Interpretation of ZIP models

[apietrek]

Dear Users,

                   I've been using N-mixture models to perform some preliminary analysis of fecundity in a single season. I have only two repeated observations across 43 sites.

 Because some colonies can have kits and some not I thought a ZIP model would be appropriate. This way I could model detection, and for abundance (or number of kits in this case), whether the colonies produce or not kits at one level, and how many kits at the other level. However I found three problems (I'm aware this may be due the few number of observations)

1) AIC indicates that ZIP models rank better than simple Poisson models. However, when I perform non-parametric bootstrapping the SSE is huge (even when chi-square tests look ok)

2) The probability of detection decreases drastically.

3) I would like to introduce covariates to model abundance at the the two levels (production and number of kits). Is this possible?

Any suggestion regarding these points will be appreciated.

Alejandro

[Jeffrey Royle]

hi Alejandro,

 

 (1) The high bootstrap SSE could be due to small-sample instability of the MLEs as you note. how many covariates, etc? Try fitting just the null model and see if that works well.

 If you're already fitting just the null model, show us the output of the bootstrap procedure.

(2) I think that is expected. If it decreases too much probably this is a small-n problem again.

(3)  Its not possible to model covariates on the zero-inflation parameter in unmarked right now (but generally it is possible). This would be easy to resolve but we probably won't be doing it in the near future due to other commitments.  It would be easy to do this in WinBUGS if you are familiar with that.
regards

any

[apietrek]

Andy,

         Thanks for your advice. I'm posting the results of the Poisson and ZIP null model (including goodness of fit assessment)

Poisson null model

Call:

pcount(formula = ~1 ~ 1, data = umf2, K = 100)

 

Abundance (log-scale):

 Estimate    SE       z P(>|z|)

  -0.0304 0.324 -0.0938   0.925

 

Detection (logit-scale):

 Estimate    SE      z P(>|z|)

   -0.147 0.577 -0.255   0.799

 

AIC: 147.9281

Number of sites: 43

optim convergence code: 0

optim iterations: 14

Bootstrap iterations: 0

Call: parboot(object = m5, statistic = fitstats, nsim = 500, report = 1)

Parametric Bootstrap Statistics:

         t0 mean(t0 - t_B) StdDev(t0 - t_B) Pr(t_B > t0)

SSE    48.5          12.10              9.5        0.112

Chisq 107.9          -7.27             24.6        0.553

t_B quantiles:

      0% 2.5% 25% 50% 75% 97.5% 100%

SSE   16   22  30  35  41    58   75

Chisq 76   83  98 111 127   178  237

t0 = Original statistic compuated from data

t_B = Vector of bootstrap samples

 

ZIP null model

Call:

pcount(formula = ~1 ~ 1, data = umf2, K = 100, mixture = "ZIP")

Abundance (log-scale):

 Estimate  SE     z P(>|z|)

      2.1 3.1 0.676   0.499

Detection (logit-scale):

 Estimate   SE     z P(>|z|)

    -2.07 3.39 -0.61   0.542

Zero-inflation (logit-scale):

 Estimate    SE      z P(>|z|)

   0.0408 0.447 0.0913   0.927

AIC: 142.7498 

Number of sites: 43

optim convergence code: 0

optim iterations: 35 

Bootstrap iterations: 0 

 

Call: parboot(object = m11, statistic = fitstats, nsim = 500, report = 1)

Parametric Bootstrap Statistics:

        t0 mean(t0 - t_B) StdDev(t0 - t_B) Pr(t_B > t0)

SSE   1091         -34498            49490        0.483

Chisq  273           -860             1264        0.483

t_B quantiles:

      0% 2.5% 25% 50%   75%  97.5%   100%

SSE   15   43 131 840 75885 150384 202706

Chisq 73   73  91 234  2468   3504   4073

t0 = Original statistic compuated from data

t_B = Vector of bootstrap samples

 

[Jeffrey Royle]

looks to me like there is one or a very small number of extreeme values being generated in the bootstrap procedure, probably the ML failed and generated a boundary estimate or something marching off to he boundary before it stopped.

I suggest looking at the bootstrap samples and seeing if thats the case, then maybe remove that one case (hopefully its just 1 or 2).

regards

andy

[Kaylan]

In unmarked using the pcount ZIP models, because I'm incorporating the zero-inflation parameter without covariates does this mean that all my models are assuming constant rates of occupancy across the board? What sort of problems could arise if this assumption is not met (which I'm guessing is a rare occurrence)?

Thanks for all your help!

KC

[Jeffrey Royle]

hi Kaylan,

 no there will not be a constant rate of occupancy if you have a bunch of models that differ in their covariates, even though the zero inflation parameter is constant.

 regards
andy

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[apietrek]

I have a question that sort of follows up the previous.

1)I'm analyzing data on beaver reproduction. A pair can either reproduce or not, and if they reproduce the counts follow a Poisson distribution. Thus a zip model arises as a natural choice.

Is it correct to say if I backTransform the zero inflation parameter I will get an estimate of the proportion of colonies that have kits?

2) Are the lambda estimates that unmarked returns unweighted (I saw a post a year ago that says they are but I was wondering if it's still the same)

Thanks,

Alejandro