You are welcome.
I am not familiar with CAR model (I will read about it!), but if you can consider you data points as independent then you can use WAIC. I think Gelman has an example where they have a time series, but for their purpose they model them as a simple linear regression and hence they can apply WAIC.
I am trying to understand the limitations of WAIC so if I find something I will let you know. Thanks for your question.