Dear Rick. Thank you for your interest. In fact, I intend to test the robustness of a causal estimation: does E, the binary exposition, really causes Y, the binary outcome? Data come from a real data set, a survey on youth (n=21000). I have E, Y, and a propensity score modeling E (conditionally on many covariates X), Ps. E and Y are binary, but Ps is continuous. the correlations between E, Y and Ps are given by the data. The covariates X are also observed in the survey ; but what about an unobserved covariate U? It is still possible that my results based on Ps and E are biased because Ps does not include U. I want to simulate an U with given correlations with E and Y, but with a null correlation with Ps. Best,
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