This question is a follow up question from this one: Controlling for an effect by adding it as covariate in R
Now that I know my model is coherent, I have some issues interpreting my results.
The model:
lmm2 <- lmer(formula = bray_curtis ~ dyad_type + proximity + matriline +
proximity*dyad_type + (1|id1) + (1|id2)
dyad_type = categorical (4 levels); matriline = categorical (2 levels); proximity = continuous.
At first, I did not include the interaction term (proximity*dyad_type), and my model yielded only a significant effect from 'proximity'.
When I added the interaction term (proximity*dyad_type), the results started to change depending on which level of dyad_type I was putting as a reference level.
reference level:
dyad_type1 –> significant diff with dyad_type4 AND proximity effect
dyad_type2 –> significant diff with dyad_type4 AND proximity effect
dyad_type3 –> NOTHING significant (not even proximity????)
dyad_type4 –> significant diff with dyad_type1 and dyad_type2 but NO proximity effect
(none of the results showed any significant effect from the interaction term even tho a likelihood ratio test confirmed that adding the interaction was better for my model)
From what I understood, changing the reference level of a categorical variable only changes the "summary" output, but the multiple comparisons between the different categorical levels shouldn't change, which is indeed okay here. Where I'm confused is that it changes results of the OTHER covariate (proximity), which has me quite confuse…
I'm not sure I understand how to interprete those results, how is the interaction level changing the effect of a covariate on its own, when there isn't even an effect from the interaction term itself?
Thank you for your help!
Best Answer
Under treatment/dummy coding as you are using, this is what happens with coefficients when predictors are involved in interaction terms. The individual coefficient for a predictor is then defined for a situation where all its interacting predictors are at reference levels or 0. Its "signficance test" is whether the coefficient differs from 0 at those levels of all interacting predictors. So re-centering a continuous predictor it interacts with, or changing the reference level of a categorical predictor it interacts with, necessarily changes the reported coefficient (and p values, etc.) for a predictor that wasn't itself modified.
This answer works this through in the context of how centering one continuous predictor affects the coefficient of a predictor with which it interacts. The principle is the same in your situation.