I've just read Elizabeth Stuart's paper on matching methods (http://biostat.jhsph.edu/~estuart/Stuart10.StatSci.pdf), which I find very informative. She discusses propensity score methods and the adjustent for covariates. On page 3 she writes (end of column 1 and beginning of column 2):
" This assumption is often more reasonable than it may sound at first since matching on or controlling for the observed covariates also matches on or controls for the unobserved covariates, in so much as they are correlated with those that are observed. Thus, the only unobserved covariates of concern are those unrelated to the observed covariates."
I figured that this could also be the case in any other regression model. In other words, when adjusting for a variable, have we also adjusted for other variables that are related to that variable, to the extent that they are related/correlated? I think this is quiet an important question as it has implications for applied research, where access to covariates are often limited, but they are in general related/correlated.
Can I assume that I have adjusted, to a certain extent, for varaibles that are correlated with the ones included in my model?
