# Model building, p value of GLM for whole model?

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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 What software are you using? – Peter Flom Oct 3 '12 at 17:05 You must subscribe to Frank Harrell's philosophy and arguments if you think stepwise regression is sinful! – Michael Chernick Oct 3 '12 at 17:19 I'm using R. I just learned about the sins of stepwise regression....my original analysis and two stats classes were pro-stepwise – Jo Lewis Oct 3 '12 at 17:25

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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