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Causal Inference The Mixtape - 5 Matching and Subclassification

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One of the main things I wanted to cover in the chapter on directed acylical graphical models was the idea of the backdoor criterion. Specifically, insofar as there exists a conditioning strategy that will satisfy the backdoor criterion, then you can use that strategy to identify some causal effect. We now discuss three different kinds of conditioning strategies. They are subclassification, exact matching, and approximate matching.1 Subclassification is a method of satisfying the backdoor criterion by weighting differences in means by strata-specific weights. These strata-specific weights will, in turn, adjust the differences in means so that their distribution by strata is the same as that of the counterfactual’s strata. This method implicitly achieves distributional balance between the treatment and control in terms of that known, observable confounder. This method was created by statisticians like Cochran (1968), who tried to analyze the causal effect of smoking on lung cancer, and

5 Matching and Subclassification – <span style='font-weight: 700'>Causal Inference</span><br/> <i style='color: #00b7ff'>The Mixtape</i> Causal Inference: The Mixtape. Buy the print version today: Buy from Amazon Buy from Yale Press \[ % Define terms \newcommand{\Card}{\text{Card }} \DeclareMathOperator*{\cov}{cov} \DeclareMathOperator*{\var}{var} \DeclareMathOperator{\Var}{Var\,} \DeclareMathOperator{\Cov}{Cov\,} \DeclareMathOperator{\Prob}{Prob} \newcommand{\independent}{\perp \!\!\! \perp} \DeclareMathOperator{\Post}{Post} \DeclareMathOperator{\Pre}{Pre} \DeclareMathOperator{\Mid}{\,\vert\,

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