Suppose an urban planner wants to understand what shapes a person’s commute. A model that predicts travel choices from survey columns is not enough to answer what might change those choices. A causal graphical model starts with assumptions about the data-generating process: which variables cause which others, including variables the survey did not measure. section 3.1.1 section 3.3
Its scaffold is a causal directed acyclic graph (DAG). Nodes are variables; an arrow from one node to another asserts that the first causes the second. The graph communicates *what causes what*, not the strength or functional form of a cause’s effect. Those details belong in a probabilistic model built on the graph. section 3.1 section 3.1.3
Modeling a commute
One proposed graph has age and gender pointing to education; education pointing to occupation and residence; and occupation and residence pointing to travel choice. If A, S, E, O, R, and T denote those variables, its joint distribution factors as P(A)P(S)P(E|A,S)P(O|E)P(R|E)P(T|O,R). Each factor conditions a variable on its direct parents. This is a set of strong causal and conditional-independence assumptions, not a pattern established merely by fitting the survey. section 3.1.1 section 3.1.6
Listing 3.2 Building the transportation DAG in pgmpy
from pgmpy.models import BayesianNetwork
model = BayesianNetwork( #1
[
('A', 'E'), #2
('S', 'E'), #2
('E', 'O'), #2
('E', 'R'), #2
('O', 'T'), #2
('R', 'T') #2
]
)
The pgmpy listing makes the proposed commuting assumptions concrete as a list of directed edges; it specifies graph structure, not learned probabilities. section 3.1.1
To make the graph generative, assign each node a causal Markov kernel: a distribution for that node given its parents. These kernels can use conditional probability tables, regressions, or neural networks; their parameters can be learned with methods such as maximum likelihood or Bayesian estimation. Treating kernels as distinct mechanisms gives the model parameter modularity and a potential source of invariance when settings change. section 3.2 section 3.5
A practical workflow is:
- Start with the causal question, then include relevant causes even when they are absent from the dataset; add variables needed for causal analysis and for a clear account of the process. section 3.3 section 3.5
- Specify arrows using domain assumptions, then choose and learn the parent-conditioned kernels. If a variable is latent, its kernel may require a method such as structural expectation maximization—and its parameters may not be identifiable from the available data. section 3.1.1 section 3.1.10
- Seek evidence against the graph. Its implied conditional independences can be checked against data; a detected dependence where independence was asserted calls for revision. Such tests are useful for refutation, not proof that the graph is true. section 4.1 section 4.3
A well-fitting graphical model is therefore not automatically a sound causal model. The graph omits mechanism details and may omit measured-data distinctions; latent variables can limit what its parameters reveal. Keep its assumptions explicit, test what can be tested, and use it as a scaffold for downstream causal questions rather than as a guarantee of causal truth. section 3.1.3 section 4.3
