Should I be concerned that Phi = 1?

posts related to the RMark library, which may not be of general interest to users of 'classic' MARK

Should I be concerned that Phi = 1?

Postby TheCarmeleon » Tue Jan 11, 2022 10:51 am

Hi everyone, I'm currently running some CJS models in RMark using capture-mark-recapture data, over a time period of 6 years. There would be more but the pandemic has put a stop to things over the past couple of years. I've run GOF tests with the data, and everything passed with flying colours (which was a relief!). Despite this, I'm slightly concerned as the top three models (based on the AIC table) are telling me that the survival estimates (Phi) are 1. When using less data (during the time when I was first learning how to use RMARK over the summer), I had some more sensible outputs, that made sense knowing what I do about our study species.

What would you suggest I can do to help troubleshoot this problem? It is a problem?

Thanks in advance for your help.
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Re: Should I be concerned that Phi = 1?

Postby cooch » Tue Jan 11, 2022 11:06 am

This question is more general than RMark-specific, but I'll leave it here for now.

TheCarmeleon wrote:Hi everyone, I'm currently running some CJS models in RMark using capture-mark-recapture data, over a time period of 6 years. There would be more but the pandemic has put a stop to things over the past couple of years.


I anticipate this will be a common issue moving forward. I'm personally dealing with lack/cessation of data collection for several very long-term data sets (>40 years minimum). If/when things start up again, there will (I suspect) be a bunch of questions of 'what to do if you have large-ish' gaps in the time series. I digress...

I've run GOF tests with the data, and everything passed with flying colours (which was a relief!). Despite this, I'm slightly concerned as the top three models (based on the AIC table) are telling me that the survival estimates (Phi) are 1. When using less data (during the time when I was first learning how to use RMARK over the summer), I had some more sensible outputs, that made sense knowing what I do about our study species.

What would you suggest I can do to help troubleshoot this problem? It is a problem?


I'd start by seeing if the parameter(s) that are being estimated close to the boundary (in your - typical - case, 1.0) are actually 1.0, or if the numerical optimization simply doesn't have enough 'information' (data) to be able to differentiate one estimate (say, 0.985) from another (say, 1.0). MARK has the ability to differentiate between 'intrinsically' or 'extrinsically' nonidentiable parameters, using 'data cloning' -- Appendix F. [You can't do data cloning automatically using RMark -- it is a function (one of several) that is built in to the classic MARK GUI. If you read Appendix F, you could probably figure out how to tackle it manually -- starting by creating a copy of the .inp file where the number of encounters is multiplied by some factor -- say 100 -- but that might be more work than you want.]

Then, if you end up concluding that - yup - some parameters really are 1.0, then there is an argument you could make that these are not estimated parameters, and you could manually reduce the parameter count(s) accordingly, which will in turn adjust the AIC.

So, thats a starting point.

Having said that, 9/10 times when you have parameters estimated at ~1.0 (99% of the time for a time-dependent model for some/all of the model parameters), the root cause is 'extrinsic nonidentifiability' (meaning, insufficient data).

Good luck...
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Re: Should I be concerned that Phi = 1?

Postby sbonner » Tue Jan 11, 2022 11:18 am

Hi Steve (?),

It sounds like it could be a problem if it's not what you expect. What is the species that you are working with? Are they particularly long lived? Nothing lives forever and with 6 years of good data you should be able to detect that survival is less than 1 even for very long-lived species. I'm thinking of experience with cetaceans that have yearly survival of .95 or above.

My first question would be about the estimated capture probabilities. Are they estimated to be very low? Also, do you have any individuals that were detected many years apart -- particularly in both the first year and the last year. If capture is low and you have a few individuals that you observe in the first and last years then it is easy to get survival probability estimates that are close to or exactly equal to 1.

If you have estimates on the boundary then you will probably also have confidence intervals that cover the entire (0,1) interval. This is because the usual math needed to compute standard errors falls apart. If this is the case then you should rerun the model using profiling for the survival parameters. This won't change the estimates, but I expect you will find that the confidence intervals are very wide (e.g., .5 to 1). Essentially, this is saying that the best guess that survival is 1 but there is a lot of uncertainty and the truth could be much different.

Unfortunately, this really sounds like a data issue. Is it possible that there might be errors identification that make it seem that individuals survived for much longer than they realistically could have? Are the capture probabilities likely to be very low?

It might help if you can provide a summary of your data. How many individuals did you capture? What is the distribution of captures per individual (number with only 1 capture up to the number with 6 captures)? What is the distribution of time between captures?

I hope this helps,

Simon
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Re: Should I be concerned that Phi = 1?

Postby TheCarmeleon » Tue Jan 11, 2022 11:57 am

Hi both,

Thanks for your really helpful advice. It's always valuable when someone with more knowledge than yourself has some input on things. First, to answer your questions Simon I'm working with snakes and as you're probably aware, they have a low detection probability to begin with so my between-year recaptures are quite low. There were also only a handful of individuals that were detected a couple of years apart, most individuals (if ever re-encountered), are done so the following year to their original detection.

I've captured and identified 936 individuals over that timespan. The distribution of captures is as follows:
* 1 capture - 831
* 2 captures - 97
* 3 captures - 5
* 4 captures - 3
* 5 captures - 0
* 6 captures - 0

The distribution of time between the captures is a just under a year, with my capture data being truncated to only count for the summer months, when there is data available for each of the six years. Given the advice so far, I'm starting to suspect that this is a data issue. Would the suggestion of the data cloning help me with determining this?

Steve
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Re: Should I be concerned that Phi = 1?

Postby cooch » Tue Jan 11, 2022 12:20 pm

TheCarmeleon wrote:Given the advice so far, I'm starting to suspect that this is a data issue. Would the suggestion of the data cloning help me with determining this?


Based on your data summary, your encounter probability is likely to be too low to satisfactorily estimate parameters near the boundary (echo everything Simon mentioned).

And yes, the larger intent of data cloning as implemented in MARK is to help you differentiate whether or not the nonidentifiability is intrinsic (a function of the model -- for a CJS model, this only applies - potentially to parameters at the end of the time series), or extrinsic (insufficient data). As I mentioned (and as Simon also surmises), very likely the latter in your case. Which basically means -- limits to what you'll be able to do (unless you are lucky enough to have strong informative covariates).
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Re: Should I be concerned that Phi = 1?

Postby TheCarmeleon » Tue Jan 11, 2022 12:23 pm

Thanks for all of your help, I really appreciate it! I know what I'm going to be doing tomorrow now then, wish me luck.

Fingers crossed it doesn't take me all day but I'll let you know how I get on.
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Re: Should I be concerned that Phi = 1?

Postby cooch » Tue Jan 11, 2022 12:35 pm

TheCarmeleon wrote:Fingers crossed it doesn't take me all day but I'll let you know how I get on.


Shouldn't take that long. Pull your .inp file into regular classic GUI-based MARK, run the default CJS model (fully time-dependent), then do the data cloning.
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