I'm using Orange dataset to illustrate my question. In this dataset, for each tree, the circumference and age were measured several times. Say we need to find the correlation coefficient between tree circumference and age. Since these two variable include repeated measures. The variables are not iid, so we should not use simple linear regression. I'm using linear mix model to model the data (lme4)
fit<-lmer(circumference~age+(1|Tree), data=Orange) summary(fit)
below is the output:
Linear mixed model fit by REML ['lmerMod'] Formula: circumference ~ age + (1 | Tree) Data: Orange REML criterion at convergence: 303.2 Scaled residuals: Min 1Q Median 3Q Max -1.8781 -0.6743 0.2320 0.5053 1.5416 Random effects: Groups Name Variance Std.Dev. Tree (Intercept) 389.6 19.74 Residual 232.9 15.26 Number of obs: 35, groups: Tree, 5 Fixed effects: Estimate Std. Error t value (Intercept) 17.399650 10.423696 1.669 age 0.106770 0.005321 20.066 Correlation of Fixed Effects: (Intr) age -0.471
In the output, we can see the correlation info (-0.471 in the last line). How to interpret this number? It seems like the correlation between age and (Intr) ? What I need to find is the correlation coefficient between age and circumference, not the fix effect slope. Does anyone know how I can extract the correlation coef? Thanks a lot in advance.