[R-sig-ME] pairwise combinations of subjects

David Duffy D@v|d@Du||y @end|ng |rom q|mrbergho|er@edu@@u
Tue Jul 16 06:27:11 CEST 2019

> I sometimes encounter data that are derived from interactions between all
> pairwise interactions of subjects (e.g., subject a vs. subject b, subject a
> vs. subject c, subject b vs. subject c). The response is the result of the
> interaction between subjects, and observations are likely to show
> correlations within subject. We are interested in the relation between a
> fixed effect predictor and the response, and not the effects of subject per se.
> This seems like a design that might be common in breeding....

Yes, we fit this flavour of model as SEMs - for example, not exactly the same but just as mechanistically plausible, you have a reciprocal causative pairwise relationship
X1      X2
|           |
v         v
Y1      Y2

detectable by its effects on total variance (correlated with values of X - so 'ware those variance stabilising transformations ;)), and distribution of the Y's.  The coefficients can be negative, so members of each pair rub each other the wrong way _OR_ if the measurement is say a rating by an external observer, then the ratings may be biased away from each other ("contrast effect"). I don't know how to do this in lme4, but on page 9 of 


you can see them fitting such a model using the R umx package.

Cheers, David Duffy

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