Models and DAGs

Question 1

What is a Model?

Answer 1

Represents our understanding of how the world works.
- Speculations about causal relationships, correlations and sequences of events.

Question 2

What are the elements of a Model?

Answer 2

1. Signature
2. Functional Relationships
3. Probability Distributions

Question 3

What are some challenges of Models?

Answer 3

• Uncertainty about the true causal model
• Difficulty writing down assumptions

Question 4

What is a Signature of the Model?

Answer 4

Describes variables and their ranges.

Question 5

What are the variables included in the Signature?

Answer 5

Exogenous and Endogenous

Question 6

What is an Exogenous variable?

Answer 6

Not caused by others, can be randomly assigned (eg, treatment)

Question 7

What is an Endogenous variable?

Answer 7

Caused by others (eg, outcomes, covariates, mediators, moderators)

Question 8

What is a Functional Relationship?

Answer 8

How endogenous variables are produced (often the outcome variable).

Question 9

What are the approaches to identifying a functional relationship?

Answer 9

• Structural causal models (SCMs) with DAGs
• Potential outcomes model

Question 10

What is Probability Distribution?

Answer 10

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.

Question 11

What is a DAG?

Answer 11

Directed Acyclic Graphs represent causal relationships between variables.

Question 12

What are outcome variables and what is its notation?

Answer 12

(Y): variables we want to understand (dependent variables)

Question 13

What are treatment variables and what is its notation?

Answer 13

(D): variables of interest that explain outcomes (independent variables)

Question 14

What are moderator variables and what is its notation?

Answer 14

(X2): additional causes of the outcome unrelated to the treatment

Question 15

What are confounder variables and what is its notation?

Answer 15

(X): variables that introduce a non-causal relationship between treatment and outcome

Question 16

What are collider variables?

Answer 16

Variables caused by both treatment and outcome (conditioning on them introduces bias)

Question 17

What are mediator variables and what is its notation?

Answer 17

(M): variables along the causal path from treatment to outcome

Question 18

What are instrument variables and what is its notation?

Answer 18

(Z): exogenous variables affecting treatment, then causing outcomes (exclusion restriction)

Question 19

What is the aim of a null model?

Answer 19

Aims to reject a null hypothesis of “zero effect”

Question 20

How do you build a model?

Answer 20

Requires theory from past research or exploratory research (model building)

Question 21

Why do you build a model?

Answer 21

Informs hypotheses about relationships between treatment and outcome

Question 22

What is Reality Tracking and how do you do it?

Answer 22

Reality tracking includes using reference models that should reflect reality (m*).
Eg, Qualitative methods (interviews, focus groups) and past research inform model development.

Question 23

What are Agnostic models used for?

Answer 23

Agnostic models are used in research to test ideas, not necessarily reflect reality. They challenge existing assumptions in a field by exploring different possibilities.

Question 24

Why is it important to assess the performance of a research design?

Answer 24

• Evaluating design performance under different models (including null models) is crucial.
• A robust design should provide reliable evidence across various scenarios.

Question 25

What is a backdoor path?

Answer 25

A backdoor path is a hidden route in a causal relationship or an indirect way a variable (D) can influence another variable (Y) through a common cause (X). This creates a spurious correlation between D and Y, making it difficult to determine the true causal effect of D on Y.

Question 26

What is an open backdoor path?

Answer 26

An open backdoor path occurs when this indirect influence (through the confounder) is not blocked, leading to bias in estimating the true effect/

Question 27

How to close back door paths?

Answer 27

1. Conditioning on confounders: This means taking the confounder (the variable creating the backdoor path) into account when analyzing the relationship between the other two variables.
   Colliders: Avoid controlling for colliders where it introduces bias

Question 28

What is Backdoor Criterion?

Answer 28

The backdoor criterion is a set of rules used in causal inference to identify situations where conditioning on certain variables (like confounders) will eliminate the bias caused by backdoor paths.

Question 29

What is the importance of DAGs in Causal inference?

Answer 29

• Provides a framework for understanding causal relationships and avoiding bias.
• Requires thorough knowledge of the data generating process and logical reasoning.
• Understanding collider bias is crucial for accurate estimation of causal effects.

Question 30

What are the steps of the Backdoor Criterion?

Answer 30

1. Identify paths
2. Check for colliders
3. Close backdoors (Conditioning on confounders or leaving colliders alone)