Untransformed Estimates of coefficients for covariates issue

questions concerning analysis/theory using program PRESENCE

Untransformed Estimates of coefficients for covariates issue

Postby nischalism » Wed Apr 05, 2023 11:25 pm

Hello everyone!

I am working on a project that requires me to use occupancy modeling. I am trying to incorporate camera trap data with single-season occupancy modeling. I have 25 sites with camera traps and 3 camera trap replicates in each site. I am using four covariates in the analysis as well which I have normalized.
I analyzed the data in PRESENCE. First, I ran the global model (will all the four covariates) in order to determine the best model for detection probability. I placed all the covariates in Occupancy and changed the detection section with covariates and constant. This resulted in the model with global in occupancy and a constant in detection as the top model.
While viewing the model output, the untransformed estimates of coefficients for covariates (Beta's) shows extremely high values for psi and the standard error shows -1.#IND00. I have attached the Beta file below:
estimate std.error
A1 psi.a1 : -96.760763 -1.#IND00
A2 psi.crown_cover : 637.571835 -1.#IND00
A3 psi.slope : 879.662465 -1.#IND00
A4 psi.presence_termite : 753.653862 -1.#IND00
A5 psi.distance_road : 1666.162959 -1.#IND00
B1 P[3].b1 : -0.570545 0.346989
I wanted to show the how the covariates have influenced the detection of the species from this output from the detectability model, But the estimates as well as the standard error values does not seem to be interpretable.

And while viewing the individual site estimates of psi, I have been constantly getting the similar issues
Individual Site estimates of <psi>
Site estimate Std.err 95% conf. interval
psi 1 site1 : 0.0000 -1.#IND 1.#QNB - 1.#QNB
psi 2 site2 : 1.0000 -1.#IND 1.#QNB - 1.#QNB
[This is listed for just the first two sites. The rest 23 sites has the similar estimates]

Can anyone help me out with this issue?

Looking forward to hear your advise.
Thank you very much for your time in advance.
nischalism
 
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Joined: Wed Apr 05, 2023 9:46 am

Re: Untransformed Estimates of coefficients for covariates i

Postby darryl » Wed Apr 05, 2023 11:45 pm

Your model is over-parameterised (ie includes too many covariates). With a sample size of 25 I wouldn't recommend fitting models with anymore that 1 covariate on occupancy at a time as there's unlikely to be enough information in the data to estimate the effect sizes reliably.

As an aside, did you check that your covariate variables and relatively uncorrelated with each other?

Cheers
Darryl
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Re: Untransformed Estimates of coefficients for covariates i

Postby nischalism » Thu Apr 06, 2023 3:40 am

Hello Darryl,

I did ran the analysis with just two covariates only. While doing so and running the model, the one with the constants in both occupancy and detection [psi(.), p(.)] stood as the top model and while viewing the output, the beta values resulted as:
Untransformed Estimates of coefficients for covariates (Beta's)
======================================================================
estimate std.error
A1 psi.a1 : 22.643394 177278.221055
B1 P[3].b1 : -1.562185 0.305044

Even on this model, the standard error on psi was unpredictably high.

And even if I considered this model as the best one and proceeded further by making the detection constant and changing the occupancy, one covariate resulted with similar issues as stated in the previous post. ie.,
Untransformed Estimates of coefficients for covariates (Beta's)
======================================================================
estimate std.error
A1 psi.a1 : 17.219484 -1.#IND00
A2 psi.presence_termite : -8.465541 -1.#IND00
B1 P[3].b1 : -1.555629 0.345705

The individual site estimates of <psi> is also getting similar output as stated previously/ i.e.,
Site estimate Std.err 95% conf. interval
psi 1 site1 : 0.9807 0.4770 0.0000 - 1.0000
psi 2 site2 : 1.0000 -1.#IND 1.#QNB - 1.#QNB
[This is listed for just the first two sites. The rest 23 sites has the similar estimates]

And yes, I did checked the covariates for the multicollinearity.

Regards,
Nischal
nischalism
 
Posts: 2
Joined: Wed Apr 05, 2023 9:46 am

Re: Untransformed Estimates of coefficients for covariates i

Postby jhines » Thu Apr 06, 2023 9:03 am

Hi Nischal,

Since your dot model (psi(.)p(.)) gives an estimate of psi=1.0, I'm guessing that every site has at least one detection. In this case, the variance of psi is undefined (ie., there is no variation as it is always 1.0). Also, if there is no variation in psi, it cannot vary as a function of any covariates, so it isn't beneficial to construct models with covariates on psi. Since detection < 1.0, you can model it with covariates.

With psi=1.0, perhaps you need to re-think about the scale of the study area. If sites within the study area are too large, all sites will be occupied. Or, if the survey period is too long, the species may be entering/exiting the sites over time, which would require a multi-season model.

Jim
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Re: Untransformed Estimates of coefficients for covariates i

Postby darryl » Thu Apr 06, 2023 5:08 pm

In addition to Jim's points, the reason you get the large SE in the psi(.)p(.) model is due to the sigmoidal shape of the logit link. Once you convert the est and SE on the logit scale to the probability you get an estimate = 1 and SE=0. So large SE on the logit scale. So very large SEs on the logit scale aren't necessarily incorrect if the associated estimate is also has a large magnitude (eg < -20 or > 20), it may be an indication that the probabilities are being estimated as very close to 1 or 0. However, when you get SE's that include non-numeric values or negative values, something is going wrong, and there should be some warnings in the output to inform you.
Cheers
Darryl
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