Builds a design in which two pieces of evidence are sought and used to update about whether X caused Y using Bayes' rule.

process_tracing_designer(N = 100, prob_X = 0.5,
  process_proportions = c(X_causes_Y = 0.25, Y_regardless = 0.25,
  X_causes_not_Y = 0.25, not_Y_regardless = 0.25), prior_H = 0.5,
  p_E1_H = 0.3, p_E1_not_H = 0, p_E2_H = 0.8, p_E2_not_H = 0.2,
  cor_E1E2_H = 0, cor_E1E2_not_H = 0, label_E1 = "Smoking Gun",
  label_E2 = "Straw in the Wind")

Arguments

N

An integer. Size of population of cases from which a single case is selected.

prob_X

A number in [0,1]. Probability that X = 1 for a given case (equal throughout population of cases).

process_proportions

A vector of numbers in [0,1] that sums to 1. Simplex denoting the proportion of cases in the population in which, respectively: 1) X causes Y; 2) Y occurs regardless of X; 3) X causes the absence of Y; 4) Y is absent regardless of X.

prior_H

A number in [0,1]. Prior probability that X causes Y in a given case in which X and Y are both present.

p_E1_H

A number in [0,1]. Probability of observing first piece of evidence given hypothesis that X caused Y is true.

p_E1_not_H

A number in [0,1]. Probability of observing first piece of evidence given hypothesis that X caused Y is not true.

p_E2_H

A number in [0,1]. Probability of observing second piece of evidence given hypothesis that X caused Y is true.

p_E2_not_H

A number in [0,1]. Probability of observing second piece of evidence given hypothesis that X caused Y is not true.

cor_E1E2_H

A number in [-1,1]. Correlation between first and second pieces of evidence given hypothesis that X caused Y is true.

cor_E1E2_not_H

A number in [-1,1]. Correlation between first and second pieces of evidence given hypothesis that X caused Y is not true.

label_E1

A string. Label for the first piece of evidence (e.g., "Smoking Gun").

label_E2

A string. Label for the second piece of evidence (e.g., "Straw in the Wind").

Value

A process-tracing design.

Details

The model posits a population of N cases, each of which does or does not exhibit the presence of some outcome, Y. With probability prob_X, each case also exhibits the presence or absence of some potential cause, X. The outcome Y can be realized through four distinct causal relations, distributed through the population of cases according to process_proportions. First, the presence of X might cause Y. Second, the absence of X might cause Y. Third, Y might be present irrespective of X. Fourth, Y might be absent irrespective of X.

Our inquiry is a "cause of effects" question. We wish to know whether a specific case was one in which the presence (absence) of X caused the presence (absence) of Y.

Our data strategy consists of selecting one case at random in which both X and Y are present. As part of the data strategy we seek two pieces of evidence in favor of or against the hypothesized causal relationship, H, in which X causes Y.

The first (second) piece of evidence is observed with probability p_E1_H (p_E2_H) when H is true, and with probability p_E1_not_H (p_E2_not_H) when H is false.

Conditional on H being true (false), the correlation between the two pieces of evidence is given by cor_E1E2_H (cor_E1E2_not_H).

The researcher uses Bayes’ rule to update about the probability that X caused Y given the evidence. In other words, they form a posterior inference, Pr(H|E). We specify four answer strategies for forming this inference. The first simply ignores the evidence and is equivalent to stating a prior belief without doing any causal process tracing. The second conditions inferences only on the first piece of evidence, and the third only on the second piece of evidence. The fourth strategy conditions posterior inferences on both pieces of evidence simultaneously.

We specify as diagnosands for this design the bias, RMSE, mean(estimand), mean(estimate) and sd(estimate).

Examples

# Generate a process-tracing design using default arguments: pt_1 <- process_tracing_designer() draw_estimands(pt_1)
#> estimand_label estimand #> 1 did_X_cause_Y FALSE
draw_estimates(pt_1)
#> estimator_label posterior_H result estimand_label #> 1 No tests (Prior) 0.5 TRUE did_X_cause_Y #> 2 Smoking Gun 1.0 TRUE did_X_cause_Y #> 3 Straw in the Wind 0.8 TRUE did_X_cause_Y #> 4 Smoking Gun and Straw in the Wind 1.0 11 did_X_cause_Y
draw_data(pt_1)
#> ID causal_process X Y S_inclusion_prob fab_ID_1 test_results E1 #> 1 033 X_causes_Y TRUE TRUE 0.025 1 00 FALSE #> E2 #> 1 FALSE
# NOT RUN { diagnose_design(pt_1, sims = 1000) # }
# A design in which the smoking gun and straw-in-the-wind are correlated pt_2 <- process_tracing_designer(cor_E1E2_H = .32)
# NOT RUN { diagnose_design(pt_2, sims = 1000) # }
# A design with two doubly-decisive tests pointing in opposite directions pt_3 <- process_tracing_designer(p_E1_H = .80,p_E1_not_H = .05, label_E1 = "Doubly-Decisive: H", p_E2_H = .05,p_E2_not_H = .80, label_E2 = "Doubly-Decisive: Not H") draw_estimates(pt_3)
#> estimator_label posterior_H result #> 1 No tests (Prior) 0.500000 TRUE #> 2 Doubly-Decisive: H 0.173913 FALSE #> 3 Doubly-Decisive: Not H 0.826087 FALSE #> 4 Doubly-Decisive: H and Doubly-Decisive: Not H 0.500000 00 #> estimand_label #> 1 did_X_cause_Y #> 2 did_X_cause_Y #> 3 did_X_cause_Y #> 4 did_X_cause_Y
# NOT RUN { diagnose_design(pt_3, sims = 1000) # }

Author

DeclareDesign Team