Hi,
sorry for taking quite long to respond:
One way to understand what interactions as condition * item mean is to expand the dummy coding that will be used in the model. Assuming the reference levels are new and K, we get four cases:
Case Intercept item condition item:condition
[new, K] 1 0 0 0
[new, E] 1 0 1 0
[old, K] 1 1 0 0
[old, E] 1 1 1 1
I.e. ignoring all other elements in the formula the linear predictor for [new, E] will equal 1 * b_Intercept + 0 * b_itemold + 1* b_conditionE + 0 * b_itemconditionoldE = b_conditionE. Similarly for old,E the linear predictor will equal 1 * b_Intercept + 1 * b_itemold + 1* b_conditionE + 1 * b_itemconditionoldE. With that in mind we can see that:
([old,E] - [new,E]) - ([old,K] - [new, K]) = 1 * b_itemconditionoldE
or equivalently
([old,E] - [old,K]) - ([new, K] - [new, E]) = 1 * b_itemconditionoldE
Thinking about how the actual linear predictors are built is a very general way to understand what the interactions means even in more complex scenarios (e.g. factors with more than two levels).
The condition * item interaction would involve both time points, condition * item * time2 would let you estimate it separately for each time point.
Hope that answers this part of you inquiry :-)
No. First I am not sure you are correctly describing what the interaction term actually does. Second you need to interpret the uncertainty in the coefficient. If by “non-significant” you mean something like “the 95% posterior interval includes 0” it is also important, how wide the interval is. If the interval is narrow around 0 then you can be somewhat confident that the interaction really is negligible. If it is wide it means your data aren’t enough to learn much useful about the interaction. Also note that “significant” is a frequentist term and does not directly translate to a Bayesian context.
Finally, you can’t ignore that you also have the (1 + item * condition * time2 | i | ID_T1T2 ) and for some inference tasks it might be important to consider this term as well. I discussed this in a slightly different context at: Inferences marginal of random effects in multi-level models - #3 by martinmodrak
It means that all the terms that use | i | share a correlation matrix, e.g. if the 1 + item * condition * time2 coefficients tend to be similar/different for some values of ID_T1T2 then the coefficient for 0 + old will also be more likely to be similar/different for those values of ID_T1T2. The benefit depends on whether this assumption is correct. I find it slightly weird in your case, because I would not necessarily expect the disc and overall response to behave similarly.
Overall, this seems to be a very ambitious model that would require A LOT of data to learn anything useful about the parameters.
Best of luck with your project!