Unequal time intervals between seasons

[Brenda Shepherd]

Hi Everyone

 

I'm following up on this post entitled “missing year in dynamic model”.

https://groups.google.com/forum/#!searchin/unmarked/missing$20year%7Csort:relevance/unmarked/yVUu8CYOrn8/YFXjce557B8J

 

I have 4 years of amphibian detection data with 3 site-visits/year for 2010, 2011, 2012, and 2015 and I will continue to have data on a 3-year interval (again in 2018 and so on). In the previous post, Jeffrey suggested using a model that has a separate set of parameters for the longer time interval.  I want to make sure that I understand how to fit the models using the colext function.

 

Does this simply mean that all the models I fit have year-dependent colonization and extinction? Am I correct in using this approach as long as I interpret that the parameters for “year 3” actually represent colonization / extinction over a 3-year period.  If I’m way off, I’d be very happy to hear any thoughts on how to approach this in a better way.

 

Thanks,

Brenda

[Evan Cooch]

The issue of unequal intervals between primary sampling periods problematic, and has been discussed in some detail in the MARK book wrt to multi-state and robust design models (being, two models where individuals can move between states). The occupancy models (which are now covered in the MARK book) are a model clearly based on the robust design, so some of the 'discussion' in the MARK book probably applies (although how strictly it does depends on how unmarked handles unequal intervals. In MARK, you can specify the interval length at the outset of the analysis, but (and its a big but), how this works, and how to interpret the results, depends on the type of model you're using. 

For starters, have a look at section 15.9 in Bill Kendall's robust deisgn chapter: http://www.phidot.org/software/mark/docs/book/pdf/chap15.pdf#page=49

The basic point is, if the intervals between seasons are unequal, interpreting gamma and epsilon can get tricky.  For example, if epsilon over a single year interval is 0.5, and epsilon over a 3 year interval is 0.5, what can you comfortably conclude? Perhaps nothing -- over a 3 year interval, who knows what the unobserved colonization/estinction transtitions really were. Simply using the 3rd root of 0.5 as an estimate of the 3 year interval makes a number of heroic assumptions. 

Hope this helps. 

[Shelby]

Hello everyone, I have a follow-up question on multiple years between sampling occasions.

https://groups.google.com/forum/#!searchin/unmarked/missing$20year%7Csort:relevance/unmarked/yVUu8CYOrn8/YFXjce557B8J

https://groups.google.com/forum/#!searchin/unmarked/years%7Csort:relevance/unmarked/CcBKtJRjr3k/Apf5MhOuAQAJ

After reading the MARK chapters and similar post (provided above) I’m still unclear on how to build models with different time intervals between primary periods. What would this look like in unmarked using colext?

For a little background, I have data from a long-term project that collects count herp data for 3 or 4 consecutive years before a treatment and 3 or 4 consecutive years after treatment.  Treatment years are not sampled (1 year gap). We have had two treatments so far, which occur every 15 years.  Therefore, as of now I have 14 sampling years spanning 22 years, with a large 6 year data gap between the two treatments.

Data within sampling years is collected fairly evenly.  Each sampling array is visited daily for 5 months during the active season. What we are attempting to do is estimate occupancy/detection for our rarer species. Since we have daily sampling, but low detections we are grouping daily sampling data into month long “surveys” and designating year as our primary (closed) periods.

My goal is to run single-species, multi-season occupancy models with site covariates, yearly covariates, and observation covariates. My concern is that the estimates for col/ext will be biased after the 6 year gap, since it seems illogical to estimate col/ext for 2008 from 2001 estimates.  I am hoping that the 6 year gap doesn’t prevent us from running multi-season models, and if it does what would be a good alternative?

Any advice would be appreciated and an example would be great!

Thank you,

Shelby

[Kery Marc]

Dear Shelby,

a comment on what you say at the bottom "My concern is that the estimates for col/ext will be biased after the 6 year gap, since it seems illogical to estimate col/ext for 2008 from 2001 estimates.  I am hoping that the 6 year gap doesn’t prevent us from running multi-season models, and if it does what would be a good alternative?".

Why would you expect a bias ? I don't see why the estimates from a model with long intervals lacking observations should be biased. Presumably, you will get pretty bad estimates, in terms of the precision, but this is exactly what you would like to have: that your model accounts for the added uncertainty induced by the lacking observations.

As so often, one could say "Simulation is the answer" :) If you are worried about the behaviour of the model in this specific situation, then why not run a simple simulation, say, with exactly your sample size (and missing value pattern) specifications and perhaps with all parameters (psi1, col, ext, p) varying randomly according to 4 uniform distributions over the range that you expect for your species ? Then, you fit the model to 100 simulated data sets and see how good the estimates become.

We have a function dynocc.fn in the AHMbook package, which simulates regular (i.e., balanced) dynocc data. You can then shoot missing values into the resulting data sets to create a data set that looks like yours in terms of the missing values.

Best regards  --  Marc

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From: unma...@googlegroups.com [unma...@googlegroups.com] on behalf of Shelby [shelb...@gmail.com]
Sent: 18 December 2017 15:43
To: unmarked
Subject: [unmarked] Re: Unequal time intervals between seasons

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[Shelby]

Hi Marc, Thank you for your quick response and suggestions.

I've realized I may not have described my data well, currently I am only using 14 primary periods (years) that span 22 years. I have not included periods (with just NA's) for the large 6 year gap or the year gaps that occur during a treatment.  Is that what you were suggesting by saying "long intervals lacking observations" or I'm I misunderstanding you? If unmarked understands that there is a gap by providing a 'year' covariate and provides estimates that account for the lack of data then ignore the rest of my message.

If not...

I am not sure how unmarked handles the gaps when making estimates. Does unmarked assume equal amounts of time between primary periods?

My assumption with how my data is currently set up was that unmarked couldn't tell there was a gap and would therefore calculate the col/ext estimates for 2008 directly from 2001 estimates and therefore be "biased" for 2008. If so, is there a way I can tell unmarked that there is a large data gap between 2001 and 2008, or should I create periods for the long intervals with missing data? Would creating these long periods with missing observations make it harder for models to converge?

As Brenda mentioned earlier Jeffrey suggested using a model that has a separate set of parameters for the longer time interval, but I'm not sure what that model would look like.

Sorry in advance for so many questions. I am new to both unmarked and R so I greatly appreciate the guidance.

Thank you,

Shelby

[Kery Marc]

hi Shelby,

OK, that makes sense to me. In Markov models such as the dynocc model, when you have missing occasions, I think the easiest is to "fill them up" in the data with NAs. Now, to be honest, I don't know whether colext will take that, but you ought to try. If not, you could use BUGS software, there such things are easy.

In a model without NA-filled-in data for missing primary occasions, there is nothing wrong with fitting a model with full time-dependence in the col-ext parameters: the params for the long intervals will simply have a different meaning from those associated wit the regular interval length. But problems start as soon as you want to constrain that fully time-dep model for instance by making the parameters constant or covariate dependent.

Best regards  --- Marc

---

From: unma...@googlegroups.com [unma...@googlegroups.com] on behalf of Shelby [shelb...@gmail.com]

Sent: 18 December 2017 18:56
To: unmarked
Subject: Re: [unmarked] Re: Unequal time intervals between seasons

[Izabela Barata]

Hello everybody,

 

I have come across this topic and I have some questions related to my data analysis since I have unequal time intervals (survey gap) between primary periods.

I am looking at population trends and fitting multi-season occupancy models for a frog species that is restricted to bromeliads (plants) and has low dispersal capability. My sampling sites (plants) are tagged with a number that allowed repeated visits from 2014-2017. I did 1-4 monthly visits each year, which consisted of 4-6 survey occasions (1 occasion = 1 survey night). I am considering month as a primary period (T=10) and survey occasions as secondary periods (t=6, I included missing values for unsampled occasions). To make this clear, I am attaching a .csv file with an example of my data and also with the summary of my umf. 

I am using unmarked to run my analysis. I am concerned about the variation in interval between my primary periods: within each year the gap between primary periods is short (ca.  1 month), but then the gap between the last primary period of that year and the first primary period of the following year is quite big. In other words, the gap between April 2015 (primary period #4) to May 2015 (primary period #5) is much smaller that the gap between May 2015 and February 2016 (primary period #6).

 

Would that be a problem in the likelihood function which could lead to potential misleading estimates of col/ext parameters? Or can I obtain the estimates and consider, as Mark mentioned, that the params for the long intervals will have a different meaning from those associated with the short intervals?

 

Any thoughts on that would be much appreciated!

Best regards, Bela

[Evan Cooch]

For closed sampling/modeling, unequal intervals is a non-issue. For open, dynamic models, in general, it is (potentially) an issue, for the state transition parameters, like (say) epsilon or gamma in a multi-season dynamic occupancy model. The usual 'trick' is to use an algebraic approach by evaluating the 'nth root' of the parameter, where the assumption is there are n time units over a particular interval. Some software makes this trivially easy to do. You end up with estimates that are the nth root of the interval.

However, this is not always a perfect solution, and can (and has) lead to problems in interpretation. I would suggest that, as a starting point, you have a look (again, or for the first time) at several sections of the MARK book: http://www.phidot.org/software/mark/docs/book/

In particular, pp. 24-34 in Chapter 4 (the material in the - sidebar -), and then section 15.9 in Chapter 15 (the robust design chapter Bill Kendall wrote, where said RD is, of course, the structural basis for a dynamic occupancy model), and section 10.6 in Chapter 10 (the multi-state chapter). Some of the arm-waving alludes to things you do in Program MARK (where there is an easy and explicit way to model unequal intervals between primary samples), but the larger points to be cautious about are 'software neutral'. The short form is -- modeling the unequal intervals is one thing (and can be mechanically easy) -- interpreting what comes out of those models is potentially less easy.

Some of this is a re-hash of earlier posts in this thread, but at one point, the focus seemed to be (to me, at least) on mechanics. I submit (again, I suspect) that mechanics isn't necessarily the problem (heavy unmarked users can/will adivse) -- interpretation might generally be. Again, the problem isn't unevenness between secondary samples, where the assumption of closure allows you to do any number of things, including messy sampling intervals. The problem is the 'open parameters'.


Hope this helps.

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