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I am running mixed effects regression in R, utilizing glmer, and am hoping someone can help clarify the difference between using coef and ranef on the results. Specifically, I have fixed effects $f_1,f_2,f_3$ and random effects $r_1,r_2,r_3.$ When I run coef I get certain coefficent values for each of the fixed and random effects. Additionally when I use the ranef function I get coefficients for my random effects. These two coefficients are not equal for each respective random effect $r_1,r_2,r_3.$ Why are these coefficients different and what information each coefficient tells us?

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  • $\begingroup$ coef returns coefficients and ranef returns modes of random effects - what i not clear in it for you? $\endgroup$ – Tim Oct 20 '15 at 19:36
  • $\begingroup$ @Tim Why doesn't coef = ranef. Shouldn't the coefficient = mode of random effect = mean of random effect? $\endgroup$ – OuijiBoard Oct 20 '15 at 19:41
  • $\begingroup$ @Tim Then what information is being given to me when coef() returns a coefficient of a random effect? $\endgroup$ – OuijiBoard Oct 20 '15 at 19:47
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From lme4 documentation you can learn that

coef: Computes the sum of the random and fixed effects coefficients for each explanatory variable for each level of each grouping factor

and ranef is

A generic function to extract the conditional modes of the random effects from a fitted model object. For linear mixed models the conditional modes of the random effects are also the conditional means.

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