# lmer interpretation of correlation

I have the following output:

Linear mixed model fit by REML
Formula: Value ~ Group + (1 | Koralle)
Data: dat
AIC  BIC logLik deviance REMLdev
5988 6008  -2990     5985    5980
Random effects:
Groups   Name        Variance Std.Dev.
Koralle  (Intercept)  4.1737  2.0430
Residual             15.4811  3.9346
Number of obs: 1070, groups: Koralle, 5

Fixed effects:
Estimate Std. Error t value
(Intercept)       10.463      1.468   7.127
GroupTreatment    -1.071      1.895  -0.565

Correlation of Fixed Effects:
(Intr)
GroupTrtmnt -0.775


I am not sure how to interprete the -0.775 from the Correlation of the Fixed Effects. I even don't know which correlation this is? Can someone help me?

Thanks in advance.

## 1 Answer

Correlation of Fixed Effects: refers to the estimated correlation between the fixed-effect parameters (Intercept) and GroupTreatment*. Usually these correlations arise when the data is not centered.

You can center continuous data by subtracting the mean. This will avoid slope-intercept correlations and thus make the interpretation of main effects more straight forward in cases where the data range is far away from zero. E.g. a main effect of gender when a model is fit to heights measured across ages would indicate a height difference at age 0. Centering age at a particular value will allow to test for gender differences at a particular age.

In your example you presumably have a factor Group with two levels Treatment and NoTreatment. Here centering might make less sense, because there is no group with HalfTreatment. This factor level might even be impossible. Thus you do not need to worry about the slope-intercept correlation.

*edited to incorporate Ben Bolker's correction

• Okay thank you! Is this correlation the pearson correlation? Or in other words can I calculate this correlation without making a LMM? For example with cor(dat$Group, dat$Koralle, method="pearson") or something similar? – Giuseppe Feb 2 '13 at 9:40
• This is generally a good, useful answer, but your first sentence is wrong: This is not the correlation among random effects (the random effects in this model are assumed to be independent), but rather the estimated correlation between the fixed-effect parameters (Intercept) and GroupTreatment (abbreviated as necessary). – Ben Bolker Feb 3 '13 at 21:57