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This helper function does the heavy lifting for optimize_effect_2. For a given casual query, it computes either a lower or an upper bound on the corresponding causal effect.

Usage

opt_effect(opt, obj)

Arguments

opt

A string. Either "min" or "max" for a lower or an upper bound, respectively.

obj

An object as returned by the function analyze_graph. Contains the casual query to be estimated.

Value

An object of class optbound; a list with the following named components:

  • expr is the main output; an expression of the bound as a print-friendly string,

  • type is either "lower" or "upper" according to the type of the bound,

  • dual_vertices is a numeric matrix whose rows are the vertices of the convex polytope of the dual LP,

  • dual_vrep is a V-representation of the dual convex polytope, including some extra data.