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.