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I am looking a counts of fish within different size classes (0-10, 10-20 etc) between 3 different reef sites, 3 different depths and 2 different survey methods. However, naturally on all observations I did not identify fish to fit all size classes and hence my data has a lot of zeros and is counts.

Because of this I assumed I would need to use a ZIP GLM so I compared the fit of a GLM with a regular poisson distribution and a ZIP poisson GLM as well:

model1<-glm(vs~method+site+depth,data=length.dat,family="poisson")
model2<-zeroinfl(vs~method+site+depth,data=length.dat,dist="poisson")
vuong(model1,model2)

I then compared the fit of the two models using the vuong test and results showed that a ZIP model was most appropriate.

I then ran the model for one of my response variables the size class 'very small' and this was the output:

Pearson residuals:
       Min         1Q     Median         3Q        Max 
-8.276e-01 -1.814e-01 -1.615e-03 -6.804e-06  3.727e+00 

Count model coefficients (poisson with log link):
            Estimate Std. Error z value Pr(>|z|)   
(Intercept)   3.3414   106.4449   0.031  0.97496   
method.L     -1.5128     0.4864  -3.110  0.00187 **
site.L       -8.4777   225.7975  -0.038  0.97005   
site.Q       -7.7973   130.3643  -0.060  0.95231   
depth.L      -8.8354   225.7980  -0.039  0.96879   
depth.Q      -3.9120   130.3721  -0.030  0.97606   

Zero-inflation model coefficients (binomial with logit link):
            Estimate Std. Error z value Pr(>|z|)
(Intercept)   4.2989    34.3016   0.125    0.900
method.L      0.8108     1.1095   0.731    0.465
site.L       -9.4201    72.9885  -0.129    0.897
site.Q      -14.6625   110.7111  -0.132    0.895
depth.L     -16.8747   114.8328  -0.147    0.883
depth.Q      -8.5142    66.4256  -0.128    0.898
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1 

From what I understand, zero inflated models treat the data as two sets. One that is all zeros and one that is zeros and counts is that correct? I think this is telling me that fish within this size class are significantly different between the sampling methods but I am unsure and what does it mean if there is a significant result in the zero inflated poisson in comparison to the zero inflated binomial?

Also do i need to check for overdispersion with a ZIP model and is the analysis over, I have seen some people using chi2?

Would love some help.

Thanks

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