Influence of scaling of continuous predictor on main effect of categorical predictor in LMM I have a linear mixed model that analyses the effect of multiple continuous and a categorical (two level, deviation coding of contrasts) predictor on a normally distributed outcome variable (dv). Following Barr (2021, https://psyteachr.github.io/stat-models-v1/multiple-regression.html?q=scal#standardizing-coefficients) I wanted to z-transform the continuous predictors (using scale()) to standardise the coefficients of the continuous predictors. In one of the models, R also gave back the following warning: ## Warning: Some predictor variables are on very different scales: consider rescaling.
However, I noticed that scaling changes the main effect of the categorical predictor. For the purpose of clarity, I will present a smaller but representative version of the actual model here to illustrate my point. This is the lmer command I used for this smaller model:
m = lmer(formula = dv ~ cat * cont + (1 |sub) + (1 | stm), data = df_sel)

I did this once with the raw and once with the scaled continuous predictor:

As you can see, it changes the main effect of the categorical predictor while the continuous and the interaction stay the same. I would have expected that none of the statistical values change, just the estimates. When investigating a bit, the only difference I found was that scaling gets rid of some moderate colinearity:

Can this really have such a large effect on the main effect of the categorical predictor? Am I justified in scaling the predictor?
Edit: Here are the outputs plot_model(m2, type = "int"):



There are a number of principles at play here.

*

*Scaling is generally a bad idea, except for the internal scaling that's done in the software that does the estimation.  It assumes linearity of effects and assumes that standard deviations are good scale measures.  Especially for asymmmetrically distributed variables the SD is not a good measure.  And it is greatly affected by extreme values.

*Scaling makes interpretation harder.  Interpretations are easiest on the original scale.

*Categorical variables should not be scaled

*Even if you don't scale the categorical variable but you do allow it to interact with a (scaled) continuous predictor, all of the categorical effects will be changed by scaling.

*Check that the correlation pattern assumed in your model reflects the actual correlations seen in the data.  Mixed effect models when used with default correlation structures often do not fit.  See this for more.

