I have three GLM models (poisson distribution) that each have different factors but the same response variable. I plan to compare the fit of the models using AIC, but first I want to see if any of the models are significant according to a p value. Is is possible to get a p value for a whole model w/glm? Each model has 1 significant factor and one or two non-significant factors, but I was told to leave these non-significant factors in the models instead of removing them with sinful backwards stepwise regression.
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There are "whole model" tests such as likelihood ratio, Wald, and the score test. These are described in detail in Frank Harrell's book. You might also consider evaluating each model using $R^2$ and each model's predictive accuracy in cross-validation. For the latter, it's helpful to use the same cross-validation "folds" with each of your models. |
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Yes. Many GLMs can be tested using a likelihood ratio test comparing the model with a restricted model that has only no covariates. |
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