# [R-sig-ME] partial correlation and mixed models in R

Cristiano Alessandro cri@@le@@@ndro @ending from gm@il@com
Wed Oct 17 17:50:37 CEST 2018

```Hello all,

I have Nr repeated measures of four continuous variables Aij, Bij, Cij,
Dij, i=1...Nr, for each subject j=1...Ns. The repeated measures within each
subject are sequential in time, and therefore correlated. I need to compute
the correlation between each pair of the four variables, and compare the
correlations across the 6 pairs.

The initial, very naive, idea I had to perform this analysis was to compute
the Pearson correlation for each pair of variables (they are approximately
normally distributed) within each subject, and then run a linear mixed
effect models (LMEM) using the correlation coefficients as the independent
variables and subject as a random effect. I have the strong feeling this
approach is wrong though. Right?

I then figured that people have approached this problem by fitting a LMEM
directly on the variables A, B, C, D (using subject as a random effect),
specifying appropriate covariance matrices in order to reflect the
correlation between the repeated measures within subjects, as well as the
correlations between pairs of variables. Fitting such a model would give
estimates of the correlations that I need to compare.
https://www.ncbi.nlm.nih.gov/pubmed/12708508

I have the following questions:
- Do I need to use partial correlation (or something similar) when I
compute the correlation between pairs of variables to control for the
values of the remaining two variables?
- If so, how do I integrate partial correlation into the LMEM approach that
uses the variables A,B,C,D as the independent variables?
no matter how I estimates the correlations, how do I compare the
correlation coefficients across the pairs of variables? can I use Fisher’s
r to z transformation, and then compare the z scores? Still, I would need
to compare 6 pairs, not only two.
- Is the naive approach (fitting a LMEM on the correlation coefficients
previously computed) inherently wrong? why?

Thanks
Cristiano

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