Check linearity of objective function implied by a causal model and effect

Usage

check_linear_objective(causal_model, effectt)

Arguments

causal_model: An object of class "causalmodel" as produce by create_causalmodel
effectt: A character string that represents the causal effect of interest

Value

A logical value that is TRUE if the objective function is linear

Details

The effectt parameter describes your causal effect of interest. The effectt parameter must be of the form

p{V11(X=a)=a; V12(X=a)=b;...} op1 p{V21(X=b)=a; V22(X=c)=b;...} op2 ...

where Vij are names of variables in the graph, a, b are numeric values from 0:(nvals - 1), and op are either - or +. You can specify a single probability statement (i.e., no operator). Note that the probability statements begin with little p, and use curly braces, and items inside the probability statements are separated by ;. The variables may be potential outcomes which are denoted by parentheses. Variables may also be nested inside potential outcomes.

All of the following are valid effect statements:

p{Y(X = 1) = 1} - p{Y(X = 0) = 1}

p{X(Z = 1) = 1; X(Z = 0) = 0}

p{Y(M(X = 0), X = 1) = 1} - p{Y(M(X = 0), X = 0) = 1}

The effect must be fully specified, that is, all parents of a variable that is intervened upon need to be specified. The function cannot infer missing values or marginalize over some parents but not others.

Examples

 ## regular IV case

ivgraph <- initialize_graph(graph_from_literal(Z -+ X, X -+ Y, Ur -+ X, Ur -+ Y))
prob.form <- list(out = c("Y", "X"), cond = "Z")

iv_model <- create_causalmodel(graph = ivgraph,
            prob.form = prob.form)
check_linear_objective(iv_model, effectt = "p{Y(X = 1) = 1}")
#> [1] TRUE

#'  ## contaminated IV case

civgraph <- initialize_graph(graph_from_literal(Z -+ X, X -+ Y, Z-+ Y, Ur -+ X, Ur -+ Y))

cont_iv <- create_causalmodel(graph = civgraph, prob.form = prob.form)

check_linear_objective(cont_iv, effectt = "p{Y(X = 1) = 1}")
#> [1] FALSE