I am interested in the effect of a continuous variable on some Y. I have 4 conditions crossed with participant and 1 observation per participant per condition. I fitted a linear mixed model using lme4 looking like this:
model <- lmer(Y ~ Cont + (1|Participant) + (1|Condition))
The model overfit when I included a random slope for participant (correlation of random slope and random intercept for participant close to 1.) so I left this out.
Now I looked at the fit regarding my participant intercepts and participants means and found a bias (depicted below, the solid line indicates the identity function). So intercepts were systematically overestimated for participants with low means and underestimated for participants with high means. I also looked at the correlation of the fixed effects and found a correlation of 0 (I did not center my continuous variable).
Am I still overfitting my data with this model or is this normal?
The residual plot looks like this: