Transcription of Causal inference using regression on the treatment variable
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Causal inference using regression on the treatment variable
CHAPTER 9 Causal inference using regression on thetreatment Causal inference and predictive comparisonsSo far, we have been interpreting regressionspredictively: given the values of severalinputs, the fitted model allows us to predicty, considering thendata points as asimple random sample from a hypothetical infinite superpopulation or probabilitydistribution. Then we can make comparisons across differentcombinations of valuesfor these chapter and the next considercausal inference , which concerns whatwouldhappento an outcomeyas a result of a hypothesized treatment or a regression framework, the treatment can be written as a variableT:1Ti={1 if unitireceives the treatment 0 if unitireceives the control, or, for a continuous treatment ,Ti= level of the treatment assigned to the usual regression context, predictive inference relates to comparisonsbetweenunits, whereas Causal inference addresses comparisons of different treatments ifapplied to thesameunits. More generally, Causal inference can be viewed as aspecial case of prediction in which the goal is to predict whatwould have happenedunder different treatment options.}
CHAPTER 9 Causal inference using regression on the treatment variable 9.1 Causal inference and predictive comparisons So far, we have been interpreting regressions predictively: given the values of several inputs, the fitted model allows us to predict y, considering the n data points as a
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