using occuRN when my data don't follow the Poisson distribution

[Yaelle Blais]

Hello everybody, 

I am using the occuRN function to estimate the occupancy of 38 sites and it exists heterogeneity in detection probability as a result of variation in abundance (Royle & Nichols 2003).

However, my data do not follow the Poisson distribution, there are to many zeros in the detection occasions (so the models I tried don't fit)

I tried next to log my data (as it seems to follow a log-normal distribution) but this model does not fit either. 

Do you have an idea of how I can solve this ? 

Best, 

Yaelle Blais

[Marc Kery]

Dear Yaelle,

can you give some more information about the goodness of fit of the RN model for your data set ?

If you really have too many zeros, then one might develop a variant of the model with zero-inflated Poisson for latent abundance. However, this model is not in unmarked, but would have to be specified in JAGS/NIMBLE/Stan. Another alternative abundance distribution that allows for more variability than the Poisson is the negative binomial. However, in the original paper by R & N they tried to fit a model with negbin mixture and failed.

Overall, detection/nondetection data alone don't contain much information about abundance. Personally, I think that many applications of the RN model may be on the edge of asking too much. In addition, your data set is small, statistically speaking (sorry !), so that does not improve matters either.

Best regards  --- Marc

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Subject: [unmarked] using occuRN when my data don't follow the Poisson distribution

 

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[Yaelle Blais]

Hello Mark, 

Thanks for your answer. 

Here is the result of  mb.gof.test of the best model, which is not too bad, but this model doesn't have effet on lambda (only on r).

MacKenzie and Bailey goodness-of-fit for Royle-Nichols occupancy model

Chi-square statistic = 2795.127 Number of bootstrap samples = 1000 P-value = 0.423 Quantiles of bootstrapped statistics: 0% 25% 50% 75% 100% 1468 2314 2672 3327 16879 Estimate of c-hat = 0.88

The problem is that there are 9 models with a delta AICc under 2. When I do a model averaging of these 9 models, only one of my covariate has a significant effect on r, none have a significant effect on lambda. So I impute this to the fact that, in fact, my data (frequences of detection per site) don't follow a Poisson distribution (I did a chi-squared test) and has more zeros. 

I hope my explanations are clear enough. 

In the study, we would like to use our detection/non detection from camera trap to see the intensity of use of the territory, the abundance is here seen has the frequency of detection. That's the reason why we want to use a RN model. I hope it makes sense.

Best regards, 

Yaelle