I run the generalized linear model on Poisson distribution with offset term to account for the differences in sampled area. The response variable is the count of aquatic insect larva and the explanatory variables are the physical characteristic of lake environment.
The frequency of my data is below: 0-13 (zero is a count and 13 is a frequency); 1-6; 2 -1; 3-3; 4-1; 5-1; 11-1; 36-1; 44-1; 65-1; 80-1; 99-1; 117-1; 175-1; 202-1; 270-1; 289-1; 474-1; 523-1; 1783-1
model5<- glm(Organism_Count ~ offset(log(AreaSampler)) + Freq5 + Depth5 + Volume5, family = poisson(link=log), data=a)
The residual deviance of the model is 10713 on 34 degrees of freedom.
According to Zuur 2009, if the ratio of 10716/34=315 is bigger than 1, it provides the evidence of overdispersion.
But overdispersion test does support the overdispersion if I understand output correctly.
dispersiontest(model5)
data: model5 z = 1.1174, p-value = 0.1319 alternative hypothesis: true dispersion is greater than 1 sample estimates: dispersion 687.1288
I attached residual plots. Point # 7, which look like an outlier, is not a mistake of data entrance or count.
An additional question is if there is no overdispersion, does Poisson model work for my data or do I need to consider Negative binomial distribution?
