LLR_test in chapter 7: Fitting Higher - Lag AR Models for Prices.

I understand that AR(8) satisfied both the Non-significant p-value for the LLR test & the Non-significant p-value for the highest lag coefficients. Thus, we stop with AR(7). However, at the end of the Fitting Higher-Lag AR Models for Prices, we perform the LLR Test again with print("LLR test: ", LLR_test(model_ar, model_ar7, DF=6))

Why do we need to do this again? What are we trying to check? What is the degree of freedom exactly?

Thanks for answering my questions in advance.