How can you use diagrams to analyze causal relationships?

Causal relationships are connections between events or variables that imply a cause-and-effect mechanism. For example, smoking causes lung cancer, or education increases income. However, causal relationships are not always easy to identify or prove, especially when there are confounding factors, alternative explanations, or hidden assumptions involved. That's why diagrams can be useful tools to analyze causal relationships, as they can help you visualize, clarify, and test your causal hypotheses. In this article, you will learn how to use three types of diagrams to analyze causal relationships: causal graphs, causal trees, and causal diagrams.

1 Causal graphs

A causal graph is a simple way to represent the causal relationships between variables using nodes and arrows. Nodes are the variables of interest, and arrows indicate the direction of causation. For example, a causal graph for the smoking-lung cancer relationship could look like this: Smoking ---> Lung cancer This graph shows that smoking is a cause of lung cancer, but not the other way around. However, a causal graph can also include other variables that may affect or mediate the causal relationship, such as age, genetics, or air pollution. For example:

Smoking ---> Lung cancer <--- Air pollution
Age ---> Smoking
Genetics ---> Lung cancer

This graph shows that smoking and air pollution are both causes of lung cancer, but they may also interact with each other. Age is a cause of smoking, but not of lung cancer directly. Genetics is a cause of lung cancer, but not of smoking. A causal graph can help you identify the potential confounders, mediators, and moderators of your causal hypothesis, and guide your data collection and analysis.

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Darshi. A.
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I am baffled that age causes smoking. On the other hand, (Smoking, Air pollution) -----> Lung cancer seems to make more sense.

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Meaghan Anderson

M.S. Exercise and Health Science • B.S. Biology & Exercise and Health Science • U.S. Coast Guard & Army National Guard Veteran
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I disagree with the phrase “Age is a cause of smoking, but not of lung cancer directly.” I believe that a better way to say this, for better overall comprehension, would be to say “Age is a risk factor of smoking but not of lung cancer directly.”

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2 Causal trees

A causal tree is a way to represent the causal relationships between events using a branching structure. A causal tree starts with a root event, which is the outcome of interest, and then traces back the possible causes or pathways that lead to that event. For example, a causal tree for the lung cancer outcome could look like this:

Lung cancer
  |
  +-- Smoking
  |     |
  |     +-- Age
  |     +-- Peer pressure
  |     +-- Addiction
  |
  +-- Air pollution
  |     |
  |     +-- Location
  |     +-- Occupation
  |
  +-- Genetics
        |
        +-- Family history
        +-- Mutation

This tree shows that lung cancer can have multiple causes, and each cause can have multiple sub-causes or factors. A causal tree can help you explore the different scenarios or counterfactuals that could lead to or prevent the outcome of interest. For example, you could ask: What if the person did not smoke? What if the person lived in a less polluted area? What if the person had a different genetic makeup?

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Darshi. A.
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This graph makes more sense than the previous one. However this gives equal weights to all factors. This may not be appropriate.

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3 Causal diagrams

A causal diagram is a way to represent the causal relationships between variables using mathematical symbols and equations. A causal diagram can also be called a structural equation model or a directed acyclic graph. A causal diagram combines the features of a causal graph and a causal tree, as it shows both the direction and the magnitude of the causal effects. For example, a causal diagram for the smoking-lung cancer relationship could look like this:

S = Smoking
L = Lung cancer
A = Air pollution
G = Genetics
L = a*S + b*A + c*G + e

This diagram shows that lung cancer is a function of smoking, air pollution, genetics, and an error term. The coefficients a, b, and c represent the strength of the causal effects, and the error term e represents the unexplained variation. A causal diagram can help you estimate and compare the causal effects of different variables, and test your causal hypotheses using statistical methods.

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Meaghan Anderson

M.S. Exercise and Health Science • B.S. Biology & Exercise and Health Science • U.S. Coast Guard & Army National Guard Veteran
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This makes sense to me. This is how you build an equation to establish one’s risk with signification risk factors. However, the error coefficient can be elaborated upon by explaining that it is calculated specifically for the model (equation) to emphasize that while it is random influence it is not random to the equation itself.

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Darshi. A.
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Cannot understand why not the proper equation with a warning about statistical variations instead of this sort of a psedo-equation?

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4 Here’s what else to consider

This is a space to share examples, stories, or insights that don’t fit into any of the previous sections. What else would you like to add?

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How can you use diagrams to analyze causal relationships?

1

2

3

4

1 Causal graphs

2 Causal trees

3 Causal diagrams

4 Here’s what else to consider

Statistics

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How can you use diagrams to analyze causal relationships?

1

2

3

4

1 Causal graphs

2 Causal trees

3 Causal diagrams

4 Here’s what else to consider

Statistics

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