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 of chunk unnamed-chunk-3
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()
| 0.5515163 |
0.4484837 |
0.2847141 |
0.1177726 |
0.5741150 |
0.0233983 |
| 0.5265501 |
0.4734499 |
0.1473281 |
0.2074736 |
0.6224344 |
0.0227639 |
| 0.4597457 |
0.5402543 |
0.2233002 |
0.1362462 |
0.3923527 |
0.2481008 |
| 0.5754801 |
0.4245199 |
0.1631742 |
0.1542270 |
0.6013710 |
0.0812279 |
| 0.6779082 |
0.3220918 |
0.1429733 |
0.1443515 |
0.6242878 |
0.0883874 |
| 0.5075180 |
0.4924820 |
0.0409841 |
0.2349819 |
0.6799476 |
0.0440865 |
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| 0.008| 0.722|
#> |Y[X=1] > Y[X=0] |posteriors | 0.552| 0.104| 0.327| 0.725|
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 | 0.498| 0.288| 0.027| 0.971|
#> |Y[X=1] > Y[X=0] given X == 1 & Y == 1 |posteriors | 0.779| 0.126| 0.514| 0.983|
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 | 0.494| 0.291| 0.020| 0.977|
#> |Y[X=1] > Y[X=0] given Y[X=1] != Y[X=0] |posteriors | 0.829| 0.085| 0.673| 0.991|
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 |
-0.64 |
0.62 |
| ATE |
Y[X=1] - Y[X=0] |
- |
posteriors |
FALSE |
0.43 |
0.09 |
0.24 |
0.59 |
| Positive effect given any effect |
Y[X=1] > Y[X=0] |
Y[X=1] != Y[X=0] |
priors |
FALSE |
0.50 |
0.29 |
0.03 |
0.98 |
| Positive effect given any effect |
Y[X=1] > Y[X=0] |
Y[X=1] != Y[X=0] |
posteriors |
FALSE |
0.83 |
0.09 |
0.67 |
0.99 |
plot of chunk unnamed-chunk-14