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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!

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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.

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  • $\begingroup$ thank you for your answer! I'm not completely sure I understand, even if it's normal that the reference level changes my coefficients and significance levels, in this case, which final result should I use? (how do I chose which reference level to stick to? ) $\endgroup$
    – Juliette
    Commented Jul 31, 2022 at 7:57
  • $\begingroup$ @Juliette it doesn't matter which reference level you choose. The overall model is the same regardless, as are any predictions you make from the model. The "significance" of an individual coefficient for a predictor involved in interactions doesn't matter. To evaluate the significance of a predictor in an interaction, you need to do a combined test of its individual coefficient along with the coefficients of its interaction terms. That's done for example by the Anova() function of the R car package. $\endgroup$
    – EdM
    Commented Jul 31, 2022 at 13:06
  • $\begingroup$ this is where I get confused, because it's when I look at the significance of a predictor with the Anova function, it is there that I see A different X2 and p value for proximity depending on my reference level of dyad_type. This is what gets me confused, not the change in the individual levels of my covariate but the change in the predictor in itself, and I'm not sure which results to rely on. I hope this makes sense? $\endgroup$
    – Juliette
    Commented Aug 1, 2022 at 9:35

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