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), but there's also a lot of discussion regarding the necessity of including the lower order term interaction when quadratic interaction is in the model. Thus the dilemma.

I appreciate your time.