![]() Horvitz-Thompson estimators require information about the probability each unit is in treatment and control, as well as the joint probability each unit is in the treatment, in the control, and in opposite treatment conditions. This is particularly useful when there are clusters of different sizes being randomized into treatment or when the treatment assignment is complex and there are dependencies across units in the probability of being treated. Horvitz-Thompson estimators yield unbiased treatment effect estimates when the randomization is known. Below is an example, and more can be seen on the function reference page lm_lin and some formal notation can be seen in the mathematical notes. ![]() The only difference is in the second argument covariates, where one specifies a right-sided formula with all of your pre-treatment covariates. This function is a wrapper for lm_robust(), and all arguments that work for lm_robust() work here. We dub this estimator the Lin estimator and it can be accessed using lm_lin(). To facilitate this, we provide a wrapper that processes the data and estimates the model. This can require a non-trivial amount of data pre-processing. Lin ( 2013) proposes centering all pre-treatment covariates, interacting them with the treatment variable, and regressing the outcome on the treatment, the centered pre-treatment covariates, and all of the interaction terms. In response, Lin ( 2013) proposed an alternative estimator that would reduce this bias and improve precision. However, Freedman ( 2008) demonstrated that pre-treatment covariate adjustment biases estimates of average treatment effects. ![]() Adjusting for pre-treatment covariates when using regression to estimate treatment effects is common practice across scientific disciplines.
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