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Some asked before "Why do random effect models require the effects to be uncorrelated with the input variables, while fixed effect models allow correlation?"

My question is: how do you check this assumption?

What I did is plot the residuals of the "fixed" effects against the residuals of "random effect"

v <- m.lme$residuals
attr(v,"std") <- NULL      # get rid of the additional attribute
plot(v[,1],v[,2] )

Then it shows a plot with correlated residuals. Is this the right way to test the assumption stated above? If yes, the assumption does not hold in this case. Is there anything else I can do?

Correlation of residuals in multilevel model

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No, what you want to check is if there is a correlation of the REs with the fixed effect predictors, which would signify that you absorb fixed effect misspecification in the REs.

In R: extract the REs via ranef(m1) from model m1 (note the substructure) and plot them against the predictors, and interpret this like a usual normal residual plot.

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