address Ben's notes

Signed-off-by: Nathaniel <NathanielF@users.noreply.github.com>

Author: NathanielF

docs/source/quasi_dags.ipynb

@@ -277,7 +277,7 @@
             "source": [
                 "## Propensity Score Weighting\n",
                 "\n",
-                "In this exposition we follow the presentation of {cite:t}`steiner2017graphical`. The idea they discuss is that we should conceive of the propensity score adjustment techniques as a primarily an offset aimed at balancing the existing degree of confounding. The focus is on recovering the condition of __strong ignorability__ such that $Y(1), Y(0) \\perp\\!\\!\\!\\!\\perp Z | X$. Achieving this status removes the backdoor path between the measured covariates $X$ and the treatment $Z$ thereby giving us license to causal conclusions. They emphasise this point in that the PS is a collider variable we can use to disentangle the confounding influence of the covariates $X$ influencing selection into the treatment. \n",
+                "In this exposition we follow the presentation of {cite:t}`steiner2017graphical`. The idea they discuss is that we should conceive of the propensity score adjustment techniques as a primarily an offset aimed at balancing the existing degree of confounding. The focus is on recovering the condition of __strong ignorability__ such that $Y(1), Y(0) \\perp\\!\\!\\!\\!\\perp Z | X$. This constraint is phrased in terms of potential outcomes $Y(0), Y(1)$, which we won't define here, but basically we're saying the outcomes are independent of the treatment when we condition on the covariates to determine selection effects. Achieving this status removes the backdoor path between the measured covariates $X$ and the treatment $Z$ thereby giving us license to causal conclusions. They emphasise this point in that the PS (propensity score) is a collider variable we can use to disentangle the confounding influence of the covariates $X$ influencing selection into the treatment. \n",
                 "\n",
                 "> \"This general result is obtained because the PS _itself_ is a collider variable and, thus, conditioning on the PS offsets the confounding relation $X \\rightarrow Z$  regardless of the choice of a specific PS design— matching, stratification, or weighting\" -pg 176 \"Graphical Models\n",
                 "for Quasi-experimental Designs\"\n",
@@ -288,7 +288,11 @@
         {
             "cell_type": "code",
             "execution_count": 36,
-            "metadata": {},
+            "metadata": {
+                "tags": [
+                    "remove-input"
+                ]
+            },
             "outputs": [
                 {
                     "data": {