# Getting Started

    library(CausalQueries)
    library(dplyr)
    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(xy_model)

Simple model

Simple summaries: You can access a simple summary using `summary()`

    summary(xy_model)
    #>
    #> Causal statement:
    #> X -> Y
    #>
    #> Nodal types:
    #>
    #> Nodal types for X:
    #> 0  1
    #>
    #> Nodal types for Y:
    #> 00  10  01  11
    #>
    #> Guide to interpreting nodal types for Y:
    #>
    #>   index  interpretation
    #> 1    *-  Y = * if X = 0
    #> 2    -*  Y = * if X = 1
    #>
    #> Number of nodal types by node:
    #> X Y
    #> 2 4
    #>
    #> Number of causal types:  8
    #>
    #> Note: Model does not contain: posterior_distribution, stan_objects;
    #> to include these objects use update_model()
    #>
    #> Note: To pose causal queries of this model use query_model()

or you can examine model details using `inspect()`.

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

    xy_model |> inspect("parameters_df")
    #>
    #> parameters_df
    #> Mapping of model parameters to nodal types:
    #>
    #>   param_names: name of parameter
    #>   node:        name of endogeneous node associated
    #>                with the parameter
    #>   gen:         partial causal ordering of the
    #>                parameter's node
    #>   param_set:   parameter groupings forming a simplex
    #>   given:       if model has confounding gives
    #>                conditioning nodal type
    #>   param_value: parameter values
    #>   priors:      hyperparameters of the prior
    #>                Dirichlet distribution
    #>
    #>   param_names node gen param_set nodal_type given param_value priors
    #> 1         X.0    X   1         X          0              0.50      1
    #> 2         X.1    X   1         X          1              0.50      1
    #> 3        Y.00    Y   2         Y         00              0.25      1
    #> 4        Y.10    Y   2         Y         10              0.25      1
    #> 5        Y.01    Y   2         Y         01              0.25      1
    #> 6        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):

    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")
    #> 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 | 1 | 1
1 | 0 | 0
1 | 0 | 1
1 | 1 | 1

# Update the model

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

    df <-
      data.frame(X = rbinom(100, 1, .5)) |>
      mutate(Y = rbinom(100, 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
--- | --- | --- | --- | --- | ---
0.5237547 | 0.4762453 | 0.1948964 | 0.0523208 | 0.5664182 | 0.1863645
0.4261285 | 0.5738715 | 0.0597984 | 0.1743038 | 0.6544728 | 0.1114249
0.5796467 | 0.4203533 | 0.1538045 | 0.1640282 | 0.4844825 | 0.1976849
0.5133653 | 0.4866347 | 0.0667460 | 0.1497083 | 0.5849814 | 0.1985644
0.5559260 | 0.4440740 | 0.1106234 | 0.1599240 | 0.6523280 | 0.0771246
0.5738242 | 0.4261758 | 0.0211059 | 0.3386846 | 0.5650897 | 0.0751198

where each row is a draw of parameters.

# Query the model

## Arbitrary queries

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"))
    #>
    #> Causal queries generated by query_model (all at population level)
    #>
    #> |label           |using      |  mean|    sd| cred.low| cred.high|
    #> |:---------------|:----------|-----:|-----:|--------:|---------:|
    #> |Y[X=1] > Y[X=0] |priors     | 0.249| 0.195|    0.009|     0.705|
    #> |Y[X=1] > Y[X=0] |posteriors | 0.529| 0.102|    0.313|     0.705|

This query asks the probability that \(Y(1)> Y(0)\).

Examples of conditional queries:

    xy_model |>
      query_model("Y[X=1] > Y[X=0] :|: X == 1 & Y == 1", using = c("priors", "posteriors"))
    #>
    #> Causal queries generated by query_model (all at population level)
    #>
    #> |label                                 |using      |  mean|    sd| cred.low| cred.high|
    #> |:-------------------------------------|:----------|-----:|-----:|--------:|---------:|
    #> |Y[X=1] > Y[X=0] given X == 1 & Y == 1 |priors     | 0.499| 0.283|    0.023|     0.970|
    #> |Y[X=1] > Y[X=0] given X == 1 & Y == 1 |posteriors | 0.751| 0.134|    0.479|     0.978|

This query asks the probability that \(Y(1) > Y(0)\) given \(X=1\) and \(Y=1\); it is a type of “causes of effects” query. Note that “:|:” is used to separate the main query element from the conditional statement to avoid ambiguity, since “|” is reserved for the “or” operator.

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] :|: Y[X=1] != Y[X=0]",
                  using = c("priors", "posteriors"))
    #>
    #> Causal queries generated by query_model (all at population level)
    #>
    #> |label                                  |using      |  mean|   sd| cred.low| cred.high|
    #> |:--------------------------------------|:----------|-----:|----:|--------:|---------:|
    #> |Y[X=1] > Y[X=0] given Y[X=1] != Y[X=0] |priors     | 0.492| 0.29|    0.027|     0.974|
    #> |Y[X=1] > Y[X=0] given Y[X=1] != Y[X=0] |posteriors | 0.809| 0.09|    0.648|     0.980|

Note that we use “:” to separate the base query from the condition rather than “|” to avoid confusion with logical operators.

## Output

Query output is ready for printing as tables, but can also be plotted, which is especially useful with batch requests:

    batch_queries <- xy_model |>
      query_model(queries = list(ATE = "Y[X=1] - Y[X=0]",
                                 `Positive effect given any effect` = "Y[X=1] > Y[X=0] :|: Y[X=1] != Y[X=0]"),
                  using = c("priors", "posteriors"),
                  expand_grid = TRUE)

    batch_queries |> kable(digits = 2, caption = "tabular output")

tabular output
label | query | given | using | case_level | mean | sd | cred.low | cred.high
--- | --- | --- | --- | --- | --- | --- | --- | ---
ATE | Y[X=1] - Y[X=0] | - | priors | FALSE | 0.00 | 0.31 | -0.64 | 0.63
ATE | Y[X=1] - Y[X=0] | - | posteriors | FALSE | 0.39 | 0.09 | 0.21 | 0.56
Positive effect given any effect | Y[X=1] > Y[X=0] | Y[X=1] != Y[X=0] | priors | FALSE | 0.50 | 0.29 | 0.02 | 0.97
Positive effect given any effect | Y[X=1] > Y[X=0] | Y[X=1] != Y[X=0] | posteriors | FALSE | 0.81 | 0.09 | 0.65 | 0.98

    batch_queries |> plot()

Simple query