Use of goodness of fit statistics in Poisson GLMI'm using JMP Pro 15 to run a generalized linear model with a Poisson distribution and log link function. I was told to use Poisson because I have count data with values ranging from a min of 1 to a max of 118 with most falling in the 5 to 50 range. The model shows 2 goodness of fit statistics (pearson, deviance) that both have p-values less than 0.05. Does this mean that the model results are invalid and I need to reanalyze using a different distribution? This blog below seems to indicate that the results of the deviance test alone are somewhat unreliable.
https://thestatsgeek.com/2014/04/26/deviance-goodness-of-fit-test-for-poisson-regression/
Data Exploration and VisualizationRe: Use of goodness of fit statistics in Poisson GLMThe Poisson distribution uses a single parameter for the mean and the variance. As such, it might under-fit the data. The over-dispersion parameter allows for more variance than the mean.
Re: Use of goodness of fit statistics in Poisson GLMI did not originally, but just tried it. The overdispersion value is 2.5197 (for Pearson). I've never used this option before so not sure how to interpret it.
Re: Use of goodness of fit statistics in Poisson GLMDid you invoke the over-dispersion option in the launch dialog when you fit the Poisson distribution?
Re: Use of goodness of fit statistics in Poisson GLMThanks Mark. There were some over-dispersion issues, I believe, with the data. This morning I tried a negative binomial distribution and that fit seems much better.
Re: Use of goodness of fit statistics in Poisson GLMThe whole model LRT is significant. The goodness of fit tests indicate lack of fit. Perhaps include an interaction term?
What do the diagnostic plots look like?
