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Latent class models for the causal effect of a treatment

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In randomized experiments involving humans, there is often evidence that subjects who tend not to comply are also more likely to benefit less (or perhaps more) from the treatment. Such situations may be modelled by a directed acyclic graph involving a latent variable which represents unobserved individual attitudes related to compliance and response. In this talk a probabilistic approach free of counterfactuals will be presented. Though this model is not identifiable, the conditions under which a suitable average causal effect (across latent classes) is equal to the instrumental variable estimand will be discussed. These conditions are the probabilistic analog of the conditions derived in the counterfactual literature (Angrist, Imbens and Rubin, Jasa, 1996; Hermàn and Robins, Epidemiology, 2006).

When additional information, like individual covariates, is available, probabilistic models involving causal effects within latent classes may become identifiable; a technique for checking model identifiability will be outlined together with numerical methods for computing maximum likelihood estimates of the parameters of interest. However, even with additional information, the price for model identifiabilility is a suitable set of modelling assumption. A few examples will be used as an illustration.

This talk is part of the Statistics series.

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