# Mixed-effects model for MZ twin data: avoiding overparametrization

I'm trying to fit a (simple) linear regression using MZ twin data. The reason why mixed-effects are used here is just to correct for correlated responses from the twins.

The current model looks like this:

out.fit.1 <- lmer(outcome ~ cov1 + cov2 + cov3 + predictor + (1 | PairNumber ),
data = MZtwins1 )


The 3rd covariate is a dummy variable for diagnostic status (healthy/affected); hence there are "concordant", "discordant" and "healthy" pairs.

Taking into account that concordant pairs may have a strong genetic influence in their diagnostic status (ie, the disease might have been caused by genes) and that the "affected" status of a twin in a discordant pair is likely due to environmental factors, I'm wondering how to include this in the model.

I've been considering using

out.fit.2 <- lmer(outcome ~ cov1 + cov2 + cov3 + cov4 + predictor + (1 | PairNumber ),
data = MZtwins1 )


where cov4 would be a categorical variable for concordant/discordant/healthy... But the fact that cov3 already contains the diagnostic status makes it look overparametrized.

EDIT: cov3 has only two levels ("affected", "healthy"), and cov4 (as I've thought about it) would have three levels ("healthy_pair", "concordant_pair", "discordant_pair").

Do you have any ideas on how to model this?

           cov3 cov4

• Yes, indeed. But as cov3's class is factor, R handles it as a dummy variable by default. I'm editing the original question so as to include more details... – Elabore May 13 '13 at 8:39