# Controlling for covariates in twin(-family-)-models

I sometimes find papers (like for example this one: https://www.psych.uni-goettingen.de/de/biopers/publications_department/pdfs/Kandler_et_al_2016_The_Nature_of_Creativity.pdf) that apply an interesting approach: Within a twin-model, they control for covariates and interpret how this changes the variance components. As far as I know, including covariates is equivalent to residualising the variable of interest as it is often done for age and gender. However so far I was unable to find a detailed justification for this much more extended utilization of this technique, especially using variables that differ between the twins. Is the aforementioned interpretation of changes in the variance components due to adding these control-variables justified? And can this technique also be used in more complex twin-family-models? I guess we would have to assume that the effects of the covariates (and the explained variance) are roughly constant for the parents and the children but is there anything else that I am missing?

Thanks for your help!

Tobias

## Head for multivariate analysis

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## The necessity of exogeneity

Thank you for your reply! However, I am not quite sure whether I fully understand your point about assuming exogeneity. Of course, it makes sense most of the time, but is it a necessity? Let's take a hypothetical example in which we deliberately and blatantly violate this assumption: Our outcome is intelligence. We fit a baseline model without any covariates, which tells us that A explains 80% and E 20% of the variance. We then introduce a predictor, income. This model gives us A = 70%, E = 20%, R2 = 10%. Would it be wrong to interpret this without any allusion to causality, as in "Controlling for income reduces A by 10%, while not affecting E. Therefore the covariance between both variables is mainly mediated by genetic factors."? Needless to say, one might ask why not just use a standard multivariate model in such a situation, but is the interpretation itself invalid?

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In reply to The necessity of exogeneity by twolf

## OK to say it, not ok to do it?

this paper for example which is in my TLDR list at the moment.

Stating clearly what you did is definitely a plus! Interpreting what you have done would seem to require a lot more caution. A simulation study might clarify what goes wrong when we control for covariates that are sequelae.

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In reply to OK to say it, not ok to do it? by AdminNeale

## How does this compare to

Thanks in advance, really helpful these answers.

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