I am modeling claim severity by GLM in r. I want to check whether all predictors are significant. I use the likelihood ratio test (by the function anova()) in turn for all predictors. Finally, I get the reduced model
> anova(severity,model.severity,test="LRT") Model 1: claimcst0 ~ gender + area + agecat Model 2: claimcst0 ~ veh_value + veh_age + veh_body + gender + area + agecat Resid. Df Resid. Dev Df Deviance Pr(>Chi) 1 4612 7558.0 2 4596 7488.7 16 69.371 0.09736 .
We can see the p-value of the test is greater than 0.05. We do not reject the smaller model.
But the funny thing is that the smaller model has greater residual deviance and AIC.
model A Residual deviance: 7558.0 on 4612 degrees of freedom AIC: 85079 model B Residual deviance: 7488.7 on 4596 degrees of freedom AIC: 85055
What is the reason for it? Is the model A still the better model compared to model B?