Through the front door

library(CausalQueries)
library(dplyr)
library(knitr)

Here is an example of a model in which X causes M and M causes Y. There is, in addition, unobservable confounding between X and Y. This is an example of a model in which you might use information on M to figure out whether X caused Y making use of the “front door criterion.”

The DAG is defined using dagitty syntax like this:

model <- make_model("X -> M -> Y <-> X")

We might set priors thus:

model <- set_priors(model, distribution = "jeffreys")
#> Altering all parameters.

You can plot the dag thus.

plot(model)

Updating is done like this:

# Lets imagine highly correlated data; here an effect of .9 at each step
data <- data.frame(X = rep(0:1, 2000)) |>
  mutate(
    M = rbinom(n(), 1, .05 + .9*X),
    Y = rbinom(n(), 1, .05 + .9*M))

# Updating
model <- model |> update_model(data, refresh = 0)

Finally you can calculate an estimand of interest like this:

query_model(
    model = model, 
    using = c("priors", "posteriors"),
    query = "Y[X=1] - Y[X=0]",
    ) |>
  kable(digits = 2)

This uses the posterior distribution and the model to assess the average treatment effect estimand.

Let’s compare now with the case where you do not have data on M:

model |>
  update_model(data |> dplyr::select(X, Y), refresh = 0) |>
  query_model(
    using = c("priors", "posteriors"),
    query = "Y[X=1] - Y[X=0]") |>
  kable(digits = 2)

Here we update much less and are (relatively) much less certain in our beliefs precisely because we are aware of the confounded related between X and Y, without having the data on M we could use to address it.