Critical thinking
Article: Foster (2010)
Causal Inference and Developmental Psychology
(the part needed for psychology at the UvA)

Four premises

• Causal inference is essential to accomplishing the goals of developmental psychologists
• In many analyses, psychologists unfortunately are attempting causal inference but doing so badly, based on many implicit and, in some cases, implausible assumptions.
• These assumptions should be identified explicitly and checked empirically and conceptually
• Once introduced to the broader issues, developmental psychologists will recognize the central importance of causal inference and naturally embrace the methods available.

Why causal inference?

Causal thinking and causal inference are unavoidable.

• Even if researchers can distinguish associations from causal relationships, lay readers, journalists, policymakers, and other researchers generally cannot.
• If a researcher resist the urge to jump form association to causality, other researchers seem willing to do so on his or her behalf.

Causal inference as the goal of developmental psychology

the lesson is not that causal relationships can never be established outside of random assignment, but that they cannot be inferred from associations alone. Some additional assumptions are required.

The goal of this research should be to make causal inference as plausible as possible.
Doing so involves applying the best methods available among a growing set of tools.
As part of the proper use of those tools, the researcher should identify the key assumptions on which they rest and their plausibility in any particular application.
The researcher should check the consistency of those assumptions as much as possible using the available data. In many instances key assumptions will remain untestable.
The plausibility of those assumptions need to be assessed in the light of substantive knowledge.

What constitutes credible or plausible is not without debate.

At this point, much of developmental psychology involves implausible causal inference.

• Such inference could be improved even without dramatically changing the complexity of the analysis.

Two frameworks for causal inference

Two conceptual tools are especially helpful in moving from associations to causal relationships.

• The directed acyclic graph (DAG)

This tool assists researchers in identifying the implications of a set of associations for understanding causality and the set of assumptions under which those associations imply causality
Moving from association to causality requires ruling out potential confounders: variables associated with both treatment and outcome.
The DAG is particularly useful for helping the research to identify covariates and for perhaps understanding unanticipated consequences of incorporating these variables.

Tool 1: DAGs

Because they are directional, causal relationships among sets of variables imply different covariance matrices.
When placed in the context of their relationship to other variables, a given pattern of covariances (associations) can rule in or out causal relationships working in different directions involving two variables.
For that reason, computer scientists have developed a symbolic representation of dependencies among variables, the DAG.
A DAG compromises variables and arrows linking them.
The DAG should be grounded in one’s conceptual understanding of the treatment or exposure of interest.

The DAG is directed in the sense that the arrows represent causal relationships. The model assumes a certain correspondence between the arrows in the graph and the relationships between the variables.

A key feature of the DAG is structural stability: an intervention on one component of the model does not alter the broader structure.

The DAG also assumes a preference for simplicity and probabilistic stability.
Simplicity means that models that represent data with fewer linkages are preferred to the more complex.
Stability: the robustness of a set of relationships across a range of possible magnitudes.

A DAG looks like a path diagram or a structural equations model. Key features distinguish DAGs.

• The DAG is not linear or even parametric
• The DAG contains no bidirectional arrows implying simultaneity