find repeated measure correlation coefficient using linear mixed model

Question

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.

Mateusz1981 Mateusz1981 · Accepted Answer · 2018-02-05T07:36:38

I use nlme package and I get the correlations like here:

library(nlme)
fit <- lme(circumference~age, random = ~1|Tree, data=Orange)
summary(fit)$cor

I could not extract correlation from lme4 summary output.

find repeated measure correlation coefficient using linear mixed model

1 Answers