Ch 5 & ch 6 edits

chapters/04-dags.qmd

@@ -64,13 +64,13 @@ dag_data |>
   )
 ```
 
-The type of causal diagrams we use are also called directed acyclic graphs (DAGs)[^05-dags-1].
+The type of causal diagrams we use are also called directed acyclic graphs (DAGs)[^04-dags-1].
 These graphs are directed because they include arrows going in a specific direction.
 They're acyclic because they don't go in circles; a variable can't cause itself, for instance.
 DAGs are used for various problems, but we're specifically concerned with *causal* DAGs.
 This class of DAGs is sometimes called Structural Causal Models (SCMs) because they are a model of the causal structure of a question [@hernan2021; @Pearl_Glymour_Jewell_2021].
 
-[^05-dags-1]: An essential but rarely observed detail of DAGs is that dag is also an [affectionate Australian insult](https://en.wikipedia.org/wiki/Dag_(slang)) referring to the dung-caked fur of a sheep, a *daglock*.
+[^04-dags-1]: An essential but rarely observed detail of DAGs is that dag is also an [affectionate Australian insult](https://en.wikipedia.org/wiki/Dag_(slang)) referring to the dung-caked fur of a sheep, a *daglock*.
 
 DAGs depict causal relationships between variables.
 Visually, the way they depict variables is as *edges* and *nodes*.
@@ -752,26 +752,97 @@ sim_data <- podcast_dag |>
 sim_data
 ```
 
-Since we have simulated this data, we know that this is a case where we can estimate the causal effect using a basic linear regression model.
-@fig-dag-sim shows a forest plot of the simulated data based on our DAG.
-Notice the model that only included the exposure resulted in a spurious effect (an estimate of -0.1 when we know the truth is 0).
-In contrast, the model that adjusted for the two variables as suggested by `ggdag_adjustment_set()` is not spurious (much closer to 0).
+@fig-dag-sim shows a forest plot of estimates using the simulated data based on our DAG.
+One estimate is unadjusted and the other is adjusted for `mood` and `prepared`.
+Notice the unadjusted estimate resulted in a spurious effect (an estimate of -0.1 when we know the truth is 0).
+In contrast, the estimate that adjusted for the two variables as suggested by `ggdag_adjustment_set()` is not spurious (it's much closer to 0).
 
 ```{r}
 #| label: fig-dag-sim
 #| fig-cap: "Forest plot of simulated data based on the DAG described in @fig-dag-podcast."
+#| code-fold: true
 ## Model that does not close backdoor paths
 library(broom)
 unadjusted_model <- lm(exam ~ podcast, sim_data) |>
   tidy(conf.int = TRUE) |>
   filter(term == "podcast") |>
-  mutate(formula = "podcast")
+  mutate(formula = "unadjusted")
 
 ## Model that closes backdoor paths
 adjusted_model <- lm(exam ~ podcast + mood + prepared, sim_data) |>
   tidy(conf.int = TRUE) |>
   filter(term == "podcast") |>
-  mutate(formula = "podcast + mood + prepared")
+  mutate(formula = "mood + prepared")
+
+bind_rows(
+  unadjusted_model,
+  adjusted_model
+) |>
+  ggplot(aes(x = estimate, y = formula, xmin = conf.low, xmax = conf.high)) +
+  geom_vline(xintercept = 0, linewidth = 1, color = "grey80") +
+  geom_pointrange(fatten = 3, size = 1) +
+  theme_minimal(18) +
+  labs(
+    y = NULL,
+    caption = "correct effect size: 0"
+  )
+```
+
+Of course, we know we're working with the true DAG.
+Let's say that, not knowing the true DAG (@fig-dag-podcast), we drew @fig-dag-podcast-wrong.
+
+```{r}
+#| label: fig-dag-podcast-wrong
+#| fig-cap: "Proposed DAG to answer the question: Does listening to a comedy podcast the morning before an exam improve graduate students' test scores? This time, we proposed the wrong DAG."
+#| fig-width: 4
+#| fig-height: 4
+#| warning: false
+podcast_dag_wrong <- dagify(
+  podcast ~ humor + prepared,
+  exam ~ prepared,
+  coords = time_ordered_coords(
+    list(
+      # time point 1
+      c("prepared", "humor"),
+      # time point 2
+      "podcast",
+      # time point 3
+      "exam"
+    )
+  ),
+  exposure = "podcast",
+  outcome = "exam",
+  labels = c(
+    podcast = "podcast",
+    exam = "exam score",
+    humor = "humor",
+    prepared = "prepared"
+  )
+)
+ggdag(podcast_dag_wrong, use_labels = "label", text = FALSE) +
+  theme_dag()
+```
+
+Since the DAG is wrong, it doesn't help us get the right answer.
+It says we only need to adjust for `prepared`, but we are missing a causal pathway that is confounding the relationship.
+Now, neither estimate is right.
+
+```{r}
+#| label: fig-dag-sim-wrong
+#| fig-cap: "Forest plot of simulated data based on the DAG described in @fig-dag-podcast. However, we've analyzed it using the adjustment set from @fig-dag-podcast-wrong, giving us the wrong answer."
+#| code-fold: true
+## Model that does not close backdoor paths
+library(broom)
+unadjusted_model <- lm(exam ~ podcast, sim_data) |>
+  tidy(conf.int = TRUE) |>
+  filter(term == "podcast") |>
+  mutate(formula = "unadjusted")
+
+## Model that closes backdoor paths
+adjusted_model <- lm(exam ~ podcast + prepared, sim_data) |>
+  tidy(conf.int = TRUE) |>
+  filter(term == "podcast") |>
+  mutate(formula = "prepared")
 
 bind_rows(
   unadjusted_model,
@@ -1237,7 +1308,7 @@ That's a good thing: you know now where there is uncertainty in your DAG.
 You can then examine the results from multiple plausible DAGs or address the uncertainty with sensitivity analyses.
 
 If you have more than one candidate DAG, check their adjustment sets.
-If two DAGs have overlapping adjustment sets, focus on those sets; then, you can move forward in a way that satisfies the plausible assumptions you have.
+If two DAGs have any adjustment sets that are identical between them, focus on those sets; then, you can move forward in a way that satisfies the plausible assumptions you have.
 
 ### Consider your question
 
@@ -1276,7 +1347,7 @@ It's tempting to visualize that relationship like this:
 #| label: fig-feedback-loop
 #| fig-width: 4.5
 #| fig-height: 3.5
-#| fig-cap: "A DAG representing the reciprocal relationship between A/C use and global temperature because of global warming. Feedback loops are useful mental shorthands to describe variables that impact each other over time compactly, but they are not true causal diagrams."
+#| fig-cap: "A conceptual diagram representing the reciprocal relationship between A/C use and global temperature because of global warming. Feedback loops are useful mental shorthands to describe variables that impact each other over time compactly, but they are not true causal diagrams."
 dagify(
   ac_use ~ global_temp,
   global_temp ~ ac_use,

chapters/05-not-just-a-stats-problem.qmd

@@ -169,7 +169,7 @@ causal_quartet |>
 
 Standardizing numeric variables to have a mean of 0 and standard deviation of 1, as implemented in `scale()`, is a common technique in statistics.
 It's useful for a variety of reasons, but we chose to scale the variables here to emphasize the identical correlation between `covariate` and `exposure` in each dataset.
-If we didn't scale the variables, the correlation would be the same, but the plots would look different because their standard deviation are different.
+If we didn't scale the variables, the correlation would be the same, but the plots would look different because their standard deviations are different.
 The beta coefficient in an OLS model is calculated with information about the covariance and the standard deviation of the variable, so scaling it makes the coefficient identical to the Pearson's correlation.
 
 @fig-causal_quartet_covariate_unscaled shows the unscaled relationship between `covariate` and `exposure`.