# Getting Started

    if(!requireNamespace("fabricatr", quietly = TRUE)) {
      install.packages("fabricatr")
    }

    library(CausalQueries)
    library(fabricatr)
    library(knitr)

# Make a model

Generating: To make a model you need to provide a DAG statement to `make_model`.
For instance

- `"X->Y"`
- `"X -> M -> Y <- X"` or
- `"Z -> X -> Y <-> X"`.

    # examples of models
    xy_model <- make_model("X -> Y")
    iv_model <- make_model("Z -> X -> Y <-> X")

Graphing: Once you have made a model you can inspect the DAG:

    plot(iv_model)

Inspecting: The model has a set of parameters and a default distribution over these.

    xy_model |> grab("parameters_df") |> kable()

param_names | node | gen | param_set | nodal_type | given | param_value | priors
--- | --- | --- | --- | --- | --- | --- | ---
X.0 | X | 1 | X | 0 |  | 0.50 | 1
X.1 | X | 1 | X | 1 |  | 0.50 | 1
Y.00 | Y | 2 | Y | 00 |  | 0.25 | 1
Y.10 | Y | 2 | Y | 10 |  | 0.25 | 1
Y.01 | Y | 2 | Y | 01 |  | 0.25 | 1
Y.11 | Y | 2 | Y | 11 |  | 0.25 | 1

Tailoring: These features can be edited using `set_restrictions`, `set_priors` and `set_parameters`. Here is an example of setting a monotonicity restriction (see `?set_restrictions` for more):

Here is an example of setting a monotonicity restriction (see `?set_restrictions` for more):

    iv_model <-
      iv_model |> set_restrictions(decreasing('Z', 'X'))

Here is an example of setting priors (see `?set_priors` for more):

    iv_model <-
      iv_model |> set_priors(distribution = "jeffreys")
    #> No specific parameters to alter values for specified. Altering all parameters.

Simulation: Data can be drawn from a model like this:

    data <- make_data(iv_model, n = 4)

    data |> kable()

Z | X | Y
--- | --- | ---
0 | 0 | 0
0 | 1 | 1
1 | 1 | 0
1 | 1 | 0

# Model updating

Updating: Update using `update_model`. You can pass all `rstan` arguments to `update_model`.

    df <- fabricatr::fabricate(N = 100, X = rbinom(N, 1, .5), Y = rbinom(N, 1, .25 + X*.5))

    xy_model <-
      xy_model |>
      update_model(df, refresh = 0)

Inspecting: You can access the posterior distribution on model parameters directly thus:

    xy_model |> grab("posterior_distribution") |>
      head() |> kable()

X.0 | X.1 | Y.00 | Y.10 | Y.01 | Y.11
--- | --- | --- | --- | --- | ---
0.5827775 | 0.4172225 | 0.0233412 | 0.0701335 | 0.7357021 | 0.1708232
0.5642018 | 0.4357982 | 0.0235635 | 0.0810704 | 0.7693509 | 0.1260152
0.4762298 | 0.5237702 | 0.0531399 | 0.1344577 | 0.7478659 | 0.0645365
0.5994208 | 0.4005792 | 0.1813373 | 0.0074846 | 0.6458922 | 0.1652859
0.5107444 | 0.4892556 | 0.1725456 | 0.0276954 | 0.5015323 | 0.2982266
0.5321877 | 0.4678123 | 0.0033239 | 0.2271665 | 0.6855110 | 0.0839986

where each row is a draw of parameters.

# Query model

Querying: You ask arbitrary causal queries of the model.

Examples of unconditional queries:

    xy_model |>
      query_model("Y[X=1] > Y[X=0]", using = c("priors", "posteriors")) |>
      kable()

query | given | using | case_level | mean | sd | cred.low | cred.high
--- | --- | --- | --- | --- | --- | --- | ---
Y[X=1] > Y[X=0] | - | priors | FALSE | 0.2538711 | 0.1942515 | 0.0081513 | 0.7246379
Y[X=1] > Y[X=0] | - | posteriors | FALSE | 0.6842948 | 0.0774336 | 0.5148700 | 0.8156070

Examples of conditional queries:

    xy_model |>
      query_model("Y[X=1] > Y[X=0]", using = c("priors", "posteriors"),
                  given = "X==1 & Y == 1") |>
      kable()

query | given | using | case_level | mean | sd | cred.low | cred.high
--- | --- | --- | --- | --- | --- | --- | ---
Y[X=1] > Y[X=0] | X==1 & Y == 1 | priors | FALSE | 0.5009433 | 0.2870361 | 0.0253237 | 0.9714109
Y[X=1] > Y[X=0] | X==1 & Y == 1 | posteriors | FALSE | 0.8540662 | 0.0835568 | 0.6756953 | 0.9895221

Queries can even be conditional on counterfactual quantities. Here the probability of a positive effect given some effect:

    xy_model |>
      query_model("Y[X=1] > Y[X=0]", using = c("priors", "posteriors"),
                  given = "Y[X=1] != Y[X=0]") |>
      kable()

query | given | using | case_level | mean | sd | cred.low | cred.high
--- | --- | --- | --- | --- | --- | --- | ---
Y[X=1] > Y[X=0] | Y[X=1] != Y[X=0] | priors | FALSE | 0.4963668 | 0.2899275 | 0.0269070 | 0.9737914
Y[X=1] > Y[X=0] | Y[X=1] != Y[X=0] | posteriors | FALSE | 0.8956273 | 0.0597769 | 0.7776668 | 0.9945446