Under the assumption that treatment assignment has no direct effect on the response, a non parametric probabilistic model of the distribution involving the latent confounder under partial compliance leads to a generalized definition of the effect of treatment on the treated and reveals that the instrumental variable estimand equals a suitable average of such causal effects only when certain restrictions hold. An application to a popular data set concerning reduction of cholesterol level is used as an illustration. © Springer-Verlag Berlin Heidelberg 2011.
CITATION STYLE
Forcina, A. (2011). Partial compliance, effect of treatment on the treated and instrumental variables. In Studies in Classification, Data Analysis, and Knowledge Organization (pp. 317–324). Kluwer Academic Publishers. https://doi.org/10.1007/978-3-642-13312-1_33
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