi represents -- especially if you think it 'all-important'. As per section 10.6 in Chapter 10 (the MS models chapter), MARK will attempt to 'correct' estimates of survival for unequal intervals (for whatever reason intervals are unequal -- discussed in some detail in chapter 4), but doesn't do anything for estimates of psi. Largely because psi is not unambiguously interpretable over multiple intervals, short of heroic assumptions and/or constraints, or both.

[X33277]

Thanks Evan that is a good point. Jeff mentioned as well that fixing S=1 also will be problematic if we are obtaining recoveries over the missing occasions. One group was not harvested so they will be fine but may need to rethink for the harvested group. The one piece we do have is telemetry data for the missing years although only a decent sample size for the 2019-2020 missing year. Perhaps it could be reasonably justifiable to fix psi for 2019 to 2020 to that of the gps data. Although we are dealing with 20 individuals between 2 states it is not a large sample size but would close the gap and 2020 to 2021 psi could then be estimated on its own.

[cooch]

Remember that a MS approach to dead recoveries (which is described in Chapter 10), and a mixture of dead things with other (typically live things) is not. Meaning, if you are using a MS approach to handle joint estimators, you need to do a *lot* of work up front. I've seen people simply assume that 'dead' is a simple absorbing state, but it requires more care than that. My general advice is that unless you have a really compelling reason to us MS approaches, then don't. The 2 examples in Chapter 10 were simply designed to demonstrate that you *could* in theory use MS in MARK to handle various data types (specifically 'live encounter CJS', and 'dead recovery Seber'). But...the salient question in many cases is...why would you?

There are situations I could imagine, but then the job is to work out exactly how to set things up, what constraints are needed, and how to interpret things correctly. Simulation is your friend.

[jlaake]

I'll intervene here because David and I have been talking off-list. He is switching over to the MSLD format but will still have the same problem with the missing year. What I think David was mentioning was that because he has harvest data during the covid year, he can estimate S for the missing year from the recovery data rather than assuming it is 1. But he still cannot estimate Psi. I suggested that if he sets Psi to stay in same stratum like Jim suggested then to represent the 2 year Psi he would have to use time dependent Psi (at least for the 2 year period) when in fact either time constant or other constraint like he mentioned might be better.

[cooch]

Fair enough. I concur. There is no perfect solution, but what has been suggested seems solid.

[X33277]

Yes my formulation of the MS live recovery data using an absorbing state for harvest was incorrect. Thanks again for the help, suggestions and clarification.