On my original dataset, I ran a multilevel regression with an intercept and a variable. I found that the random slopes were perfectly correlated with the random intercepts.

I figured I could get around this issue by just mean-centering the values for each subject which would eliminate any variance in the intercept preventing the intercept effects from impacting the random slopes. However, when I do this before running my multilevel model, I still find that the intercept and slope are perfectly correlated! Should this be happening? Even if this correlation is perfect, are the results on the random slopes legitimate? I also double-checked and the mean-centering is being done correctly, and I am not getting any convergence error.

Notably (?), for some tests when I do mean-centering I don't get a perfect correlation, but I instead get a NaN correlation.


I cannot share the data, but summary(...) results from not-mean-centered, and mean-centered tests can be seen here: https://imgur.com/a/W9ppsXV

EDIT: I found out I can just exclude the intercept from my lmer using: "Y ~ 0 + X + (0 + X | group)." However, when I do this after mean-centering, I find that my random slopes have absolutely zero variance!?!? My data itself clearly has variance, and the residuals seem to have variance.


  • $\begingroup$ Perfect correlation between variance components is often called a "singular fit". Try removing the random slopes. Also see here $\endgroup$ – Robert Long Aug 26 '19 at 10:59

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