I do not think anyone has answered this.

> I'm trying to run a simple one-way ANCOVA with the lmer 
> function in R  package lme4, but have encountered some
> conceptual problem. The data file MyData.txt is like this:
> 
> Group Subj Cov Resp
> A    1   3.90   4.05
> A      2   4.05       4.25
> A      3   4.25       3.60
> A      4   3.60       4.20
> A      5   4.20       4.05
> A      6   4.05       3.85
> B      7   3.85       4.15
> B      8   4.15       4.60
> B      9   4.60       4.15
> B      10  4.15       4.40
> B      11  4.40       3.35
> B      12  3.35       3.80
> B      13  3.80   3.90
> 
> Since I would like to treat subject (Subj) as a random 
> factor, my one- way ANCOVA (with covariate, Cov) is:

This is a conceptual problem, indeed. To be able to estimate a subject effect, 
you need to have repeated measurements (several lines) per observed subject ...

Cheers, Lorenz

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