# Model Deviance lower than Residual Degree of Freedom

I am trying to calculate the Variance inflation factor (VIF) for a Generalized Additive Model (GAM). The GAM model contains both constant terms and splines.

The VIF is defined as Deviance of model divided by residual degree of freedom of model.

I am getting a deviance value using deviance(model) and residual degree of freedom value using df.residual(model).

The value of deviance is lower than residual degree of freedom resulting in the VIF value being lower than 1.

It is common knowledge that VIF cannot be lower than 1. So am I missing something or doing something wrong?

The eventual goal is to use the VIF value in the QAIC function, of MuMIn package, as QAIC(model,chat=vif) to calculate the qualsi-AIC value of the model.

All function written above are from R.