Causal Modeling Homework 4 (final)

Homework 4 covers the following topics:

  1. Markov equivalence classes (of directed acyclic graphs)
    1. define ‘equivalent graphs’ in terms of d-separations implied by each class of graphs
  2. From a set of d-separations,
    1. determine adjacent pairs of vertices, unshielded colliders, corresponding Markov equivalence class, CPDAG (complete partial directed acyclic graph)
  3. Given a joint distribution P(a,b,c,d,e) that factorizes according to an unknown DAG G* with a set of conditional independence rlationships,
    1. Inferring structure of DAG G*
    2. Assumptions on DAG G* (about inferences)
  4. PC algorithm
    1. Interpreting steps, understanding how the PC algorithm uses significance of associations to remove/direct edges
    2. orienting undirected edges in resulting CPDAG consistent with time-ordering of variables (common-sense causal relations)
  5. Single-world intervention graphs (SWIGs)
    1. intervene on x, read implications
    2. Applying the backdoor formula to adjust for confounding
  6. Intent-to-treat (ITT) effect of treatment assignment (Z) on outcome (Y) given treatment (X)
    1. Verifying IV inequalities (to verify no direct effect of treatment assignment Z on outcome Y, so only effect of treatment X influences Y)
    2. Constructing 3-d polytope for (%Helped, %Hurt, %Always recover, %never recover) compatible with data in Z=0 (control assignment), Z=1 (treatment assignment), and combination of both
      1. (recall: intersection before projection yields a subset compared to projecting THEN intersecting 3-d polytopes in 2-d)
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