20260505 - DAGs

Author: isaactpetersen

dags.qmd

@@ -4,7 +4,7 @@ title: "Directed Acyclic Graphs (DAGs)"
 
 When conceptualizing and designing a study, or when developing plans to test a research question, it is important to draw a directed acyclic graph (DAG).
 DAGs, like [path diagrams](figures.qmd#sec-pathDiagrams), are causal diagrams.
-Causal diagrams depict the hypoothesized causal processes that link two or more variables.
+Causal diagrams depict the hypothesized causal processes that link two or more variables.
 Path diagrams are typically used after analysis to describe and report the findings in analysis (when using path analysis, [factor analysis](factorAnalysis.qmd), or [structural equation modeling](sem.qmd)).
 By contrast, DAGs are particularly useful when designing a study or before analysis, because they can help specify which variables it is important to control for and—just as importantly—which variables it is important not to control for.
 
@@ -16,10 +16,13 @@ That is, it is okay to control for variables that influence `Y` that do not infl
 When including these variable as control variables in a model, they are called precision variables.
 You do not need to include precision variables in the model because the estimate of the association is already unbiased if you have controlled for all confounds.
 However, including precision variables in the model reduces residual variance in the outcome variable and can yield more precise estimates (i.e., smaller standard errors) of the association between the predictor variable and outcome variable.
+It is also possibly okay to control for ancestors of the predictor variable that are not confounds.
+That is, it is possibly okay to control for variable that influence `X` that do not influence `Y` and that are not influenced by `X`.
+However, controlling for ancestors of the predictor variable (that are not confounds) can reduce precision of the estimate of the causal effect because you are reducing useful variation in `X`.
 
 In addition, there are some variables that are important not to control for.
 It is important not to control for mediators of two variables for which you want to determine the estimate of the causal effect—unless you are interested in the direct causal effect of the predictor variable on the outcome variable above and beyond the mediator.
-In addition, it is is important not to control for a) ancestors of the predictor variable that are not confounds, b) descendants of the outcome variable, and c) colliders (unless the collider is also a confound).
+In addition, it is is important not to control for a) descendants of the outcome variable and b) colliders (unless the collider is also a confound).
 
 For more information on DAGs, including ancestors, descendants, confounders, and colliders, see here: <https://isaactpetersen.github.io/Fantasy-Football-Analytics-Textbook/causal-inference.html#sec-causalDiagrams>.