individual site psi estimates

[tpinn]

Hello again,
I noticed in models for a few species I have individual site estimates of psi = 1 for all sites (but in models where naive occupancy is only around 0.1 - 0.2). I am wondering if this is evidence that the model just does not fit, but wasn't sure. The GOF stats are fine, but I thought perhaps the psi estimates indicated a problem. Does anyone have an idea? Thanks for any help!

Tracy

[jhines]

Hi,

If naive psi is 10-20%, then 10-20% of the sites must have detections. If you're getting psi=1, then detection probability must be very low, causing the model to 'think' that most all non-detections are due to the low detection probability. Does your data look like the detection probability is very low?

Another possibility is that you have insufficient data for the number of parameters you're estimating. How many 'Beta' parameters are you estimating, and how many sites/surveys do you have?

Jim

[murray.efford]

I think it's a systemic issue. Guillera-Arroita (2011 Methods in Ecology and Evolution) noted on p 403 "Occupancy estimates at the boundary of the parameter space (psi = 1) were always obtained for the case where there was only one occupied subunit at all sites that were occupied, that is, when there was at most one detection in the history per occupied site. Indeed, these results match the theory regarding the conditions for obtaining boundary estimates under the standard single-season occupancy model (Guillera-Arroita, Ridout, & Morgan 2010), thus supporting the validity of the simulations."

I noticed the same in some simulations and treated these cases separately (Efford & Dawson 2012 Ecosphere Fig 6).
Murray

[tpinn]

Thanks for the replies! I have 282 sites, 5 surveys at each site, and 10 parameters. For occupied sites, species were detected at more than one survey sometimes, but detection probabilities are probably low. But I also noticed that the standard error for the psi estimate is quite high (>50,000). So I am thinking this signifies a problem with the model?

[jhines]

If psi is 1.0 (or 0.0), the standard error is undefined, so you can ignore the 50,000.

Did you try simpler models? I recommend starting with the 2 parameter model (psi(),p()), then the survey-specific model (psi(),p(t)), then adding covariates one at a time. Sometimes, a covariate may cause the model to not converge, or converge on unreasonable estimates due to the distribution of the covariate with respect to a parameter.

[tpinn]

I am using the spatial correlation model, and when I removed the covariates I still get psi estimates of 1. Interestingly, when I use the regular single-season model (even with covariates), I do not have this issue (psi varies per site, but is pretty low, as would be expected). But the spatial correlation method is a better fit for my data. The data sets with this issue are pretty sparse, so perhaps that is the trouble?

[darryl]

You are aware that the 'spatial' correlation model relates to the detection process and assumes some correlation of the detection probability in successive surveys? It's not spatial correlation in terms of occupancy. It is called the 'spatial' correlation model becuase in the original motivating problem the repeat surveys of a site were spatial replicates (segments of a transect) rather than temporal, although I can imagine a similar type of correlation can occur for temporal surveys. Do you have some reason to expect correlation in the detection process? 5 survey's won't give you a lot of information about any underlying correlation, but it's a start.

You may of course just be finding a spurious result, estimates that fit the data really well, but without biological meaning. If the regular single-season model is giving you believable results, I'd be nervous about these results, but it's hard to say more without seeing more detail of the analysis.

Darryl

[tpinn]

Hello,
My data are from back-to-back bird point counts, and so they are temporally correlated. In general, I've found that the spatial correlation model is best for my data, but I have also compared it with the regular single-season model, as well a model with a survey-specific detection covariate (following a recommendation by you, Darryl, from another forum post!). I am inclined to exclude the species with the issues I am posting about here, but I just wanted to check with others to see if there was something else I should be considering. Thanks for the reply!