Question on variable significance in dynamic occupancy model (unmarked)

[Mathilde]

Hello,

I am currently investigating how pond characteristics influence newt's breeding pond selection. To account for two sampling periods, I use dynamic occupancy modelling with colext in unmarked.

My dataset includes 53 ponds sampled over 6 visits. The newt species was observed in 15 ponds. One of my site covariates, “Fish” (presence/absence of predatory fish), has a very strong effect: among the 17 ponds with fish, none had detections of the newt species.

However, in the model output the p-value associated with “Fish” is not significant, although its relative importance (AICc weights) is 1.00 (i.e. always included in the best models). I tested both the simplest model possible :

mod1 <- colext(psiformula = ~ Fish, gammaformula = ~1, epsilonformula = ~1,
               pformula = ~1, data = umf)

> summary(mod1) Call: colext(psiformula = ~Fish, gammaformula = ~1, epsilonformula = ~1, pformula = ~1, data = umf_TC) Initial (logit-scale): Estimate SE z P(>|z|) (Intercept) -0.101 0.394 -0.257 0.798 Fish1 -9.554 31.809 -0.300 0.764

as well as more complex models including other site-specific and visit-specific variables. The issue remains in all cases. 

My questions are:

1. Why would a covariate with such a strong exclusionary effect (complete separation: no overlap between fish and newt presence) show a non-significant p-value?

2. Is this expected behavior due to the way colext estimates parameters, or is it related to the data structure (complete separation, small sample size)?

3. How should I interpret this result in practice — should relative importance be given more weight than the p-value in this case?

Any guidance or references would be very helpful.

Best regards,
Mathilde

[Jeffrey Royle]

hi Mathilde,

 Unfortunately you're out of luck in this situation -- complete separation means that effect is not identifiable and so you cannot make an inference about that using likelihood methods.   The non-identifiability is suggested in these results by the effect being essentially 0 (if you inverse-logit -9.55 == 0 roughly) and the extremely large SE.

 There may be suggestions in the literature for dealing with this situation and I don't want to recommend a specific course of action. That said, what I would do is use a Bayesian analysis of the model and put a uniform prior on psi for both groups and then compute the posterior distribution of psi[1] - psi[2].  

 I don't know what a frequentist would do.

regards

andy

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