Models and DAGs
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What is a Model?
Represents our understanding of how the world works. - Speculations about causal relationships, correlations and sequences of events.
What are the elements of a Model?
• Signature • Functional Relationships • Probability Distributions
What are some challenges of Models?
• Uncertainty about the true causal model • Difficulty writing down assumptions
What is a Signature of the Model?
Describes variables and their ranges.
What are the variables included in the Signature?
Exogenous and Endogenous
What is an Exogenous variable?
Not caused by others, can be randomly assigned (eg, treatment)
What is an Endogenous variable?
Caused by others (eg, outcomes, covariates, mediators, moderators)
What is a Functional Relationship?
How endogenous variables are produced (often the outcome variable).
What are the approaches to identifying a functional relationship?
• Structural causal models (SCMs) with DAGs • Potential outcomes model
What is Probability Distribution?
A way to describe the likelihood or chance of different outcomes occurring for a particular event or variable. It shows how probable each outcome is, often represented by a mathematical function or a table.
What is a DAG?
Directed Acyclic Graphs represent causal relationships between variables.
What are outcome variables and what is its notation?
(Y): variables we want to understand (dependent variables)
What are treatment variables and what is its notation?
(D): variables of interest that explain outcomes (independent variables)
What are moderator variables and what is its notation?
(X2): additional causes of the outcome unrelated to the treatment
What are confounder variables and what is its notation?
(X): variables that introduce a non-causal relationship between treatment and outcome
What are collider variables?
Variables caused by both treatment and outcome (conditioning on them introduces bias)
What are mediator variables and what is its notation?
(M): variables along the causal path from treatment to outcome
What are instrument variables and what is its notation?
(Z): exogenous variables affecting treatment, then causing outcomes (exclusion restriction)
What is the aim of a null model?
Aims to reject a null hypothesis of “zero effect”
How do you build a model?
Requires theory from past research or exploratory research (model building)
Why do you build a model?
Informs hypotheses about relationships between treatment and outcome
What is Reality Tracking and how do you do it?
Reality tracking includes using reference models that should reflect reality (m*). Eg, Qualitative methods (interviews, focus groups) and past research inform model development.
What are Agnostic models used for?
Agnostic models are used in research to test ideas, not necessarily reflect reality. They challenge existing assumptions in a field by exploring different possibilities.
Why is it important to assess the performance of a research design?
• Evaluating design performance under different models (including null models) is crucial. • A robust design should provide reliable evidence across various scenarios.