I'm investigating the effect of a continuous variable A on a measurement variable M stratified by another factor variable C in an observational dataset.
Due to heteroscedasticity I decided to use a bootstrapped regression analysis. However looking at the data, the background set of variables are not evenly distributed if I dichotomise A (present or not). I've just finished running another analysis where I do the same analysis after having matched the dataset for confounders (using CEM in R).
Now the problem is which analysis to trust: the bootstrapped regression approach on the entire dataset or the bootstrapped version of the matched data? Under one of the factors in C the results diverge.
Any ideas how this can be analyzed?