# Logistic regression correcting for twin data

3 posts / 0 new Offline
Joined: 07/04/2015 - 18:52
Logistic regression correcting for twin data

Hi OpenMX community!

I would like to run a simple logistic regression model, but with a classical twin dataset, correcting for the fact that they are twins and their zygosity MZ or DZ. Is there a way for such analysis using OpenMx?

Thanks! Offline
Joined: 01/24/2014 - 12:15
Probit regression via threshold model

It would more like probit than logistic regression, but you could set up your analysis as an ordinal-threshold model. You'd set up your dataset to have one row per pair of twins. You'd have separate groups (submodels) for MZ and DZ twins, and allow the twin correlation to be different for MZs and DZs. The variance of the latent continuum would be fixed to 1. You'd need to fix one of either the latent mean or the threshold to zero. You'd use definition variables to condition the value of the other parameter, for each twin in each row of the dataset, upon his/her values of the predictors. That is, the value of the other parameter for twin j in twin pair i would be b0 + b1x1ij + b2x2ij + ..., where b0 is a regression intercept, x1ij is twin ij's score on covariate #1, b1 is the regression slope for covariate #1, and so forth. The covariates would be definition variables, and the regression coefficients would be free parameters, constrained equal across zygosity groups.

All together, this would model (1) the dependence of twins within pairs, (2) the greater degree of within-pair resemblance for MZs compared to DZs (which will be so for any trait having nonzero heritability), and (3) the regression of a dichotomous phenotype onto one or more predictors. But, be advised that the sign of the regression coefficients will depend on whether they predict the threshold or the mean, and that the coefficients don't have the same interpretation as those from logistic regression. Offline
Joined: 07/31/2009 - 15:14
What Rob said

I agree that Rob's approach seems the closest to what you want. Note that multiple regression with data from relatives was the subject of an article way back when...

Neale, M.C., Eaves, L.J., Hewitt, J.K. & Kendler, K.S. (1994) Multiple regression with data collected from relatives: Testing assumptions of the model. Multivariate Behavioral Research 29: 33-61.

This does the same thing, with classic Mx as OpenMx had not yet been invented. It also notes that switching independent and dependent variables with twin data doesn't give the same fit to the data (i.e. you can get some traction on direction of causation), unlike the case for unrelated individuals.