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:
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()
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()
| 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
| 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 |
Simple query