I am referring to the question. When estimating random effect (RE) variance or correlation, the estimations are different in
VarCorr(mod) function and when calculating the variance or correlation among REs with
cor(ranef(mod)). The question above explains why this is so.
I am interested which values are better for interpretation (best linear unbiased predictions (BLUPs) or
VarCorr) results and why?
What do we get with each option? Because the conclusions can obviously be different.
Finally, is there any difference in BLUPs interpretation in
EDIT: providing a concrete example
Let's say we have the following model
Random effects: Groups Name Variance Std.Dev. Corr subject (Intercept) 0.24513 0.4951 X 0.03209 0.1791 -0.83 Number of obs: 13037, groups: subject, 218 Fixed effects: Estimate Std. Error z value Pr(>|z|) (Intercept) 1.49331 0.04184 35.69 <2e-16 *** X -0.32162 0.02815 -11.42 <2e-16 ***
We are predicting Accuracy (0 or 1) from intelligence (X, continuous scale), while controlling for the REs in subjects.
These are manually correlated correlations and variances of REs
(Intercept) C.RT (Intercept) 1.000000 -0.977063 C.RT -0.977063 1.000000
Then varinace-covariance matrix
(Intercept) C.RT (Intercept) 0.16267598 -0.04952407 C.RT -0.04952407 0.01579298
Now, how does the concrete interpretation of marginal and conditional effects look like?
My general interpretation would be: Variance of normally distributed logit accuracy values of individual subjects around the mean logit accuracy for all participants (1.49) is 0.24
Also the correlation between individual logit accuracy values of individual participants and individual "intelligence" slopes is -.83 => the higher the accuracy for individual participant, the lower the relationship between intelligence and accuracy for this participant.
Are these interpretations of marginal or conditional models? How would the interpretation of the other model look like?
EDIT 2: Other questions related to this issue Here I list other questions on cross validated, but in neither case did I get the precise answer I was looking for.