Reversed signs on Beta estimates?

[EGNolte]

I'm a new MARK user, attempting to model detectability from double-observer counts using Huggins closed-capture models. I seem to have run into a problem. Using binary individual covariates, I created a model that included the identities of the observers who detetcted each animal. When I reconstituted the estimates of p for each observer, they turned out to be much lower than I expected, all less than .5, when I knew that observations by primary observers vastly outnumbered detections by secondary observers. Furthermore, the most experienced observer had the lowest estimate of p, less than .1, while the first-time observers had the highest estimates of p. It would seem as though the signs for all the beta estimates have been reversed, so that the model is estimating the probability of non-detection. Has anyone run into this problem before? What did I do wrong?

[bacollier]

EG,
I saw no one has responded to your post yet. You might need to post a snippet of your .inp file. I assume that for each set of paired observer surveys you ran, you would have designated 1 observer to be the primary (1st) and 1 to be the secondary (2nd) observer, and they would not change within a survey period (such as set of 10 point counts) ? Or, do you have the observers switching between primary and secondary at each survey location (observer 1 is primary on surveys 1, 3, 5, 7,9, observer 2 is primary on surveys 2, 4, 6, 8 10)?

Can you provide a bit more detail on how your study was designed/some or all of your .inp file (appropriately annotated) and I will see if I can lend a hand.

Bret

[EGNolte]

Bret,

Thanks for responding. I'm sorry I stopped checking the forum after a few days. I still have not figured this issue out.

My experiment involves an hourly count of migrating raptors. Two pairs of observers are present. One pair is designated primary, and the other secondary, and they perform roles analogous to those described by Nichols (2000) for point counts. I have coded the capture histories of birds detected by the primary observers as '10' and birds detected by the secondary observers as '01.' Because detection by the secondary observers is dependent on non-detection by the primary observers, I have set c=0. The structure of my input is demonstrated below. The fields labeled with two-letter codes in caps are dummy variables indicating whether or not a given observer was on the detecting observer team (So for each record there are two of these 9 fields marked 1, and the rest 0, Unless the second observer of the pair was not one of the 9 regular observers, in which case there is only one). My design matrix includes columns for each of these variables.

/*...Field List: #Identifier#, History, Frequency, DK, DR, EN, GM, ID, JG, JK,
PA, SC, Accipiter, Buteo, Circus, Eagle, Falco, Osprey,
Alt/Dist, Wingspan, BPH, CldCover, WindV, WindNS, WindVNS, Temp,
Baro, Date, Year, Day, Hour*/

/* 1 */ 10 1 0 1 0 0 0 0 1 0 0 0 0 1 0 0 0 4 43 9 1 7.2 -1 -7.2 34 24.43 40052 1 3 15.0 ;
/* 2 */ 10 1 0 1 0 0 0 0 1 0 0 0 1 0 0 0 0 4 49 9 1 7.2 -1 -7.2 34 24.43 40052 1 3 15.0 ;
/* 3 */ 10 1 0 1 0 0 0 0 1 0 0 0 0 0 0 1 0 5 22 9 1 7.2 -1 -7.2 34 24.43 40052 1 3 15.0 ;
/* 4 */ 10 1 0 1 0 0 0 0 1 0 0 0 1 0 0 0 0 5 49 9 1 7.2 -1 -7.2 34 24.43 40052 1 3 15.0 ;

[jlaake]

Not sure whether it exaplains your results, but typically a removal (dependent) observer is coded as 11 and 01 and c=1. Offhand your approach seems like it should give the same result. Maybe you are misintepreting the beta/p estimates. Did your observers rotate between primary/secondary roles? If not then you'll have problems as well. Also, is it 2 pairs of observers so you have 4 observers with 2 being primary as a team and 2 as a secondary team? Also it sounds like there are observers not included in the covariates. Is that correct?

--jeff

[EGNolte]

Hi Jeff,
I've tried both schemes, and you are correct, they are exactly identical in results. The paper first describing the removal double-observer method for bird surveys uses the 10, 01 coding, so that's what I've decided to use. I could be talked out of it, if 11,01 is much more easily understood.

I did rotate observers between primary and secondary roles every hour- all combinations were in each role roughly half the time.

Now- here's something you got me thinking about...
Numbers of birds-per-hour at this site are highly variable and unpredictable- one hour is often very different than either the one before or after. Some observers may have been "lucky" enough to have been in the primary role on more "big hours" than others, just by chance, and this would lead to an artificially inflated estimate of that observer's effect on detectability, due to the asymmetry in the dependent design, am I right?

Looking at my Spearman correlation matrix, the signs of the correlation coefficients of observers with birds-per-hour all match the signs of the estimates of Beta for those observers!

I feel I may have found the smoking gun here. Now how do I fix this? Can I force MARK to fit the effect of BPH before the observer effects?

--Eric

[EGNolte]

I've had a lightbulb moment. Bear with me.

Hows this for a solution:

What I want to do is condition the estimate of beta for each observer on the total number of birds detected in the hours in which that observer was in the primary role. This is a single number for each observer. let's call it 'g subscript x'

What if, in my design matrix, I change my observer dummy variable columns to read "product(DK, g subscript 1)", "product(DR, g subscript 2)", and so on for all the observers?

Would this do what I think it would?


--Eric

[jlaake]

Eric-

I think you are off track. The number of detections per se does not influence your estimates of detection probability unless somehow with a lower number they are bored and more likely to miss and when they are high they are move attentive. This seems unlikely. I suggest you look through your data and design to make sure you have things correct.

--jeff

[EGNolte]

Jeff, I understand you are correct in that the total number of birds observed has no effect on the overall degree of effect of observers, or any other variable, on detectability.

This is merely a matter of correctly apportioning that overall effect among my observers- the overall degree of effect is unchanged. I would simply be calculating my betas on a per-bird basis, which should give numbers that more accurately reflect the RELATIVE effect of each individual observer.

For a grouping variable the marginal totals do effectively determine the estimates of beta, unless I'm horrily mistaken.


--Eric