Thinking Clearly About Correlations and Causation: Graphical Causal Models for Observational Data - Rohrer - 2018 - Article

What is the purpose of the article?

The article discusses causal inference based on observational data, introducing readers to graphical causal models that can provide a powerful tool for thinking more clearly about the interrelations between variables.

Researchers from different areas use different strategies to deal with weak observational data (manipulating the independent variable can sometimes be unfeasible, unethical, or impossible).

• E.g. using surrogates can lead to valuable insights but also comes with a trade-off of decreased external validity.
• Some researchers try to cautiously avoid causal language.
• Many have tried to statistically control for third variables. Often these attempts lack proper justification.

This article aims to give psychologists a primer to a more principles approach to make causal inferences based on observational data. It discusses the improvement of causal inferences on observational data through using directed acyclic graphs (DAGs). They provide visual representations of causal assumptions.

What are directed acyclic graphs?

DAG’s consist of nodes (representing variables in research) and arrows (indicating the direction of the relationship). It can display the direction of causation or a lurking (confounding) variable and only contain one headed arrow. They are ‘acyclic’ because they don’t allow for cyclic paths in which variables become their own ancestors. A variable cannot causally affect itself.

What is a back-door path?

If we want to derive a valid causal conclusion we need a causal DAG that’s complete because it includes all common causes of all pairs of variables that are included in the DAG. After such a DAG is built, ‘back-door paths’ can be recognized. These are (non-causal) paths starting with an arrow pointing to the independent variable and ending with an arrow pointing to the dependent variable (indicating there may be a common factor affecting both treatment and outcome). They are problematic whenever they convey an association and can show a spurious association.

The purpose of third variable control is to block back-door paths. If all back-door paths between variables can be blocked, the causal effect connecting the independent and dependent variables can be identified.

How do we control for a variable?

• Stratified analysis: stratify the sample controlling for confounders. Maybe unfeasible if the third variable needing control has many levels, if it is continuous, or if multiple third variables and interactions need to be accounted for.
• Including third variables in regression models: dependent variable can be regressed on both the independent variable and the covariate to control for the covariate’s effects. Does not guarantee adequate adjustment for the covariate.
• Matching: when there is a need to control for many third variables. Propensity-score matching is popular in social sciences but it fails to properly identify the causal effect.

What are examples of collider bias?

• Nonresponse bias: example, if a researcher analyzes only completed questionnaires, and the variables of interest are associated with questionnaire completion. Assuming we are interested in the association between grit and intelligence and our assessment is burdensome. Grit and intelligence make it easier for respondents to push through and finish it. Questionnaire completion is therefore a collider between grit and intelligence.
• Attrition bias: systematic errors caused by unequal loss of participants. If only remaining respondents are included in analysis, spurious associations may arise and open up back-door paths between variables of interest.

What are some definitions?

• Ancestor: variable causally affecting another variable, influencing it directly (ancestor > X) or indirectly (ancestor > mediator > X). direct ancestors are called parents.
• Blocked path: path containing (a) collider that the analysis has not been conditioned on or (b) a non-collider (confounder or mediator) that the analysis has been conditioned on. Does not transmit an association between variables.
• Causal path: path consisting of only chains that can convey a causal association if unblocked.
• Chain: causal structure of the form A > B > C.
• Collider: a variable in the middle of an inverted fork (A > collider
• Conditioning on a variable: process of introducing information about a variable into an analysis (statistical control or sample selection).
• Confounder: variable in the middle of a fork (A C).
• Descendant: variable causally affected by another variable, directly (X > descendant) or indirectly (X > mediator > descendant). Direct descendants are called children.
• Fork: structure of the form A C.
• Inverted fork: structure of the form A > B
• Mediator: variable middle in a chain (A > mediator > C.
• Node: variable in a DAG.
• Non-causal path: path containing at least one fork or inverted fork and can show a non-causal association when unblocked.

What are some examples of DAGs?

• Educational attainment grades (fork).
• Intelligence > educational attainment > grades (chain).
• Intelligence > grades

Summary

The practice of making causal inferences based on observational data depends on awareness of potential confounders and meaningful statistical control (or non-control) taking into account estimation issues like nonlinear confounding and measurement error. Back-door paths should be considered before data is collected to make sure all relevant variables are measured. Additionally, variables that should not be controlled for (colliders and mediators) need to be considered.