I am running a series of mixed effect models, which include both linear and quadratic term of a variable T (continuous) and the main IV I (categorical), and facing a dilemma.

Model 1 include interaction terms with both the linear and quadratic T. Model 2 include only the quadratic interaction.

With Model 2, I obtained the lowest AIC and BIC. In comparison, for Model 2 the AIC is 5.8 higher and BIC is 26 higher. If I followed the rule of thumb for AIC/BIC-based selection, Model 1 is the one I should select (and the one I preferred).

On the other hand, there's also a lot of discussion regarding the necessity of including the lower order term interaction when quadratic interaction is in the model.

However, it will be very difficult for me to justify the selection of a model that's very unlikely (probability: exp(-5.8/2)=5%) to be better than the one with AICmin. Thus the dilemma.

I appreciate your time.