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In causal inference, principal stratification is a framework for dealing with a posttreatment intermediate variable between a treatment and an outcome, in which the principal strata are defined by the joint potential values of the intermediate variable. Because the principal strata are not fully observable, the causal effects within them, also known as the principal causal effects, are not identifiable without additional assumptions. Several previous empirical studies leveraged auxiliary variables to improve the inference of principal causal effects. We establish a general theory for identification and estimation of the principal causal effects with auxiliary variables, which provides a solid foundation for statistical inference and more insights for model building in empirical research. In particular, we consider two commonly-used strategies for principal stratification problems: principal ignorability, and the conditional independence between the auxiliary variable and the outcome given principal strata and covariates. For these two strategies, we give non-parametric and semi-parametric identification results without modeling assumptions on the outcome. When the assumptions for neither strategies are plausible, we propose a large class of flexible parametric and semi-parametric models for identifying principal causal effects. Our theory not only establishes formal identification results of several models that have been used in previous empirical studies but also generalizes them to allow for different types of outcomes and intermediate variables.
We developed a novel approach to identification and model testing in linear structural equation models (SEMs) based on auxiliary variables (AVs), which generalizes a widely-used family of methods known as instrumental variables. The identification pr
Causal inference concerns not only the average effect of the treatment on the outcome but also the underlying mechanism through an intermediate variable of interest. Principal stratification characterizes such mechanism by targeting subgroup causal e
Although social and biomedical scientists have long been interested in the process through which ideas and behaviors diffuse, the identification of causal diffusion effects, also known as peer and contagion effects, remains challenging. Many scholars
In survey sampling, calibration is a very popular tool used to make total estimators consistent with known totals of auxiliary variables and to reduce variance. When the number of auxiliary variables is large, calibration on all the variables may lea
In this paper, we extend graph-based identification methods by allowing background knowledge in the form of non-zero parameter values. Such information could be obtained, for example, from a previously conducted randomized experiment, from substantiv