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 missin values or marginalize over some parents but not others.

Examples

 ## regular IV case

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

observed.variables <- V(graph)[V(graph)$latent == 0]
p.vals <- expand.grid(Z = 0:1, X = 0:1, Y = 0:1)

respvars <- create_response_function(graph)
prob.form <- list(out = c("Y", "X"), cond = "Z")

effectt <- "p{Y(X = 1) = 1}"

iv_model <- create_causalmodel(graph = NULL, respvars = respvars,
                p.vals = p.vals, prob.form = prob.form)
check_linear_objective(iv_model, effectt = effectt)
#> [1] TRUE

#'  ## contaminated IV case

graph <- initialize_graph(graph_from_literal(Z -+ X, X -+ Y, Z-+ Y, Ur -+ X, Ur -+ Y))
p.vals <- expand.grid(Z = 0:1, X = 0:1, Y = 0:1)

prob.form <- list(out = c("Y", "X"), cond = "Z")

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

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