# 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:
    #> $X
    #> 0  1
    #>
    #>   node position display interpretation
    #> 1    X       NA      X0          X = 0
    #> 2    X       NA      X1          X = 1
    #>
    #> $Y
    #> 00  10  01  11
    #>
    #>   node position display interpretation
    #> 1    Y        1   Y[*]*      Y | X = 0
    #> 2    Y        2   Y*[*]      Y | X = 1
    #>
    #> Number of 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 | 0 | 1
0 | 1 | 0
0 | 1 | 0
1 | 0 | 0

# 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
--- | --- | --- | --- | --- | ---
0.4802981 | 0.5197019 | 0.1754291 | 0.1730648 | 0.5101839 | 0.1413222
0.5969120 | 0.4030880 | 0.0672990 | 0.1458238 | 0.5314693 | 0.2554079
0.4081154 | 0.5918846 | 0.1279818 | 0.0784327 | 0.6366884 | 0.1568971
0.5074739 | 0.4925261 | 0.1346880 | 0.0945238 | 0.6796534 | 0.0911348
0.5293336 | 0.4706664 | 0.1725529 | 0.0041493 | 0.4037340 | 0.4195638
0.5379008 | 0.4620992 | 0.0359858 | 0.1687144 | 0.6990939 | 0.0962059

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     | 0.252| 0.192|    0.008|     0.702|
    #> |Y[X=1] > Y[X=0] |posteriors | 0.586| 0.088|    0.401|     0.740|

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     | 0.504| 0.285|    0.030|     0.972|
    #> |Y[X=1] > Y[X=0] given X == 1 & Y == 1 |posteriors | 0.737| 0.106|    0.528|     0.940|

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     | 0.501| 0.290|    0.027|     0.973|
    #> |Y[X=1] > Y[X=0] given Y[X=1] != Y[X=0] |posteriors | 0.863| 0.074|    0.725|     0.989|

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 | 0.01 | 0.32 | -0.62 | 0.64
ATE | Y[X=1] - Y[X=0] | - | posteriors | FALSE | 0.49 | 0.08 | 0.32 | 0.64
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 | 0.98
Positive effect given any effect | Y[X=1] > Y[X=0] | Y[X=1] != Y[X=0] | posteriors | FALSE | 0.86 | 0.07 | 0.72 | 0.99

    batch_queries |> plot()

Simple query