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I'm studying GLM models in software R. I have a dataset with the follow distribution: age, sex, years of study (ys), road or hightway (usop), and claims. I'm adjusting my model to claimns where it is been consider as Poisson distribution.

Then, I did four models as follow.

Model 1 - Satured model (all variables)

model.glm.pois <- glm(claims ~ ys + age + usop + sex, family = poisson, data = dataset)

Model 2

model.glm.pois2 <- glm(claims ~ age + sex + usop, family = poisson, data = dataset)

Model 3

model.glm.pois3 <- glm(claims ~ age + sex + ys, family = poisson, data = dataset)

Model 4

model.glm.pois4 <- glm(claims ~ age*sex + ys, family = poisson, data = dataset)

As noticed, the last model has an interation between age and sex. To compare the models I took the deviance and logLink, putting all values in a table:

|Models   |  Log Link| Deviance|
|:--------|---------:|--------:|
|Model 1  | -784.2589| 581.5254|
|Model 2  | -784.3731| 581.7538|
|Model 3  | -790.0154| 593.0384|
|Model 4  | -780.8325| 574.6727|

How do I decide what is the best fit model having as comparation Log Link and Deviance? Would Anova chi-square test give me better informations about the fit model?

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