diff --git a/slides/raw/07-using-pscores.qmd b/slides/raw/07-using-pscores.qmd index 24da616..62ec523 100644 --- a/slides/raw/07-using-pscores.qmd +++ b/slides/raw/07-using-pscores.qmd @@ -247,54 +247,6 @@ $$\Large w_{ATE} = \frac{Z_i}{p_i} + \frac{1-Z_i}{1 - p_i}$$ (Z / p) + ((1 - Z) / (1 - p)) ``` - - -## Target estimands: ATT & ATC {background-color="#23373B"} - -. . . - -Average Treatment Effect Among the Treated (ATT) -$$\Large w_{ATT} = \frac{p_i Z_i}{p_i} + \frac{p_i (1-Z_i)}{1-p_i}$$ - -```{r} -#| eval: false -((p * Z) / p) + ((p * (1 - Z)) / (1 - p)) -``` - -## Target estimands: ATT & ATC {background-color="#23373B"} - -Average Treatment Effect Among the Controls (ATC) -$$\Large w_{ATC} = \frac{(1-p_i)Z_i}{p_i} + \frac{(1-p_i)(1-Z_i)}{(1-p_i)}$$ - -```{r} -#| eval: false -(((1 - p) * Z) / p) + (((1 - p) * (1 - Z)) / (1 - p)) -``` - -## Target estimands: ATM & ATO {background-color="#23373B"} - -. . . - -Average Treatment Effect Among the Evenly Matchable (ATM) -$$\Large w_{ATM} = \frac{\min \{p_i, 1-p_i\}}{Z_ip_i + (1-Z_i)(1-p_i)}$$ - - -```{r} -#| eval: false -pmin(p, 1 - p) / (Z * p + (1 - Z) * (1 - p)) -``` - -## Target estimands: ATM & ATO {background-color="#23373B"} - -Average Treatment Effect Among the Overlap Population -$$\Large w_{ATO} = (1-p_i)Z_i + p_i(1-Z_i)$$ - - -```{r} -#| eval: false -(1 - p) * Z + p * (1 - Z) -``` - ## Histogram of propensity scores ```{r} @@ -350,6 +302,28 @@ ggplot(df, aes(.fitted)) + theme(legend.position = "bottom") ``` +## Target estimands: ATT & ATC {background-color="#23373B"} + +. . . + +Average Treatment Effect Among the Treated (ATT) +$$\Large w_{ATT} = \frac{p_i Z_i}{p_i} + \frac{p_i (1-Z_i)}{1-p_i}$$ + +```{r} +#| eval: false +((p * Z) / p) + ((p * (1 - Z)) / (1 - p)) +``` + +## Target estimands: ATT & ATC {background-color="#23373B"} + +Average Treatment Effect Among the Controls (ATC) +$$\Large w_{ATC} = \frac{(1-p_i)Z_i}{p_i} + \frac{(1-p_i)(1-Z_i)}{(1-p_i)}$$ + +```{r} +#| eval: false +(((1 - p) * Z) / p) + (((1 - p) * (1 - Z)) / (1 - p)) +``` + ## ATT ```{r} @@ -384,6 +358,31 @@ ggplot(df, aes(.fitted)) + theme(legend.position = "bottom") ``` + +## Target estimands: ATM & ATO {background-color="#23373B"} + +. . . + +Average Treatment Effect Among the Evenly Matchable (ATM) +$$\Large w_{ATM} = \frac{\min \{p_i, 1-p_i\}}{Z_ip_i + (1-Z_i)(1-p_i)}$$ + + +```{r} +#| eval: false +pmin(p, 1 - p) / (Z * p + (1 - Z) * (1 - p)) +``` + +## Target estimands: ATM & ATO {background-color="#23373B"} + +Average Treatment Effect Among the Overlap Population +$$\Large w_{ATO} = (1-p_i)Z_i + p_i(1-Z_i)$$ + + +```{r} +#| eval: false +(1 - p) * Z + p * (1 - Z) +``` + ## ATM ```{r}