Dear all,

I have simple question regarding how to fit a model (i.e. linear) to the
data.
Say I have 10 subjects with different phenotypes (dependent var Y,
identical for a particular subject) and one predictor variable measured 3
times for each subject (X). By other words:

Y Subj X
1 1 1.2
1 1 1.3
1 1 0.7
3 2 2.1
3 2 2.5
3 2 4
5 3 3
5 3 4
5 3 4
...
20 10 12
20 10 13
20 10 12.5

Subj is a grouping variable.




I would like know the correlation of Y with X (Y~X) and the effect of
within subject variance on this correlation. And thus, overall significance
and correlation.

Will it be valid fitting lm to all combinations of x and y and take an
average values of p and R-squared?

Usually, I estmate the correlation using simple lm between outcome and
averaged predictor (1-to-1, i.e. 20 outcomes versus 20 predictors).
However, I would like to take in account variations associated with
replicated measurements (i.e. the same 20 outcomes versus 20 predictors
replicated say 3 times), and, therefore, evaluate slope and intercept
variabilities. Do mixed model regression analysis suitable for such an
analysis for example using lme function from nlme package? If not, what
kind of analysis is most appropriate? Weighted least squares?Thank you.

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