make_model uses causal statements encoded as strings to specify
the nodes and edges of a graph. Implied causal types are calculated
and default priors are provided under the assumption of no confounding.
Models can be updated with specification of a parameter matrix, P, by
providing restrictions on causal types, and/or by providing informative
priors on parameters.
Arguments
- statement
character string. Statement describing causal relations between nodes. Directed relations can be specified using '->' or '<-' and can be combined. For instance "X -> Y", "Y <- X" or "X1 -> Y <- X2; X1 -> X2". Confounded relations can be specified using a double headed arrow, "X <-> Y", to indicate unobserved confounding between X and Y.
- add_causal_types
Logical. Whether to create and attach causal types to
model. Defaults to `TRUE`.- nodal_types
List of nodal types associated with model nodes
Value
An object of class causal_model.
An object of class "causal_model" is a list containing at least the
following components:
- statement
A character vector of the statement that defines the model
- dag
A
data.framewith columns `parent`and `children` indicating how nodes relate to each other.- nodes
A named
listwith the nodes in the model- parents_df
A
data.framelisting nodes, whether they are root nodes or not, and the number of parents they have- nodal_types
Optional: A named
listwith the nodal types in the model. List should be ordered according to the causal ordering of nodes. If NULL nodal types are generated. If FALSE, a parameters data frame is not generated.- parameters_df
A
data.framewith descriptive information of the parameters in the model- causal_types
A
data.framelisting causal types and the nodal types that produce them
By default a causal model has flat (uniform) priors and parameters that
put equal weight on each parameter within each parameter set. The parameter
ranges (range of the nodal types) can be adjusted with set_restrictions.
The priors can be adjusted with set_priors. Specific parameter
values can be adjusted with set_parameters.
See also
summary.causal_model provides summary method for
output objects of class causal_model
Examples
make_model(statement = "X -> Y")
#>
#> Causal statement:
#> X -> Y
#>
#> Number of nodal types by node:
#> X Y
#> 2 4
#>
#> Number of causal types: 8
modelXKY <- make_model("X -> K -> Y; X -> Y")
# Example where a cyclical dag is attempted
if (FALSE) { # \dontrun{
modelXKX <- make_model("X -> K -> X")
} # }
# Examples with confounding
model <- make_model("X->Y; X <-> Y")
inspect(model, "parameter_matrix")
#>
#> parameter_matrix:
#>
#> rows: parameters
#> cols: causal types
#> cells: whether a parameter probability is used
#> in the calculation of causal type probability
#>
#> X0.Y00 X1.Y00 X0.Y10 X1.Y10 X0.Y01 X1.Y01 X0.Y11 X1.Y11
#> X.0 1 0 1 0 1 0 1 0
#> X.1 0 1 0 1 0 1 0 1
#> Y.00_X.0 1 0 0 0 0 0 0 0
#> Y.10_X.0 0 0 1 0 0 0 0 0
#> Y.01_X.0 0 0 0 0 1 0 0 0
#> Y.11_X.0 0 0 0 0 0 0 1 0
#> Y.00_X.1 0 1 0 0 0 0 0 0
#> Y.10_X.1 0 0 0 1 0 0 0 0
#> Y.01_X.1 0 0 0 0 0 1 0 0
#> Y.11_X.1 0 0 0 0 0 0 0 1
model <- make_model("Y2 <- X -> Y1; X <-> Y1; X <-> Y2")
dim(inspect(model, "parameter_matrix"))
#>
#> parameter_matrix:
#>
#> rows: parameters
#> cols: causal types
#> cells: whether a parameter probability is used
#> in the calculation of causal type probability
#>
#> X0.Y100.Y200 X1.Y100.Y200 X0.Y110.Y200 X1.Y110.Y200 X0.Y101.Y200
#> X.0 1 0 1 0 1
#> X.1 0 1 0 1 0
#> Y1.00_X.0 1 0 0 0 0
#> Y1.10_X.0 0 0 1 0 0
#> Y1.01_X.0 0 0 0 0 1
#> Y1.11_X.0 0 0 0 0 0
#> Y1.00_X.1 0 1 0 0 0
#> Y1.10_X.1 0 0 0 1 0
#> Y1.01_X.1 0 0 0 0 0
#> Y1.11_X.1 0 0 0 0 0
#> Y2.00_X.0 1 0 1 0 1
#> Y2.10_X.0 0 0 0 0 0
#> Y2.01_X.0 0 0 0 0 0
#> Y2.11_X.0 0 0 0 0 0
#> Y2.00_X.1 0 1 0 1 0
#> Y2.10_X.1 0 0 0 0 0
#> Y2.01_X.1 0 0 0 0 0
#> Y2.11_X.1 0 0 0 0 0
#> X1.Y101.Y200 X0.Y111.Y200 X1.Y111.Y200 X0.Y100.Y210 X1.Y100.Y210
#> X.0 0 1 0 1 0
#> X.1 1 0 1 0 1
#> Y1.00_X.0 0 0 0 1 0
#> Y1.10_X.0 0 0 0 0 0
#> Y1.01_X.0 0 0 0 0 0
#> Y1.11_X.0 0 1 0 0 0
#> Y1.00_X.1 0 0 0 0 1
#> Y1.10_X.1 0 0 0 0 0
#> Y1.01_X.1 1 0 0 0 0
#> Y1.11_X.1 0 0 1 0 0
#> Y2.00_X.0 0 1 0 0 0
#> Y2.10_X.0 0 0 0 1 0
#> Y2.01_X.0 0 0 0 0 0
#> Y2.11_X.0 0 0 0 0 0
#> Y2.00_X.1 1 0 1 0 0
#> Y2.10_X.1 0 0 0 0 1
#> Y2.01_X.1 0 0 0 0 0
#> Y2.11_X.1 0 0 0 0 0
#> X0.Y110.Y210 X1.Y110.Y210 X0.Y101.Y210 X1.Y101.Y210 X0.Y111.Y210
#> X.0 1 0 1 0 1
#> X.1 0 1 0 1 0
#> Y1.00_X.0 0 0 0 0 0
#> Y1.10_X.0 1 0 0 0 0
#> Y1.01_X.0 0 0 1 0 0
#> Y1.11_X.0 0 0 0 0 1
#> Y1.00_X.1 0 0 0 0 0
#> Y1.10_X.1 0 1 0 0 0
#> Y1.01_X.1 0 0 0 1 0
#> Y1.11_X.1 0 0 0 0 0
#> Y2.00_X.0 0 0 0 0 0
#> Y2.10_X.0 1 0 1 0 1
#> Y2.01_X.0 0 0 0 0 0
#> Y2.11_X.0 0 0 0 0 0
#> Y2.00_X.1 0 0 0 0 0
#> Y2.10_X.1 0 1 0 1 0
#> Y2.01_X.1 0 0 0 0 0
#> Y2.11_X.1 0 0 0 0 0
#> X1.Y111.Y210 X0.Y100.Y201 X1.Y100.Y201 X0.Y110.Y201 X1.Y110.Y201
#> X.0 0 1 0 1 0
#> X.1 1 0 1 0 1
#> Y1.00_X.0 0 1 0 0 0
#> Y1.10_X.0 0 0 0 1 0
#> Y1.01_X.0 0 0 0 0 0
#> Y1.11_X.0 0 0 0 0 0
#> Y1.00_X.1 0 0 1 0 0
#> Y1.10_X.1 0 0 0 0 1
#> Y1.01_X.1 0 0 0 0 0
#> Y1.11_X.1 1 0 0 0 0
#> Y2.00_X.0 0 0 0 0 0
#> Y2.10_X.0 0 0 0 0 0
#> Y2.01_X.0 0 1 0 1 0
#> Y2.11_X.0 0 0 0 0 0
#> Y2.00_X.1 0 0 0 0 0
#> Y2.10_X.1 1 0 0 0 0
#> Y2.01_X.1 0 0 1 0 1
#> Y2.11_X.1 0 0 0 0 0
#> X0.Y101.Y201 X1.Y101.Y201 X0.Y111.Y201 X1.Y111.Y201 X0.Y100.Y211
#> X.0 1 0 1 0 1
#> X.1 0 1 0 1 0
#> Y1.00_X.0 0 0 0 0 1
#> Y1.10_X.0 0 0 0 0 0
#> Y1.01_X.0 1 0 0 0 0
#> Y1.11_X.0 0 0 1 0 0
#> Y1.00_X.1 0 0 0 0 0
#> Y1.10_X.1 0 0 0 0 0
#> Y1.01_X.1 0 1 0 0 0
#> Y1.11_X.1 0 0 0 1 0
#> Y2.00_X.0 0 0 0 0 0
#> Y2.10_X.0 0 0 0 0 0
#> Y2.01_X.0 1 0 1 0 0
#> Y2.11_X.0 0 0 0 0 1
#> Y2.00_X.1 0 0 0 0 0
#> Y2.10_X.1 0 0 0 0 0
#> Y2.01_X.1 0 1 0 1 0
#> Y2.11_X.1 0 0 0 0 0
#> X1.Y100.Y211 X0.Y110.Y211 X1.Y110.Y211 X0.Y101.Y211 X1.Y101.Y211
#> X.0 0 1 0 1 0
#> X.1 1 0 1 0 1
#> Y1.00_X.0 0 0 0 0 0
#> Y1.10_X.0 0 1 0 0 0
#> Y1.01_X.0 0 0 0 1 0
#> Y1.11_X.0 0 0 0 0 0
#> Y1.00_X.1 1 0 0 0 0
#> Y1.10_X.1 0 0 1 0 0
#> Y1.01_X.1 0 0 0 0 1
#> Y1.11_X.1 0 0 0 0 0
#> Y2.00_X.0 0 0 0 0 0
#> Y2.10_X.0 0 0 0 0 0
#> Y2.01_X.0 0 0 0 0 0
#> Y2.11_X.0 0 1 0 1 0
#> Y2.00_X.1 0 0 0 0 0
#> Y2.10_X.1 0 0 0 0 0
#> Y2.01_X.1 0 0 0 0 0
#> Y2.11_X.1 1 0 1 0 1
#> X0.Y111.Y211 X1.Y111.Y211
#> X.0 1 0
#> X.1 0 1
#> Y1.00_X.0 0 0
#> Y1.10_X.0 0 0
#> Y1.01_X.0 0 0
#> Y1.11_X.0 1 0
#> Y1.00_X.1 0 0
#> Y1.10_X.1 0 0
#> Y1.01_X.1 0 0
#> Y1.11_X.1 0 1
#> Y2.00_X.0 0 0
#> Y2.10_X.0 0 0
#> Y2.01_X.0 0 0
#> Y2.11_X.0 1 0
#> Y2.00_X.1 0 0
#> Y2.10_X.1 0 0
#> Y2.01_X.1 0 0
#> Y2.11_X.1 0 1
#> [1] 18 32
inspect(model, "parameter_matrix")
#>
#> parameter_matrix:
#>
#> rows: parameters
#> cols: causal types
#> cells: whether a parameter probability is used
#> in the calculation of causal type probability
#>
#> X0.Y100.Y200 X1.Y100.Y200 X0.Y110.Y200 X1.Y110.Y200 X0.Y101.Y200
#> X.0 1 0 1 0 1
#> X.1 0 1 0 1 0
#> Y1.00_X.0 1 0 0 0 0
#> Y1.10_X.0 0 0 1 0 0
#> Y1.01_X.0 0 0 0 0 1
#> Y1.11_X.0 0 0 0 0 0
#> Y1.00_X.1 0 1 0 0 0
#> Y1.10_X.1 0 0 0 1 0
#> Y1.01_X.1 0 0 0 0 0
#> Y1.11_X.1 0 0 0 0 0
#> Y2.00_X.0 1 0 1 0 1
#> Y2.10_X.0 0 0 0 0 0
#> Y2.01_X.0 0 0 0 0 0
#> Y2.11_X.0 0 0 0 0 0
#> Y2.00_X.1 0 1 0 1 0
#> Y2.10_X.1 0 0 0 0 0
#> Y2.01_X.1 0 0 0 0 0
#> Y2.11_X.1 0 0 0 0 0
#> X1.Y101.Y200 X0.Y111.Y200 X1.Y111.Y200 X0.Y100.Y210 X1.Y100.Y210
#> X.0 0 1 0 1 0
#> X.1 1 0 1 0 1
#> Y1.00_X.0 0 0 0 1 0
#> Y1.10_X.0 0 0 0 0 0
#> Y1.01_X.0 0 0 0 0 0
#> Y1.11_X.0 0 1 0 0 0
#> Y1.00_X.1 0 0 0 0 1
#> Y1.10_X.1 0 0 0 0 0
#> Y1.01_X.1 1 0 0 0 0
#> Y1.11_X.1 0 0 1 0 0
#> Y2.00_X.0 0 1 0 0 0
#> Y2.10_X.0 0 0 0 1 0
#> Y2.01_X.0 0 0 0 0 0
#> Y2.11_X.0 0 0 0 0 0
#> Y2.00_X.1 1 0 1 0 0
#> Y2.10_X.1 0 0 0 0 1
#> Y2.01_X.1 0 0 0 0 0
#> Y2.11_X.1 0 0 0 0 0
#> X0.Y110.Y210 X1.Y110.Y210 X0.Y101.Y210 X1.Y101.Y210 X0.Y111.Y210
#> X.0 1 0 1 0 1
#> X.1 0 1 0 1 0
#> Y1.00_X.0 0 0 0 0 0
#> Y1.10_X.0 1 0 0 0 0
#> Y1.01_X.0 0 0 1 0 0
#> Y1.11_X.0 0 0 0 0 1
#> Y1.00_X.1 0 0 0 0 0
#> Y1.10_X.1 0 1 0 0 0
#> Y1.01_X.1 0 0 0 1 0
#> Y1.11_X.1 0 0 0 0 0
#> Y2.00_X.0 0 0 0 0 0
#> Y2.10_X.0 1 0 1 0 1
#> Y2.01_X.0 0 0 0 0 0
#> Y2.11_X.0 0 0 0 0 0
#> Y2.00_X.1 0 0 0 0 0
#> Y2.10_X.1 0 1 0 1 0
#> Y2.01_X.1 0 0 0 0 0
#> Y2.11_X.1 0 0 0 0 0
#> X1.Y111.Y210 X0.Y100.Y201 X1.Y100.Y201 X0.Y110.Y201 X1.Y110.Y201
#> X.0 0 1 0 1 0
#> X.1 1 0 1 0 1
#> Y1.00_X.0 0 1 0 0 0
#> Y1.10_X.0 0 0 0 1 0
#> Y1.01_X.0 0 0 0 0 0
#> Y1.11_X.0 0 0 0 0 0
#> Y1.00_X.1 0 0 1 0 0
#> Y1.10_X.1 0 0 0 0 1
#> Y1.01_X.1 0 0 0 0 0
#> Y1.11_X.1 1 0 0 0 0
#> Y2.00_X.0 0 0 0 0 0
#> Y2.10_X.0 0 0 0 0 0
#> Y2.01_X.0 0 1 0 1 0
#> Y2.11_X.0 0 0 0 0 0
#> Y2.00_X.1 0 0 0 0 0
#> Y2.10_X.1 1 0 0 0 0
#> Y2.01_X.1 0 0 1 0 1
#> Y2.11_X.1 0 0 0 0 0
#> X0.Y101.Y201 X1.Y101.Y201 X0.Y111.Y201 X1.Y111.Y201 X0.Y100.Y211
#> X.0 1 0 1 0 1
#> X.1 0 1 0 1 0
#> Y1.00_X.0 0 0 0 0 1
#> Y1.10_X.0 0 0 0 0 0
#> Y1.01_X.0 1 0 0 0 0
#> Y1.11_X.0 0 0 1 0 0
#> Y1.00_X.1 0 0 0 0 0
#> Y1.10_X.1 0 0 0 0 0
#> Y1.01_X.1 0 1 0 0 0
#> Y1.11_X.1 0 0 0 1 0
#> Y2.00_X.0 0 0 0 0 0
#> Y2.10_X.0 0 0 0 0 0
#> Y2.01_X.0 1 0 1 0 0
#> Y2.11_X.0 0 0 0 0 1
#> Y2.00_X.1 0 0 0 0 0
#> Y2.10_X.1 0 0 0 0 0
#> Y2.01_X.1 0 1 0 1 0
#> Y2.11_X.1 0 0 0 0 0
#> X1.Y100.Y211 X0.Y110.Y211 X1.Y110.Y211 X0.Y101.Y211 X1.Y101.Y211
#> X.0 0 1 0 1 0
#> X.1 1 0 1 0 1
#> Y1.00_X.0 0 0 0 0 0
#> Y1.10_X.0 0 1 0 0 0
#> Y1.01_X.0 0 0 0 1 0
#> Y1.11_X.0 0 0 0 0 0
#> Y1.00_X.1 1 0 0 0 0
#> Y1.10_X.1 0 0 1 0 0
#> Y1.01_X.1 0 0 0 0 1
#> Y1.11_X.1 0 0 0 0 0
#> Y2.00_X.0 0 0 0 0 0
#> Y2.10_X.0 0 0 0 0 0
#> Y2.01_X.0 0 0 0 0 0
#> Y2.11_X.0 0 1 0 1 0
#> Y2.00_X.1 0 0 0 0 0
#> Y2.10_X.1 0 0 0 0 0
#> Y2.01_X.1 0 0 0 0 0
#> Y2.11_X.1 1 0 1 0 1
#> X0.Y111.Y211 X1.Y111.Y211
#> X.0 1 0
#> X.1 0 1
#> Y1.00_X.0 0 0
#> Y1.10_X.0 0 0
#> Y1.01_X.0 0 0
#> Y1.11_X.0 1 0
#> Y1.00_X.1 0 0
#> Y1.10_X.1 0 0
#> Y1.01_X.1 0 0
#> Y1.11_X.1 0 1
#> Y2.00_X.0 0 0
#> Y2.10_X.0 0 0
#> Y2.01_X.0 0 0
#> Y2.11_X.0 1 0
#> Y2.00_X.1 0 0
#> Y2.10_X.1 0 0
#> Y2.01_X.1 0 0
#> Y2.11_X.1 0 1
model <- make_model("X1 -> Y <- X2; X1 <-> Y; X2 <-> Y")
dim(inspect(model, "parameter_matrix"))
#>
#> parameter_matrix:
#>
#> rows: parameters
#> cols: causal types
#> cells: whether a parameter probability is used
#> in the calculation of causal type probability
#>
#> X10.X20.Y0000 X11.X20.Y0000 X10.X21.Y0000 X11.X21.Y0000
#> X1.0 1 0 1 0
#> X1.1 0 1 0 1
#> X2.0 1 1 0 0
#> X2.1 0 0 1 1
#> Y.0000_X1.0_X2.0 1 0 0 0
#> Y.1000_X1.0_X2.0 0 0 0 0
#> Y.0100_X1.0_X2.0 0 0 0 0
#> Y.1100_X1.0_X2.0 0 0 0 0
#> Y.0010_X1.0_X2.0 0 0 0 0
#> Y.1010_X1.0_X2.0 0 0 0 0
#> Y.0110_X1.0_X2.0 0 0 0 0
#> Y.1110_X1.0_X2.0 0 0 0 0
#> Y.0001_X1.0_X2.0 0 0 0 0
#> Y.1001_X1.0_X2.0 0 0 0 0
#> Y.0101_X1.0_X2.0 0 0 0 0
#> Y.1101_X1.0_X2.0 0 0 0 0
#> Y.0011_X1.0_X2.0 0 0 0 0
#> Y.1011_X1.0_X2.0 0 0 0 0
#> Y.0111_X1.0_X2.0 0 0 0 0
#> Y.1111_X1.0_X2.0 0 0 0 0
#> Y.0000_X1.0_X2.1 0 0 1 0
#> Y.1000_X1.0_X2.1 0 0 0 0
#> Y.0100_X1.0_X2.1 0 0 0 0
#> Y.1100_X1.0_X2.1 0 0 0 0
#> Y.0010_X1.0_X2.1 0 0 0 0
#> Y.1010_X1.0_X2.1 0 0 0 0
#> Y.0110_X1.0_X2.1 0 0 0 0
#> Y.1110_X1.0_X2.1 0 0 0 0
#> Y.0001_X1.0_X2.1 0 0 0 0
#> Y.1001_X1.0_X2.1 0 0 0 0
#> Y.0101_X1.0_X2.1 0 0 0 0
#> Y.1101_X1.0_X2.1 0 0 0 0
#> Y.0011_X1.0_X2.1 0 0 0 0
#> Y.1011_X1.0_X2.1 0 0 0 0
#> Y.0111_X1.0_X2.1 0 0 0 0
#> Y.1111_X1.0_X2.1 0 0 0 0
#> Y.0000_X1.1_X2.0 0 1 0 0
#> Y.1000_X1.1_X2.0 0 0 0 0
#> Y.0100_X1.1_X2.0 0 0 0 0
#> Y.1100_X1.1_X2.0 0 0 0 0
#> Y.0010_X1.1_X2.0 0 0 0 0
#> Y.1010_X1.1_X2.0 0 0 0 0
#> Y.0110_X1.1_X2.0 0 0 0 0
#> Y.1110_X1.1_X2.0 0 0 0 0
#> Y.0001_X1.1_X2.0 0 0 0 0
#> Y.1001_X1.1_X2.0 0 0 0 0
#> Y.0101_X1.1_X2.0 0 0 0 0
#> Y.1101_X1.1_X2.0 0 0 0 0
#> Y.0011_X1.1_X2.0 0 0 0 0
#> Y.1011_X1.1_X2.0 0 0 0 0
#> Y.0111_X1.1_X2.0 0 0 0 0
#> Y.1111_X1.1_X2.0 0 0 0 0
#> Y.0000_X1.1_X2.1 0 0 0 1
#> Y.1000_X1.1_X2.1 0 0 0 0
#> Y.0100_X1.1_X2.1 0 0 0 0
#> Y.1100_X1.1_X2.1 0 0 0 0
#> Y.0010_X1.1_X2.1 0 0 0 0
#> Y.1010_X1.1_X2.1 0 0 0 0
#> Y.0110_X1.1_X2.1 0 0 0 0
#> Y.1110_X1.1_X2.1 0 0 0 0
#> Y.0001_X1.1_X2.1 0 0 0 0
#> Y.1001_X1.1_X2.1 0 0 0 0
#> Y.0101_X1.1_X2.1 0 0 0 0
#> Y.1101_X1.1_X2.1 0 0 0 0
#> Y.0011_X1.1_X2.1 0 0 0 0
#> Y.1011_X1.1_X2.1 0 0 0 0
#> Y.0111_X1.1_X2.1 0 0 0 0
#> Y.1111_X1.1_X2.1 0 0 0 0
#> X10.X20.Y1000 X11.X20.Y1000 X10.X21.Y1000 X11.X21.Y1000
#> X1.0 1 0 1 0
#> X1.1 0 1 0 1
#> X2.0 1 1 0 0
#> X2.1 0 0 1 1
#> Y.0000_X1.0_X2.0 0 0 0 0
#> Y.1000_X1.0_X2.0 1 0 0 0
#> Y.0100_X1.0_X2.0 0 0 0 0
#> Y.1100_X1.0_X2.0 0 0 0 0
#> Y.0010_X1.0_X2.0 0 0 0 0
#> Y.1010_X1.0_X2.0 0 0 0 0
#> Y.0110_X1.0_X2.0 0 0 0 0
#> Y.1110_X1.0_X2.0 0 0 0 0
#> Y.0001_X1.0_X2.0 0 0 0 0
#> Y.1001_X1.0_X2.0 0 0 0 0
#> Y.0101_X1.0_X2.0 0 0 0 0
#> Y.1101_X1.0_X2.0 0 0 0 0
#> Y.0011_X1.0_X2.0 0 0 0 0
#> Y.1011_X1.0_X2.0 0 0 0 0
#> Y.0111_X1.0_X2.0 0 0 0 0
#> Y.1111_X1.0_X2.0 0 0 0 0
#> Y.0000_X1.0_X2.1 0 0 0 0
#> Y.1000_X1.0_X2.1 0 0 1 0
#> Y.0100_X1.0_X2.1 0 0 0 0
#> Y.1100_X1.0_X2.1 0 0 0 0
#> Y.0010_X1.0_X2.1 0 0 0 0
#> Y.1010_X1.0_X2.1 0 0 0 0
#> Y.0110_X1.0_X2.1 0 0 0 0
#> Y.1110_X1.0_X2.1 0 0 0 0
#> Y.0001_X1.0_X2.1 0 0 0 0
#> Y.1001_X1.0_X2.1 0 0 0 0
#> Y.0101_X1.0_X2.1 0 0 0 0
#> Y.1101_X1.0_X2.1 0 0 0 0
#> Y.0011_X1.0_X2.1 0 0 0 0
#> Y.1011_X1.0_X2.1 0 0 0 0
#> Y.0111_X1.0_X2.1 0 0 0 0
#> Y.1111_X1.0_X2.1 0 0 0 0
#> Y.0000_X1.1_X2.0 0 0 0 0
#> Y.1000_X1.1_X2.0 0 1 0 0
#> Y.0100_X1.1_X2.0 0 0 0 0
#> Y.1100_X1.1_X2.0 0 0 0 0
#> Y.0010_X1.1_X2.0 0 0 0 0
#> Y.1010_X1.1_X2.0 0 0 0 0
#> Y.0110_X1.1_X2.0 0 0 0 0
#> Y.1110_X1.1_X2.0 0 0 0 0
#> Y.0001_X1.1_X2.0 0 0 0 0
#> Y.1001_X1.1_X2.0 0 0 0 0
#> Y.0101_X1.1_X2.0 0 0 0 0
#> Y.1101_X1.1_X2.0 0 0 0 0
#> Y.0011_X1.1_X2.0 0 0 0 0
#> Y.1011_X1.1_X2.0 0 0 0 0
#> Y.0111_X1.1_X2.0 0 0 0 0
#> Y.1111_X1.1_X2.0 0 0 0 0
#> Y.0000_X1.1_X2.1 0 0 0 0
#> Y.1000_X1.1_X2.1 0 0 0 1
#> Y.0100_X1.1_X2.1 0 0 0 0
#> Y.1100_X1.1_X2.1 0 0 0 0
#> Y.0010_X1.1_X2.1 0 0 0 0
#> Y.1010_X1.1_X2.1 0 0 0 0
#> Y.0110_X1.1_X2.1 0 0 0 0
#> Y.1110_X1.1_X2.1 0 0 0 0
#> Y.0001_X1.1_X2.1 0 0 0 0
#> Y.1001_X1.1_X2.1 0 0 0 0
#> Y.0101_X1.1_X2.1 0 0 0 0
#> Y.1101_X1.1_X2.1 0 0 0 0
#> Y.0011_X1.1_X2.1 0 0 0 0
#> Y.1011_X1.1_X2.1 0 0 0 0
#> Y.0111_X1.1_X2.1 0 0 0 0
#> Y.1111_X1.1_X2.1 0 0 0 0
#> X10.X20.Y0100 X11.X20.Y0100 X10.X21.Y0100 X11.X21.Y0100
#> X1.0 1 0 1 0
#> X1.1 0 1 0 1
#> X2.0 1 1 0 0
#> X2.1 0 0 1 1
#> Y.0000_X1.0_X2.0 0 0 0 0
#> Y.1000_X1.0_X2.0 0 0 0 0
#> Y.0100_X1.0_X2.0 1 0 0 0
#> Y.1100_X1.0_X2.0 0 0 0 0
#> Y.0010_X1.0_X2.0 0 0 0 0
#> Y.1010_X1.0_X2.0 0 0 0 0
#> Y.0110_X1.0_X2.0 0 0 0 0
#> Y.1110_X1.0_X2.0 0 0 0 0
#> Y.0001_X1.0_X2.0 0 0 0 0
#> Y.1001_X1.0_X2.0 0 0 0 0
#> Y.0101_X1.0_X2.0 0 0 0 0
#> Y.1101_X1.0_X2.0 0 0 0 0
#> Y.0011_X1.0_X2.0 0 0 0 0
#> Y.1011_X1.0_X2.0 0 0 0 0
#> Y.0111_X1.0_X2.0 0 0 0 0
#> Y.1111_X1.0_X2.0 0 0 0 0
#> Y.0000_X1.0_X2.1 0 0 0 0
#> Y.1000_X1.0_X2.1 0 0 0 0
#> Y.0100_X1.0_X2.1 0 0 1 0
#> Y.1100_X1.0_X2.1 0 0 0 0
#> Y.0010_X1.0_X2.1 0 0 0 0
#> Y.1010_X1.0_X2.1 0 0 0 0
#> Y.0110_X1.0_X2.1 0 0 0 0
#> Y.1110_X1.0_X2.1 0 0 0 0
#> Y.0001_X1.0_X2.1 0 0 0 0
#> Y.1001_X1.0_X2.1 0 0 0 0
#> Y.0101_X1.0_X2.1 0 0 0 0
#> Y.1101_X1.0_X2.1 0 0 0 0
#> Y.0011_X1.0_X2.1 0 0 0 0
#> Y.1011_X1.0_X2.1 0 0 0 0
#> Y.0111_X1.0_X2.1 0 0 0 0
#> Y.1111_X1.0_X2.1 0 0 0 0
#> Y.0000_X1.1_X2.0 0 0 0 0
#> Y.1000_X1.1_X2.0 0 0 0 0
#> Y.0100_X1.1_X2.0 0 1 0 0
#> Y.1100_X1.1_X2.0 0 0 0 0
#> Y.0010_X1.1_X2.0 0 0 0 0
#> Y.1010_X1.1_X2.0 0 0 0 0
#> Y.0110_X1.1_X2.0 0 0 0 0
#> Y.1110_X1.1_X2.0 0 0 0 0
#> Y.0001_X1.1_X2.0 0 0 0 0
#> Y.1001_X1.1_X2.0 0 0 0 0
#> Y.0101_X1.1_X2.0 0 0 0 0
#> Y.1101_X1.1_X2.0 0 0 0 0
#> Y.0011_X1.1_X2.0 0 0 0 0
#> Y.1011_X1.1_X2.0 0 0 0 0
#> Y.0111_X1.1_X2.0 0 0 0 0
#> Y.1111_X1.1_X2.0 0 0 0 0
#> Y.0000_X1.1_X2.1 0 0 0 0
#> Y.1000_X1.1_X2.1 0 0 0 0
#> Y.0100_X1.1_X2.1 0 0 0 1
#> Y.1100_X1.1_X2.1 0 0 0 0
#> Y.0010_X1.1_X2.1 0 0 0 0
#> Y.1010_X1.1_X2.1 0 0 0 0
#> Y.0110_X1.1_X2.1 0 0 0 0
#> Y.1110_X1.1_X2.1 0 0 0 0
#> Y.0001_X1.1_X2.1 0 0 0 0
#> Y.1001_X1.1_X2.1 0 0 0 0
#> Y.0101_X1.1_X2.1 0 0 0 0
#> Y.1101_X1.1_X2.1 0 0 0 0
#> Y.0011_X1.1_X2.1 0 0 0 0
#> Y.1011_X1.1_X2.1 0 0 0 0
#> Y.0111_X1.1_X2.1 0 0 0 0
#> Y.1111_X1.1_X2.1 0 0 0 0
#> X10.X20.Y1100 X11.X20.Y1100 X10.X21.Y1100 X11.X21.Y1100
#> X1.0 1 0 1 0
#> X1.1 0 1 0 1
#> X2.0 1 1 0 0
#> X2.1 0 0 1 1
#> Y.0000_X1.0_X2.0 0 0 0 0
#> Y.1000_X1.0_X2.0 0 0 0 0
#> Y.0100_X1.0_X2.0 0 0 0 0
#> Y.1100_X1.0_X2.0 1 0 0 0
#> Y.0010_X1.0_X2.0 0 0 0 0
#> Y.1010_X1.0_X2.0 0 0 0 0
#> Y.0110_X1.0_X2.0 0 0 0 0
#> Y.1110_X1.0_X2.0 0 0 0 0
#> Y.0001_X1.0_X2.0 0 0 0 0
#> Y.1001_X1.0_X2.0 0 0 0 0
#> Y.0101_X1.0_X2.0 0 0 0 0
#> Y.1101_X1.0_X2.0 0 0 0 0
#> Y.0011_X1.0_X2.0 0 0 0 0
#> Y.1011_X1.0_X2.0 0 0 0 0
#> Y.0111_X1.0_X2.0 0 0 0 0
#> Y.1111_X1.0_X2.0 0 0 0 0
#> Y.0000_X1.0_X2.1 0 0 0 0
#> Y.1000_X1.0_X2.1 0 0 0 0
#> Y.0100_X1.0_X2.1 0 0 0 0
#> Y.1100_X1.0_X2.1 0 0 1 0
#> Y.0010_X1.0_X2.1 0 0 0 0
#> Y.1010_X1.0_X2.1 0 0 0 0
#> Y.0110_X1.0_X2.1 0 0 0 0
#> Y.1110_X1.0_X2.1 0 0 0 0
#> Y.0001_X1.0_X2.1 0 0 0 0
#> Y.1001_X1.0_X2.1 0 0 0 0
#> Y.0101_X1.0_X2.1 0 0 0 0
#> Y.1101_X1.0_X2.1 0 0 0 0
#> Y.0011_X1.0_X2.1 0 0 0 0
#> Y.1011_X1.0_X2.1 0 0 0 0
#> Y.0111_X1.0_X2.1 0 0 0 0
#> Y.1111_X1.0_X2.1 0 0 0 0
#> Y.0000_X1.1_X2.0 0 0 0 0
#> Y.1000_X1.1_X2.0 0 0 0 0
#> Y.0100_X1.1_X2.0 0 0 0 0
#> Y.1100_X1.1_X2.0 0 1 0 0
#> Y.0010_X1.1_X2.0 0 0 0 0
#> Y.1010_X1.1_X2.0 0 0 0 0
#> Y.0110_X1.1_X2.0 0 0 0 0
#> Y.1110_X1.1_X2.0 0 0 0 0
#> Y.0001_X1.1_X2.0 0 0 0 0
#> Y.1001_X1.1_X2.0 0 0 0 0
#> Y.0101_X1.1_X2.0 0 0 0 0
#> Y.1101_X1.1_X2.0 0 0 0 0
#> Y.0011_X1.1_X2.0 0 0 0 0
#> Y.1011_X1.1_X2.0 0 0 0 0
#> Y.0111_X1.1_X2.0 0 0 0 0
#> Y.1111_X1.1_X2.0 0 0 0 0
#> Y.0000_X1.1_X2.1 0 0 0 0
#> Y.1000_X1.1_X2.1 0 0 0 0
#> Y.0100_X1.1_X2.1 0 0 0 0
#> Y.1100_X1.1_X2.1 0 0 0 1
#> Y.0010_X1.1_X2.1 0 0 0 0
#> Y.1010_X1.1_X2.1 0 0 0 0
#> Y.0110_X1.1_X2.1 0 0 0 0
#> Y.1110_X1.1_X2.1 0 0 0 0
#> Y.0001_X1.1_X2.1 0 0 0 0
#> Y.1001_X1.1_X2.1 0 0 0 0
#> Y.0101_X1.1_X2.1 0 0 0 0
#> Y.1101_X1.1_X2.1 0 0 0 0
#> Y.0011_X1.1_X2.1 0 0 0 0
#> Y.1011_X1.1_X2.1 0 0 0 0
#> Y.0111_X1.1_X2.1 0 0 0 0
#> Y.1111_X1.1_X2.1 0 0 0 0
#> X10.X20.Y0010 X11.X20.Y0010 X10.X21.Y0010 X11.X21.Y0010
#> X1.0 1 0 1 0
#> X1.1 0 1 0 1
#> X2.0 1 1 0 0
#> X2.1 0 0 1 1
#> Y.0000_X1.0_X2.0 0 0 0 0
#> Y.1000_X1.0_X2.0 0 0 0 0
#> Y.0100_X1.0_X2.0 0 0 0 0
#> Y.1100_X1.0_X2.0 0 0 0 0
#> Y.0010_X1.0_X2.0 1 0 0 0
#> Y.1010_X1.0_X2.0 0 0 0 0
#> Y.0110_X1.0_X2.0 0 0 0 0
#> Y.1110_X1.0_X2.0 0 0 0 0
#> Y.0001_X1.0_X2.0 0 0 0 0
#> Y.1001_X1.0_X2.0 0 0 0 0
#> Y.0101_X1.0_X2.0 0 0 0 0
#> Y.1101_X1.0_X2.0 0 0 0 0
#> Y.0011_X1.0_X2.0 0 0 0 0
#> Y.1011_X1.0_X2.0 0 0 0 0
#> Y.0111_X1.0_X2.0 0 0 0 0
#> Y.1111_X1.0_X2.0 0 0 0 0
#> Y.0000_X1.0_X2.1 0 0 0 0
#> Y.1000_X1.0_X2.1 0 0 0 0
#> Y.0100_X1.0_X2.1 0 0 0 0
#> Y.1100_X1.0_X2.1 0 0 0 0
#> Y.0010_X1.0_X2.1 0 0 1 0
#> Y.1010_X1.0_X2.1 0 0 0 0
#> Y.0110_X1.0_X2.1 0 0 0 0
#> Y.1110_X1.0_X2.1 0 0 0 0
#> Y.0001_X1.0_X2.1 0 0 0 0
#> Y.1001_X1.0_X2.1 0 0 0 0
#> Y.0101_X1.0_X2.1 0 0 0 0
#> Y.1101_X1.0_X2.1 0 0 0 0
#> Y.0011_X1.0_X2.1 0 0 0 0
#> Y.1011_X1.0_X2.1 0 0 0 0
#> Y.0111_X1.0_X2.1 0 0 0 0
#> Y.1111_X1.0_X2.1 0 0 0 0
#> Y.0000_X1.1_X2.0 0 0 0 0
#> Y.1000_X1.1_X2.0 0 0 0 0
#> Y.0100_X1.1_X2.0 0 0 0 0
#> Y.1100_X1.1_X2.0 0 0 0 0
#> Y.0010_X1.1_X2.0 0 1 0 0
#> Y.1010_X1.1_X2.0 0 0 0 0
#> Y.0110_X1.1_X2.0 0 0 0 0
#> Y.1110_X1.1_X2.0 0 0 0 0
#> Y.0001_X1.1_X2.0 0 0 0 0
#> Y.1001_X1.1_X2.0 0 0 0 0
#> Y.0101_X1.1_X2.0 0 0 0 0
#> Y.1101_X1.1_X2.0 0 0 0 0
#> Y.0011_X1.1_X2.0 0 0 0 0
#> Y.1011_X1.1_X2.0 0 0 0 0
#> Y.0111_X1.1_X2.0 0 0 0 0
#> Y.1111_X1.1_X2.0 0 0 0 0
#> Y.0000_X1.1_X2.1 0 0 0 0
#> Y.1000_X1.1_X2.1 0 0 0 0
#> Y.0100_X1.1_X2.1 0 0 0 0
#> Y.1100_X1.1_X2.1 0 0 0 0
#> Y.0010_X1.1_X2.1 0 0 0 1
#> Y.1010_X1.1_X2.1 0 0 0 0
#> Y.0110_X1.1_X2.1 0 0 0 0
#> Y.1110_X1.1_X2.1 0 0 0 0
#> Y.0001_X1.1_X2.1 0 0 0 0
#> Y.1001_X1.1_X2.1 0 0 0 0
#> Y.0101_X1.1_X2.1 0 0 0 0
#> Y.1101_X1.1_X2.1 0 0 0 0
#> Y.0011_X1.1_X2.1 0 0 0 0
#> Y.1011_X1.1_X2.1 0 0 0 0
#> Y.0111_X1.1_X2.1 0 0 0 0
#> Y.1111_X1.1_X2.1 0 0 0 0
#> X10.X20.Y1010 X11.X20.Y1010 X10.X21.Y1010 X11.X21.Y1010
#> X1.0 1 0 1 0
#> X1.1 0 1 0 1
#> X2.0 1 1 0 0
#> X2.1 0 0 1 1
#> Y.0000_X1.0_X2.0 0 0 0 0
#> Y.1000_X1.0_X2.0 0 0 0 0
#> Y.0100_X1.0_X2.0 0 0 0 0
#> Y.1100_X1.0_X2.0 0 0 0 0
#> Y.0010_X1.0_X2.0 0 0 0 0
#> Y.1010_X1.0_X2.0 1 0 0 0
#> Y.0110_X1.0_X2.0 0 0 0 0
#> Y.1110_X1.0_X2.0 0 0 0 0
#> Y.0001_X1.0_X2.0 0 0 0 0
#> Y.1001_X1.0_X2.0 0 0 0 0
#> Y.0101_X1.0_X2.0 0 0 0 0
#> Y.1101_X1.0_X2.0 0 0 0 0
#> Y.0011_X1.0_X2.0 0 0 0 0
#> Y.1011_X1.0_X2.0 0 0 0 0
#> Y.0111_X1.0_X2.0 0 0 0 0
#> Y.1111_X1.0_X2.0 0 0 0 0
#> Y.0000_X1.0_X2.1 0 0 0 0
#> Y.1000_X1.0_X2.1 0 0 0 0
#> Y.0100_X1.0_X2.1 0 0 0 0
#> Y.1100_X1.0_X2.1 0 0 0 0
#> Y.0010_X1.0_X2.1 0 0 0 0
#> Y.1010_X1.0_X2.1 0 0 1 0
#> Y.0110_X1.0_X2.1 0 0 0 0
#> Y.1110_X1.0_X2.1 0 0 0 0
#> Y.0001_X1.0_X2.1 0 0 0 0
#> Y.1001_X1.0_X2.1 0 0 0 0
#> Y.0101_X1.0_X2.1 0 0 0 0
#> Y.1101_X1.0_X2.1 0 0 0 0
#> Y.0011_X1.0_X2.1 0 0 0 0
#> Y.1011_X1.0_X2.1 0 0 0 0
#> Y.0111_X1.0_X2.1 0 0 0 0
#> Y.1111_X1.0_X2.1 0 0 0 0
#> Y.0000_X1.1_X2.0 0 0 0 0
#> Y.1000_X1.1_X2.0 0 0 0 0
#> Y.0100_X1.1_X2.0 0 0 0 0
#> Y.1100_X1.1_X2.0 0 0 0 0
#> Y.0010_X1.1_X2.0 0 0 0 0
#> Y.1010_X1.1_X2.0 0 1 0 0
#> Y.0110_X1.1_X2.0 0 0 0 0
#> Y.1110_X1.1_X2.0 0 0 0 0
#> Y.0001_X1.1_X2.0 0 0 0 0
#> Y.1001_X1.1_X2.0 0 0 0 0
#> Y.0101_X1.1_X2.0 0 0 0 0
#> Y.1101_X1.1_X2.0 0 0 0 0
#> Y.0011_X1.1_X2.0 0 0 0 0
#> Y.1011_X1.1_X2.0 0 0 0 0
#> Y.0111_X1.1_X2.0 0 0 0 0
#> Y.1111_X1.1_X2.0 0 0 0 0
#> Y.0000_X1.1_X2.1 0 0 0 0
#> Y.1000_X1.1_X2.1 0 0 0 0
#> Y.0100_X1.1_X2.1 0 0 0 0
#> Y.1100_X1.1_X2.1 0 0 0 0
#> Y.0010_X1.1_X2.1 0 0 0 0
#> Y.1010_X1.1_X2.1 0 0 0 1
#> Y.0110_X1.1_X2.1 0 0 0 0
#> Y.1110_X1.1_X2.1 0 0 0 0
#> Y.0001_X1.1_X2.1 0 0 0 0
#> Y.1001_X1.1_X2.1 0 0 0 0
#> Y.0101_X1.1_X2.1 0 0 0 0
#> Y.1101_X1.1_X2.1 0 0 0 0
#> Y.0011_X1.1_X2.1 0 0 0 0
#> Y.1011_X1.1_X2.1 0 0 0 0
#> Y.0111_X1.1_X2.1 0 0 0 0
#> Y.1111_X1.1_X2.1 0 0 0 0
#> X10.X20.Y0110 X11.X20.Y0110 X10.X21.Y0110 X11.X21.Y0110
#> X1.0 1 0 1 0
#> X1.1 0 1 0 1
#> X2.0 1 1 0 0
#> X2.1 0 0 1 1
#> Y.0000_X1.0_X2.0 0 0 0 0
#> Y.1000_X1.0_X2.0 0 0 0 0
#> Y.0100_X1.0_X2.0 0 0 0 0
#> Y.1100_X1.0_X2.0 0 0 0 0
#> Y.0010_X1.0_X2.0 0 0 0 0
#> Y.1010_X1.0_X2.0 0 0 0 0
#> Y.0110_X1.0_X2.0 1 0 0 0
#> Y.1110_X1.0_X2.0 0 0 0 0
#> Y.0001_X1.0_X2.0 0 0 0 0
#> Y.1001_X1.0_X2.0 0 0 0 0
#> Y.0101_X1.0_X2.0 0 0 0 0
#> Y.1101_X1.0_X2.0 0 0 0 0
#> Y.0011_X1.0_X2.0 0 0 0 0
#> Y.1011_X1.0_X2.0 0 0 0 0
#> Y.0111_X1.0_X2.0 0 0 0 0
#> Y.1111_X1.0_X2.0 0 0 0 0
#> Y.0000_X1.0_X2.1 0 0 0 0
#> Y.1000_X1.0_X2.1 0 0 0 0
#> Y.0100_X1.0_X2.1 0 0 0 0
#> Y.1100_X1.0_X2.1 0 0 0 0
#> Y.0010_X1.0_X2.1 0 0 0 0
#> Y.1010_X1.0_X2.1 0 0 0 0
#> Y.0110_X1.0_X2.1 0 0 1 0
#> Y.1110_X1.0_X2.1 0 0 0 0
#> Y.0001_X1.0_X2.1 0 0 0 0
#> Y.1001_X1.0_X2.1 0 0 0 0
#> Y.0101_X1.0_X2.1 0 0 0 0
#> Y.1101_X1.0_X2.1 0 0 0 0
#> Y.0011_X1.0_X2.1 0 0 0 0
#> Y.1011_X1.0_X2.1 0 0 0 0
#> Y.0111_X1.0_X2.1 0 0 0 0
#> Y.1111_X1.0_X2.1 0 0 0 0
#> Y.0000_X1.1_X2.0 0 0 0 0
#> Y.1000_X1.1_X2.0 0 0 0 0
#> Y.0100_X1.1_X2.0 0 0 0 0
#> Y.1100_X1.1_X2.0 0 0 0 0
#> Y.0010_X1.1_X2.0 0 0 0 0
#> Y.1010_X1.1_X2.0 0 0 0 0
#> Y.0110_X1.1_X2.0 0 1 0 0
#> Y.1110_X1.1_X2.0 0 0 0 0
#> Y.0001_X1.1_X2.0 0 0 0 0
#> Y.1001_X1.1_X2.0 0 0 0 0
#> Y.0101_X1.1_X2.0 0 0 0 0
#> Y.1101_X1.1_X2.0 0 0 0 0
#> Y.0011_X1.1_X2.0 0 0 0 0
#> Y.1011_X1.1_X2.0 0 0 0 0
#> Y.0111_X1.1_X2.0 0 0 0 0
#> Y.1111_X1.1_X2.0 0 0 0 0
#> Y.0000_X1.1_X2.1 0 0 0 0
#> Y.1000_X1.1_X2.1 0 0 0 0
#> Y.0100_X1.1_X2.1 0 0 0 0
#> Y.1100_X1.1_X2.1 0 0 0 0
#> Y.0010_X1.1_X2.1 0 0 0 0
#> Y.1010_X1.1_X2.1 0 0 0 0
#> Y.0110_X1.1_X2.1 0 0 0 1
#> Y.1110_X1.1_X2.1 0 0 0 0
#> Y.0001_X1.1_X2.1 0 0 0 0
#> Y.1001_X1.1_X2.1 0 0 0 0
#> Y.0101_X1.1_X2.1 0 0 0 0
#> Y.1101_X1.1_X2.1 0 0 0 0
#> Y.0011_X1.1_X2.1 0 0 0 0
#> Y.1011_X1.1_X2.1 0 0 0 0
#> Y.0111_X1.1_X2.1 0 0 0 0
#> Y.1111_X1.1_X2.1 0 0 0 0
#> X10.X20.Y1110 X11.X20.Y1110 X10.X21.Y1110 X11.X21.Y1110
#> X1.0 1 0 1 0
#> X1.1 0 1 0 1
#> X2.0 1 1 0 0
#> X2.1 0 0 1 1
#> Y.0000_X1.0_X2.0 0 0 0 0
#> Y.1000_X1.0_X2.0 0 0 0 0
#> Y.0100_X1.0_X2.0 0 0 0 0
#> Y.1100_X1.0_X2.0 0 0 0 0
#> Y.0010_X1.0_X2.0 0 0 0 0
#> Y.1010_X1.0_X2.0 0 0 0 0
#> Y.0110_X1.0_X2.0 0 0 0 0
#> Y.1110_X1.0_X2.0 1 0 0 0
#> Y.0001_X1.0_X2.0 0 0 0 0
#> Y.1001_X1.0_X2.0 0 0 0 0
#> Y.0101_X1.0_X2.0 0 0 0 0
#> Y.1101_X1.0_X2.0 0 0 0 0
#> Y.0011_X1.0_X2.0 0 0 0 0
#> Y.1011_X1.0_X2.0 0 0 0 0
#> Y.0111_X1.0_X2.0 0 0 0 0
#> Y.1111_X1.0_X2.0 0 0 0 0
#> Y.0000_X1.0_X2.1 0 0 0 0
#> Y.1000_X1.0_X2.1 0 0 0 0
#> Y.0100_X1.0_X2.1 0 0 0 0
#> Y.1100_X1.0_X2.1 0 0 0 0
#> Y.0010_X1.0_X2.1 0 0 0 0
#> Y.1010_X1.0_X2.1 0 0 0 0
#> Y.0110_X1.0_X2.1 0 0 0 0
#> Y.1110_X1.0_X2.1 0 0 1 0
#> Y.0001_X1.0_X2.1 0 0 0 0
#> Y.1001_X1.0_X2.1 0 0 0 0
#> Y.0101_X1.0_X2.1 0 0 0 0
#> Y.1101_X1.0_X2.1 0 0 0 0
#> Y.0011_X1.0_X2.1 0 0 0 0
#> Y.1011_X1.0_X2.1 0 0 0 0
#> Y.0111_X1.0_X2.1 0 0 0 0
#> Y.1111_X1.0_X2.1 0 0 0 0
#> Y.0000_X1.1_X2.0 0 0 0 0
#> Y.1000_X1.1_X2.0 0 0 0 0
#> Y.0100_X1.1_X2.0 0 0 0 0
#> Y.1100_X1.1_X2.0 0 0 0 0
#> Y.0010_X1.1_X2.0 0 0 0 0
#> Y.1010_X1.1_X2.0 0 0 0 0
#> Y.0110_X1.1_X2.0 0 0 0 0
#> Y.1110_X1.1_X2.0 0 1 0 0
#> Y.0001_X1.1_X2.0 0 0 0 0
#> Y.1001_X1.1_X2.0 0 0 0 0
#> Y.0101_X1.1_X2.0 0 0 0 0
#> Y.1101_X1.1_X2.0 0 0 0 0
#> Y.0011_X1.1_X2.0 0 0 0 0
#> Y.1011_X1.1_X2.0 0 0 0 0
#> Y.0111_X1.1_X2.0 0 0 0 0
#> Y.1111_X1.1_X2.0 0 0 0 0
#> Y.0000_X1.1_X2.1 0 0 0 0
#> Y.1000_X1.1_X2.1 0 0 0 0
#> Y.0100_X1.1_X2.1 0 0 0 0
#> Y.1100_X1.1_X2.1 0 0 0 0
#> Y.0010_X1.1_X2.1 0 0 0 0
#> Y.1010_X1.1_X2.1 0 0 0 0
#> Y.0110_X1.1_X2.1 0 0 0 0
#> Y.1110_X1.1_X2.1 0 0 0 1
#> Y.0001_X1.1_X2.1 0 0 0 0
#> Y.1001_X1.1_X2.1 0 0 0 0
#> Y.0101_X1.1_X2.1 0 0 0 0
#> Y.1101_X1.1_X2.1 0 0 0 0
#> Y.0011_X1.1_X2.1 0 0 0 0
#> Y.1011_X1.1_X2.1 0 0 0 0
#> Y.0111_X1.1_X2.1 0 0 0 0
#> Y.1111_X1.1_X2.1 0 0 0 0
#> X10.X20.Y0001 X11.X20.Y0001 X10.X21.Y0001 X11.X21.Y0001
#> X1.0 1 0 1 0
#> X1.1 0 1 0 1
#> X2.0 1 1 0 0
#> X2.1 0 0 1 1
#> Y.0000_X1.0_X2.0 0 0 0 0
#> Y.1000_X1.0_X2.0 0 0 0 0
#> Y.0100_X1.0_X2.0 0 0 0 0
#> Y.1100_X1.0_X2.0 0 0 0 0
#> Y.0010_X1.0_X2.0 0 0 0 0
#> Y.1010_X1.0_X2.0 0 0 0 0
#> Y.0110_X1.0_X2.0 0 0 0 0
#> Y.1110_X1.0_X2.0 0 0 0 0
#> Y.0001_X1.0_X2.0 1 0 0 0
#> Y.1001_X1.0_X2.0 0 0 0 0
#> Y.0101_X1.0_X2.0 0 0 0 0
#> Y.1101_X1.0_X2.0 0 0 0 0
#> Y.0011_X1.0_X2.0 0 0 0 0
#> Y.1011_X1.0_X2.0 0 0 0 0
#> Y.0111_X1.0_X2.0 0 0 0 0
#> Y.1111_X1.0_X2.0 0 0 0 0
#> Y.0000_X1.0_X2.1 0 0 0 0
#> Y.1000_X1.0_X2.1 0 0 0 0
#> Y.0100_X1.0_X2.1 0 0 0 0
#> Y.1100_X1.0_X2.1 0 0 0 0
#> Y.0010_X1.0_X2.1 0 0 0 0
#> Y.1010_X1.0_X2.1 0 0 0 0
#> Y.0110_X1.0_X2.1 0 0 0 0
#> Y.1110_X1.0_X2.1 0 0 0 0
#> Y.0001_X1.0_X2.1 0 0 1 0
#> Y.1001_X1.0_X2.1 0 0 0 0
#> Y.0101_X1.0_X2.1 0 0 0 0
#> Y.1101_X1.0_X2.1 0 0 0 0
#> Y.0011_X1.0_X2.1 0 0 0 0
#> Y.1011_X1.0_X2.1 0 0 0 0
#> Y.0111_X1.0_X2.1 0 0 0 0
#> Y.1111_X1.0_X2.1 0 0 0 0
#> Y.0000_X1.1_X2.0 0 0 0 0
#> Y.1000_X1.1_X2.0 0 0 0 0
#> Y.0100_X1.1_X2.0 0 0 0 0
#> Y.1100_X1.1_X2.0 0 0 0 0
#> Y.0010_X1.1_X2.0 0 0 0 0
#> Y.1010_X1.1_X2.0 0 0 0 0
#> Y.0110_X1.1_X2.0 0 0 0 0
#> Y.1110_X1.1_X2.0 0 0 0 0
#> Y.0001_X1.1_X2.0 0 1 0 0
#> Y.1001_X1.1_X2.0 0 0 0 0
#> Y.0101_X1.1_X2.0 0 0 0 0
#> Y.1101_X1.1_X2.0 0 0 0 0
#> Y.0011_X1.1_X2.0 0 0 0 0
#> Y.1011_X1.1_X2.0 0 0 0 0
#> Y.0111_X1.1_X2.0 0 0 0 0
#> Y.1111_X1.1_X2.0 0 0 0 0
#> Y.0000_X1.1_X2.1 0 0 0 0
#> Y.1000_X1.1_X2.1 0 0 0 0
#> Y.0100_X1.1_X2.1 0 0 0 0
#> Y.1100_X1.1_X2.1 0 0 0 0
#> Y.0010_X1.1_X2.1 0 0 0 0
#> Y.1010_X1.1_X2.1 0 0 0 0
#> Y.0110_X1.1_X2.1 0 0 0 0
#> Y.1110_X1.1_X2.1 0 0 0 0
#> Y.0001_X1.1_X2.1 0 0 0 1
#> Y.1001_X1.1_X2.1 0 0 0 0
#> Y.0101_X1.1_X2.1 0 0 0 0
#> Y.1101_X1.1_X2.1 0 0 0 0
#> Y.0011_X1.1_X2.1 0 0 0 0
#> Y.1011_X1.1_X2.1 0 0 0 0
#> Y.0111_X1.1_X2.1 0 0 0 0
#> Y.1111_X1.1_X2.1 0 0 0 0
#> X10.X20.Y1001 X11.X20.Y1001 X10.X21.Y1001 X11.X21.Y1001
#> X1.0 1 0 1 0
#> X1.1 0 1 0 1
#> X2.0 1 1 0 0
#> X2.1 0 0 1 1
#> Y.0000_X1.0_X2.0 0 0 0 0
#> Y.1000_X1.0_X2.0 0 0 0 0
#> Y.0100_X1.0_X2.0 0 0 0 0
#> Y.1100_X1.0_X2.0 0 0 0 0
#> Y.0010_X1.0_X2.0 0 0 0 0
#> Y.1010_X1.0_X2.0 0 0 0 0
#> Y.0110_X1.0_X2.0 0 0 0 0
#> Y.1110_X1.0_X2.0 0 0 0 0
#> Y.0001_X1.0_X2.0 0 0 0 0
#> Y.1001_X1.0_X2.0 1 0 0 0
#> Y.0101_X1.0_X2.0 0 0 0 0
#> Y.1101_X1.0_X2.0 0 0 0 0
#> Y.0011_X1.0_X2.0 0 0 0 0
#> Y.1011_X1.0_X2.0 0 0 0 0
#> Y.0111_X1.0_X2.0 0 0 0 0
#> Y.1111_X1.0_X2.0 0 0 0 0
#> Y.0000_X1.0_X2.1 0 0 0 0
#> Y.1000_X1.0_X2.1 0 0 0 0
#> Y.0100_X1.0_X2.1 0 0 0 0
#> Y.1100_X1.0_X2.1 0 0 0 0
#> Y.0010_X1.0_X2.1 0 0 0 0
#> Y.1010_X1.0_X2.1 0 0 0 0
#> Y.0110_X1.0_X2.1 0 0 0 0
#> Y.1110_X1.0_X2.1 0 0 0 0
#> Y.0001_X1.0_X2.1 0 0 0 0
#> Y.1001_X1.0_X2.1 0 0 1 0
#> Y.0101_X1.0_X2.1 0 0 0 0
#> Y.1101_X1.0_X2.1 0 0 0 0
#> Y.0011_X1.0_X2.1 0 0 0 0
#> Y.1011_X1.0_X2.1 0 0 0 0
#> Y.0111_X1.0_X2.1 0 0 0 0
#> Y.1111_X1.0_X2.1 0 0 0 0
#> Y.0000_X1.1_X2.0 0 0 0 0
#> Y.1000_X1.1_X2.0 0 0 0 0
#> Y.0100_X1.1_X2.0 0 0 0 0
#> Y.1100_X1.1_X2.0 0 0 0 0
#> Y.0010_X1.1_X2.0 0 0 0 0
#> Y.1010_X1.1_X2.0 0 0 0 0
#> Y.0110_X1.1_X2.0 0 0 0 0
#> Y.1110_X1.1_X2.0 0 0 0 0
#> Y.0001_X1.1_X2.0 0 0 0 0
#> Y.1001_X1.1_X2.0 0 1 0 0
#> Y.0101_X1.1_X2.0 0 0 0 0
#> Y.1101_X1.1_X2.0 0 0 0 0
#> Y.0011_X1.1_X2.0 0 0 0 0
#> Y.1011_X1.1_X2.0 0 0 0 0
#> Y.0111_X1.1_X2.0 0 0 0 0
#> Y.1111_X1.1_X2.0 0 0 0 0
#> Y.0000_X1.1_X2.1 0 0 0 0
#> Y.1000_X1.1_X2.1 0 0 0 0
#> Y.0100_X1.1_X2.1 0 0 0 0
#> Y.1100_X1.1_X2.1 0 0 0 0
#> Y.0010_X1.1_X2.1 0 0 0 0
#> Y.1010_X1.1_X2.1 0 0 0 0
#> Y.0110_X1.1_X2.1 0 0 0 0
#> Y.1110_X1.1_X2.1 0 0 0 0
#> Y.0001_X1.1_X2.1 0 0 0 0
#> Y.1001_X1.1_X2.1 0 0 0 1
#> Y.0101_X1.1_X2.1 0 0 0 0
#> Y.1101_X1.1_X2.1 0 0 0 0
#> Y.0011_X1.1_X2.1 0 0 0 0
#> Y.1011_X1.1_X2.1 0 0 0 0
#> Y.0111_X1.1_X2.1 0 0 0 0
#> Y.1111_X1.1_X2.1 0 0 0 0
#> X10.X20.Y0101 X11.X20.Y0101 X10.X21.Y0101 X11.X21.Y0101
#> X1.0 1 0 1 0
#> X1.1 0 1 0 1
#> X2.0 1 1 0 0
#> X2.1 0 0 1 1
#> Y.0000_X1.0_X2.0 0 0 0 0
#> Y.1000_X1.0_X2.0 0 0 0 0
#> Y.0100_X1.0_X2.0 0 0 0 0
#> Y.1100_X1.0_X2.0 0 0 0 0
#> Y.0010_X1.0_X2.0 0 0 0 0
#> Y.1010_X1.0_X2.0 0 0 0 0
#> Y.0110_X1.0_X2.0 0 0 0 0
#> Y.1110_X1.0_X2.0 0 0 0 0
#> Y.0001_X1.0_X2.0 0 0 0 0
#> Y.1001_X1.0_X2.0 0 0 0 0
#> Y.0101_X1.0_X2.0 1 0 0 0
#> Y.1101_X1.0_X2.0 0 0 0 0
#> Y.0011_X1.0_X2.0 0 0 0 0
#> Y.1011_X1.0_X2.0 0 0 0 0
#> Y.0111_X1.0_X2.0 0 0 0 0
#> Y.1111_X1.0_X2.0 0 0 0 0
#> Y.0000_X1.0_X2.1 0 0 0 0
#> Y.1000_X1.0_X2.1 0 0 0 0
#> Y.0100_X1.0_X2.1 0 0 0 0
#> Y.1100_X1.0_X2.1 0 0 0 0
#> Y.0010_X1.0_X2.1 0 0 0 0
#> Y.1010_X1.0_X2.1 0 0 0 0
#> Y.0110_X1.0_X2.1 0 0 0 0
#> Y.1110_X1.0_X2.1 0 0 0 0
#> Y.0001_X1.0_X2.1 0 0 0 0
#> Y.1001_X1.0_X2.1 0 0 0 0
#> Y.0101_X1.0_X2.1 0 0 1 0
#> Y.1101_X1.0_X2.1 0 0 0 0
#> Y.0011_X1.0_X2.1 0 0 0 0
#> Y.1011_X1.0_X2.1 0 0 0 0
#> Y.0111_X1.0_X2.1 0 0 0 0
#> Y.1111_X1.0_X2.1 0 0 0 0
#> Y.0000_X1.1_X2.0 0 0 0 0
#> Y.1000_X1.1_X2.0 0 0 0 0
#> Y.0100_X1.1_X2.0 0 0 0 0
#> Y.1100_X1.1_X2.0 0 0 0 0
#> Y.0010_X1.1_X2.0 0 0 0 0
#> Y.1010_X1.1_X2.0 0 0 0 0
#> Y.0110_X1.1_X2.0 0 0 0 0
#> Y.1110_X1.1_X2.0 0 0 0 0
#> Y.0001_X1.1_X2.0 0 0 0 0
#> Y.1001_X1.1_X2.0 0 0 0 0
#> Y.0101_X1.1_X2.0 0 1 0 0
#> Y.1101_X1.1_X2.0 0 0 0 0
#> Y.0011_X1.1_X2.0 0 0 0 0
#> Y.1011_X1.1_X2.0 0 0 0 0
#> Y.0111_X1.1_X2.0 0 0 0 0
#> Y.1111_X1.1_X2.0 0 0 0 0
#> Y.0000_X1.1_X2.1 0 0 0 0
#> Y.1000_X1.1_X2.1 0 0 0 0
#> Y.0100_X1.1_X2.1 0 0 0 0
#> Y.1100_X1.1_X2.1 0 0 0 0
#> Y.0010_X1.1_X2.1 0 0 0 0
#> Y.1010_X1.1_X2.1 0 0 0 0
#> Y.0110_X1.1_X2.1 0 0 0 0
#> Y.1110_X1.1_X2.1 0 0 0 0
#> Y.0001_X1.1_X2.1 0 0 0 0
#> Y.1001_X1.1_X2.1 0 0 0 0
#> Y.0101_X1.1_X2.1 0 0 0 1
#> Y.1101_X1.1_X2.1 0 0 0 0
#> Y.0011_X1.1_X2.1 0 0 0 0
#> Y.1011_X1.1_X2.1 0 0 0 0
#> Y.0111_X1.1_X2.1 0 0 0 0
#> Y.1111_X1.1_X2.1 0 0 0 0
#> X10.X20.Y1101 X11.X20.Y1101 X10.X21.Y1101 X11.X21.Y1101
#> X1.0 1 0 1 0
#> X1.1 0 1 0 1
#> X2.0 1 1 0 0
#> X2.1 0 0 1 1
#> Y.0000_X1.0_X2.0 0 0 0 0
#> Y.1000_X1.0_X2.0 0 0 0 0
#> Y.0100_X1.0_X2.0 0 0 0 0
#> Y.1100_X1.0_X2.0 0 0 0 0
#> Y.0010_X1.0_X2.0 0 0 0 0
#> Y.1010_X1.0_X2.0 0 0 0 0
#> Y.0110_X1.0_X2.0 0 0 0 0
#> Y.1110_X1.0_X2.0 0 0 0 0
#> Y.0001_X1.0_X2.0 0 0 0 0
#> Y.1001_X1.0_X2.0 0 0 0 0
#> Y.0101_X1.0_X2.0 0 0 0 0
#> Y.1101_X1.0_X2.0 1 0 0 0
#> Y.0011_X1.0_X2.0 0 0 0 0
#> Y.1011_X1.0_X2.0 0 0 0 0
#> Y.0111_X1.0_X2.0 0 0 0 0
#> Y.1111_X1.0_X2.0 0 0 0 0
#> Y.0000_X1.0_X2.1 0 0 0 0
#> Y.1000_X1.0_X2.1 0 0 0 0
#> Y.0100_X1.0_X2.1 0 0 0 0
#> Y.1100_X1.0_X2.1 0 0 0 0
#> Y.0010_X1.0_X2.1 0 0 0 0
#> Y.1010_X1.0_X2.1 0 0 0 0
#> Y.0110_X1.0_X2.1 0 0 0 0
#> Y.1110_X1.0_X2.1 0 0 0 0
#> Y.0001_X1.0_X2.1 0 0 0 0
#> Y.1001_X1.0_X2.1 0 0 0 0
#> Y.0101_X1.0_X2.1 0 0 0 0
#> Y.1101_X1.0_X2.1 0 0 1 0
#> Y.0011_X1.0_X2.1 0 0 0 0
#> Y.1011_X1.0_X2.1 0 0 0 0
#> Y.0111_X1.0_X2.1 0 0 0 0
#> Y.1111_X1.0_X2.1 0 0 0 0
#> Y.0000_X1.1_X2.0 0 0 0 0
#> Y.1000_X1.1_X2.0 0 0 0 0
#> Y.0100_X1.1_X2.0 0 0 0 0
#> Y.1100_X1.1_X2.0 0 0 0 0
#> Y.0010_X1.1_X2.0 0 0 0 0
#> Y.1010_X1.1_X2.0 0 0 0 0
#> Y.0110_X1.1_X2.0 0 0 0 0
#> Y.1110_X1.1_X2.0 0 0 0 0
#> Y.0001_X1.1_X2.0 0 0 0 0
#> Y.1001_X1.1_X2.0 0 0 0 0
#> Y.0101_X1.1_X2.0 0 0 0 0
#> Y.1101_X1.1_X2.0 0 1 0 0
#> Y.0011_X1.1_X2.0 0 0 0 0
#> Y.1011_X1.1_X2.0 0 0 0 0
#> Y.0111_X1.1_X2.0 0 0 0 0
#> Y.1111_X1.1_X2.0 0 0 0 0
#> Y.0000_X1.1_X2.1 0 0 0 0
#> Y.1000_X1.1_X2.1 0 0 0 0
#> Y.0100_X1.1_X2.1 0 0 0 0
#> Y.1100_X1.1_X2.1 0 0 0 0
#> Y.0010_X1.1_X2.1 0 0 0 0
#> Y.1010_X1.1_X2.1 0 0 0 0
#> Y.0110_X1.1_X2.1 0 0 0 0
#> Y.1110_X1.1_X2.1 0 0 0 0
#> Y.0001_X1.1_X2.1 0 0 0 0
#> Y.1001_X1.1_X2.1 0 0 0 0
#> Y.0101_X1.1_X2.1 0 0 0 0
#> Y.1101_X1.1_X2.1 0 0 0 1
#> Y.0011_X1.1_X2.1 0 0 0 0
#> Y.1011_X1.1_X2.1 0 0 0 0
#> Y.0111_X1.1_X2.1 0 0 0 0
#> Y.1111_X1.1_X2.1 0 0 0 0
#> X10.X20.Y0011 X11.X20.Y0011 X10.X21.Y0011 X11.X21.Y0011
#> X1.0 1 0 1 0
#> X1.1 0 1 0 1
#> X2.0 1 1 0 0
#> X2.1 0 0 1 1
#> Y.0000_X1.0_X2.0 0 0 0 0
#> Y.1000_X1.0_X2.0 0 0 0 0
#> Y.0100_X1.0_X2.0 0 0 0 0
#> Y.1100_X1.0_X2.0 0 0 0 0
#> Y.0010_X1.0_X2.0 0 0 0 0
#> Y.1010_X1.0_X2.0 0 0 0 0
#> Y.0110_X1.0_X2.0 0 0 0 0
#> Y.1110_X1.0_X2.0 0 0 0 0
#> Y.0001_X1.0_X2.0 0 0 0 0
#> Y.1001_X1.0_X2.0 0 0 0 0
#> Y.0101_X1.0_X2.0 0 0 0 0
#> Y.1101_X1.0_X2.0 0 0 0 0
#> Y.0011_X1.0_X2.0 1 0 0 0
#> Y.1011_X1.0_X2.0 0 0 0 0
#> Y.0111_X1.0_X2.0 0 0 0 0
#> Y.1111_X1.0_X2.0 0 0 0 0
#> Y.0000_X1.0_X2.1 0 0 0 0
#> Y.1000_X1.0_X2.1 0 0 0 0
#> Y.0100_X1.0_X2.1 0 0 0 0
#> Y.1100_X1.0_X2.1 0 0 0 0
#> Y.0010_X1.0_X2.1 0 0 0 0
#> Y.1010_X1.0_X2.1 0 0 0 0
#> Y.0110_X1.0_X2.1 0 0 0 0
#> Y.1110_X1.0_X2.1 0 0 0 0
#> Y.0001_X1.0_X2.1 0 0 0 0
#> Y.1001_X1.0_X2.1 0 0 0 0
#> Y.0101_X1.0_X2.1 0 0 0 0
#> Y.1101_X1.0_X2.1 0 0 0 0
#> Y.0011_X1.0_X2.1 0 0 1 0
#> Y.1011_X1.0_X2.1 0 0 0 0
#> Y.0111_X1.0_X2.1 0 0 0 0
#> Y.1111_X1.0_X2.1 0 0 0 0
#> Y.0000_X1.1_X2.0 0 0 0 0
#> Y.1000_X1.1_X2.0 0 0 0 0
#> Y.0100_X1.1_X2.0 0 0 0 0
#> Y.1100_X1.1_X2.0 0 0 0 0
#> Y.0010_X1.1_X2.0 0 0 0 0
#> Y.1010_X1.1_X2.0 0 0 0 0
#> Y.0110_X1.1_X2.0 0 0 0 0
#> Y.1110_X1.1_X2.0 0 0 0 0
#> Y.0001_X1.1_X2.0 0 0 0 0
#> Y.1001_X1.1_X2.0 0 0 0 0
#> Y.0101_X1.1_X2.0 0 0 0 0
#> Y.1101_X1.1_X2.0 0 0 0 0
#> Y.0011_X1.1_X2.0 0 1 0 0
#> Y.1011_X1.1_X2.0 0 0 0 0
#> Y.0111_X1.1_X2.0 0 0 0 0
#> Y.1111_X1.1_X2.0 0 0 0 0
#> Y.0000_X1.1_X2.1 0 0 0 0
#> Y.1000_X1.1_X2.1 0 0 0 0
#> Y.0100_X1.1_X2.1 0 0 0 0
#> Y.1100_X1.1_X2.1 0 0 0 0
#> Y.0010_X1.1_X2.1 0 0 0 0
#> Y.1010_X1.1_X2.1 0 0 0 0
#> Y.0110_X1.1_X2.1 0 0 0 0
#> Y.1110_X1.1_X2.1 0 0 0 0
#> Y.0001_X1.1_X2.1 0 0 0 0
#> Y.1001_X1.1_X2.1 0 0 0 0
#> Y.0101_X1.1_X2.1 0 0 0 0
#> Y.1101_X1.1_X2.1 0 0 0 0
#> Y.0011_X1.1_X2.1 0 0 0 1
#> Y.1011_X1.1_X2.1 0 0 0 0
#> Y.0111_X1.1_X2.1 0 0 0 0
#> Y.1111_X1.1_X2.1 0 0 0 0
#> X10.X20.Y1011 X11.X20.Y1011 X10.X21.Y1011 X11.X21.Y1011
#> X1.0 1 0 1 0
#> X1.1 0 1 0 1
#> X2.0 1 1 0 0
#> X2.1 0 0 1 1
#> Y.0000_X1.0_X2.0 0 0 0 0
#> Y.1000_X1.0_X2.0 0 0 0 0
#> Y.0100_X1.0_X2.0 0 0 0 0
#> Y.1100_X1.0_X2.0 0 0 0 0
#> Y.0010_X1.0_X2.0 0 0 0 0
#> Y.1010_X1.0_X2.0 0 0 0 0
#> Y.0110_X1.0_X2.0 0 0 0 0
#> Y.1110_X1.0_X2.0 0 0 0 0
#> Y.0001_X1.0_X2.0 0 0 0 0
#> Y.1001_X1.0_X2.0 0 0 0 0
#> Y.0101_X1.0_X2.0 0 0 0 0
#> Y.1101_X1.0_X2.0 0 0 0 0
#> Y.0011_X1.0_X2.0 0 0 0 0
#> Y.1011_X1.0_X2.0 1 0 0 0
#> Y.0111_X1.0_X2.0 0 0 0 0
#> Y.1111_X1.0_X2.0 0 0 0 0
#> Y.0000_X1.0_X2.1 0 0 0 0
#> Y.1000_X1.0_X2.1 0 0 0 0
#> Y.0100_X1.0_X2.1 0 0 0 0
#> Y.1100_X1.0_X2.1 0 0 0 0
#> Y.0010_X1.0_X2.1 0 0 0 0
#> Y.1010_X1.0_X2.1 0 0 0 0
#> Y.0110_X1.0_X2.1 0 0 0 0
#> Y.1110_X1.0_X2.1 0 0 0 0
#> Y.0001_X1.0_X2.1 0 0 0 0
#> Y.1001_X1.0_X2.1 0 0 0 0
#> Y.0101_X1.0_X2.1 0 0 0 0
#> Y.1101_X1.0_X2.1 0 0 0 0
#> Y.0011_X1.0_X2.1 0 0 0 0
#> Y.1011_X1.0_X2.1 0 0 1 0
#> Y.0111_X1.0_X2.1 0 0 0 0
#> Y.1111_X1.0_X2.1 0 0 0 0
#> Y.0000_X1.1_X2.0 0 0 0 0
#> Y.1000_X1.1_X2.0 0 0 0 0
#> Y.0100_X1.1_X2.0 0 0 0 0
#> Y.1100_X1.1_X2.0 0 0 0 0
#> Y.0010_X1.1_X2.0 0 0 0 0
#> Y.1010_X1.1_X2.0 0 0 0 0
#> Y.0110_X1.1_X2.0 0 0 0 0
#> Y.1110_X1.1_X2.0 0 0 0 0
#> Y.0001_X1.1_X2.0 0 0 0 0
#> Y.1001_X1.1_X2.0 0 0 0 0
#> Y.0101_X1.1_X2.0 0 0 0 0
#> Y.1101_X1.1_X2.0 0 0 0 0
#> Y.0011_X1.1_X2.0 0 0 0 0
#> Y.1011_X1.1_X2.0 0 1 0 0
#> Y.0111_X1.1_X2.0 0 0 0 0
#> Y.1111_X1.1_X2.0 0 0 0 0
#> Y.0000_X1.1_X2.1 0 0 0 0
#> Y.1000_X1.1_X2.1 0 0 0 0
#> Y.0100_X1.1_X2.1 0 0 0 0
#> Y.1100_X1.1_X2.1 0 0 0 0
#> Y.0010_X1.1_X2.1 0 0 0 0
#> Y.1010_X1.1_X2.1 0 0 0 0
#> Y.0110_X1.1_X2.1 0 0 0 0
#> Y.1110_X1.1_X2.1 0 0 0 0
#> Y.0001_X1.1_X2.1 0 0 0 0
#> Y.1001_X1.1_X2.1 0 0 0 0
#> Y.0101_X1.1_X2.1 0 0 0 0
#> Y.1101_X1.1_X2.1 0 0 0 0
#> Y.0011_X1.1_X2.1 0 0 0 0
#> Y.1011_X1.1_X2.1 0 0 0 1
#> Y.0111_X1.1_X2.1 0 0 0 0
#> Y.1111_X1.1_X2.1 0 0 0 0
#> X10.X20.Y0111 X11.X20.Y0111 X10.X21.Y0111 X11.X21.Y0111
#> X1.0 1 0 1 0
#> X1.1 0 1 0 1
#> X2.0 1 1 0 0
#> X2.1 0 0 1 1
#> Y.0000_X1.0_X2.0 0 0 0 0
#> Y.1000_X1.0_X2.0 0 0 0 0
#> Y.0100_X1.0_X2.0 0 0 0 0
#> Y.1100_X1.0_X2.0 0 0 0 0
#> Y.0010_X1.0_X2.0 0 0 0 0
#> Y.1010_X1.0_X2.0 0 0 0 0
#> Y.0110_X1.0_X2.0 0 0 0 0
#> Y.1110_X1.0_X2.0 0 0 0 0
#> Y.0001_X1.0_X2.0 0 0 0 0
#> Y.1001_X1.0_X2.0 0 0 0 0
#> Y.0101_X1.0_X2.0 0 0 0 0
#> Y.1101_X1.0_X2.0 0 0 0 0
#> Y.0011_X1.0_X2.0 0 0 0 0
#> Y.1011_X1.0_X2.0 0 0 0 0
#> Y.0111_X1.0_X2.0 1 0 0 0
#> Y.1111_X1.0_X2.0 0 0 0 0
#> Y.0000_X1.0_X2.1 0 0 0 0
#> Y.1000_X1.0_X2.1 0 0 0 0
#> Y.0100_X1.0_X2.1 0 0 0 0
#> Y.1100_X1.0_X2.1 0 0 0 0
#> Y.0010_X1.0_X2.1 0 0 0 0
#> Y.1010_X1.0_X2.1 0 0 0 0
#> Y.0110_X1.0_X2.1 0 0 0 0
#> Y.1110_X1.0_X2.1 0 0 0 0
#> Y.0001_X1.0_X2.1 0 0 0 0
#> Y.1001_X1.0_X2.1 0 0 0 0
#> Y.0101_X1.0_X2.1 0 0 0 0
#> Y.1101_X1.0_X2.1 0 0 0 0
#> Y.0011_X1.0_X2.1 0 0 0 0
#> Y.1011_X1.0_X2.1 0 0 0 0
#> Y.0111_X1.0_X2.1 0 0 1 0
#> Y.1111_X1.0_X2.1 0 0 0 0
#> Y.0000_X1.1_X2.0 0 0 0 0
#> Y.1000_X1.1_X2.0 0 0 0 0
#> Y.0100_X1.1_X2.0 0 0 0 0
#> Y.1100_X1.1_X2.0 0 0 0 0
#> Y.0010_X1.1_X2.0 0 0 0 0
#> Y.1010_X1.1_X2.0 0 0 0 0
#> Y.0110_X1.1_X2.0 0 0 0 0
#> Y.1110_X1.1_X2.0 0 0 0 0
#> Y.0001_X1.1_X2.0 0 0 0 0
#> Y.1001_X1.1_X2.0 0 0 0 0
#> Y.0101_X1.1_X2.0 0 0 0 0
#> Y.1101_X1.1_X2.0 0 0 0 0
#> Y.0011_X1.1_X2.0 0 0 0 0
#> Y.1011_X1.1_X2.0 0 0 0 0
#> Y.0111_X1.1_X2.0 0 1 0 0
#> Y.1111_X1.1_X2.0 0 0 0 0
#> Y.0000_X1.1_X2.1 0 0 0 0
#> Y.1000_X1.1_X2.1 0 0 0 0
#> Y.0100_X1.1_X2.1 0 0 0 0
#> Y.1100_X1.1_X2.1 0 0 0 0
#> Y.0010_X1.1_X2.1 0 0 0 0
#> Y.1010_X1.1_X2.1 0 0 0 0
#> Y.0110_X1.1_X2.1 0 0 0 0
#> Y.1110_X1.1_X2.1 0 0 0 0
#> Y.0001_X1.1_X2.1 0 0 0 0
#> Y.1001_X1.1_X2.1 0 0 0 0
#> Y.0101_X1.1_X2.1 0 0 0 0
#> Y.1101_X1.1_X2.1 0 0 0 0
#> Y.0011_X1.1_X2.1 0 0 0 0
#> Y.1011_X1.1_X2.1 0 0 0 0
#> Y.0111_X1.1_X2.1 0 0 0 1
#> Y.1111_X1.1_X2.1 0 0 0 0
#> X10.X20.Y1111 X11.X20.Y1111 X10.X21.Y1111 X11.X21.Y1111
#> X1.0 1 0 1 0
#> X1.1 0 1 0 1
#> X2.0 1 1 0 0
#> X2.1 0 0 1 1
#> Y.0000_X1.0_X2.0 0 0 0 0
#> Y.1000_X1.0_X2.0 0 0 0 0
#> Y.0100_X1.0_X2.0 0 0 0 0
#> Y.1100_X1.0_X2.0 0 0 0 0
#> Y.0010_X1.0_X2.0 0 0 0 0
#> Y.1010_X1.0_X2.0 0 0 0 0
#> Y.0110_X1.0_X2.0 0 0 0 0
#> Y.1110_X1.0_X2.0 0 0 0 0
#> Y.0001_X1.0_X2.0 0 0 0 0
#> Y.1001_X1.0_X2.0 0 0 0 0
#> Y.0101_X1.0_X2.0 0 0 0 0
#> Y.1101_X1.0_X2.0 0 0 0 0
#> Y.0011_X1.0_X2.0 0 0 0 0
#> Y.1011_X1.0_X2.0 0 0 0 0
#> Y.0111_X1.0_X2.0 0 0 0 0
#> Y.1111_X1.0_X2.0 1 0 0 0
#> Y.0000_X1.0_X2.1 0 0 0 0
#> Y.1000_X1.0_X2.1 0 0 0 0
#> Y.0100_X1.0_X2.1 0 0 0 0
#> Y.1100_X1.0_X2.1 0 0 0 0
#> Y.0010_X1.0_X2.1 0 0 0 0
#> Y.1010_X1.0_X2.1 0 0 0 0
#> Y.0110_X1.0_X2.1 0 0 0 0
#> Y.1110_X1.0_X2.1 0 0 0 0
#> Y.0001_X1.0_X2.1 0 0 0 0
#> Y.1001_X1.0_X2.1 0 0 0 0
#> Y.0101_X1.0_X2.1 0 0 0 0
#> Y.1101_X1.0_X2.1 0 0 0 0
#> Y.0011_X1.0_X2.1 0 0 0 0
#> Y.1011_X1.0_X2.1 0 0 0 0
#> Y.0111_X1.0_X2.1 0 0 0 0
#> Y.1111_X1.0_X2.1 0 0 1 0
#> Y.0000_X1.1_X2.0 0 0 0 0
#> Y.1000_X1.1_X2.0 0 0 0 0
#> Y.0100_X1.1_X2.0 0 0 0 0
#> Y.1100_X1.1_X2.0 0 0 0 0
#> Y.0010_X1.1_X2.0 0 0 0 0
#> Y.1010_X1.1_X2.0 0 0 0 0
#> Y.0110_X1.1_X2.0 0 0 0 0
#> Y.1110_X1.1_X2.0 0 0 0 0
#> Y.0001_X1.1_X2.0 0 0 0 0
#> Y.1001_X1.1_X2.0 0 0 0 0
#> Y.0101_X1.1_X2.0 0 0 0 0
#> Y.1101_X1.1_X2.0 0 0 0 0
#> Y.0011_X1.1_X2.0 0 0 0 0
#> Y.1011_X1.1_X2.0 0 0 0 0
#> Y.0111_X1.1_X2.0 0 0 0 0
#> Y.1111_X1.1_X2.0 0 1 0 0
#> Y.0000_X1.1_X2.1 0 0 0 0
#> Y.1000_X1.1_X2.1 0 0 0 0
#> Y.0100_X1.1_X2.1 0 0 0 0
#> Y.1100_X1.1_X2.1 0 0 0 0
#> Y.0010_X1.1_X2.1 0 0 0 0
#> Y.1010_X1.1_X2.1 0 0 0 0
#> Y.0110_X1.1_X2.1 0 0 0 0
#> Y.1110_X1.1_X2.1 0 0 0 0
#> Y.0001_X1.1_X2.1 0 0 0 0
#> Y.1001_X1.1_X2.1 0 0 0 0
#> Y.0101_X1.1_X2.1 0 0 0 0
#> Y.1101_X1.1_X2.1 0 0 0 0
#> Y.0011_X1.1_X2.1 0 0 0 0
#> Y.1011_X1.1_X2.1 0 0 0 0
#> Y.0111_X1.1_X2.1 0 0 0 0
#> Y.1111_X1.1_X2.1 0 0 0 1
#> [1] 68 64
inspect(model, "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
#>
#>
#> snippet (use grab() to access full 68 x 8 object):
#>
#> param_names node gen param_set nodal_type given param_value
#> 1 X1.0 X1 1 X1 0 0.5000
#> 2 X1.1 X1 1 X1 1 0.5000
#> 3 X2.0 X2 2 X2 0 0.5000
#> 4 X2.1 X2 2 X2 1 0.5000
#> 5 Y.0000_X1.0_X2.0 Y 3 Y.X1.0.X2.0 0000 X1.0, X2.0 0.0625
#> 6 Y.1000_X1.0_X2.0 Y 3 Y.X1.0.X2.0 1000 X1.0, X2.0 0.0625
#> 7 Y.0100_X1.0_X2.0 Y 3 Y.X1.0.X2.0 0100 X1.0, X2.0 0.0625
#> 8 Y.1100_X1.0_X2.0 Y 3 Y.X1.0.X2.0 1100 X1.0, X2.0 0.0625
#> 9 Y.0010_X1.0_X2.0 Y 3 Y.X1.0.X2.0 0010 X1.0, X2.0 0.0625
#> 10 Y.1010_X1.0_X2.0 Y 3 Y.X1.0.X2.0 1010 X1.0, X2.0 0.0625
#> priors
#> 1 1
#> 2 1
#> 3 1
#> 4 1
#> 5 1
#> 6 1
#> 7 1
#> 8 1
#> 9 1
#> 10 1
# A single node graph is also possible
model <- make_model("X")
# Unconnected nodes not allowed
if (FALSE) { # \dontrun{
model <- make_model("X <-> Y")
} # }
nodal_types <-
list(
A = c("0","1"),
B = c("0","1"),
C = c("0","1"),
D = c("0","1"),
E = c("0","1"),
Y = c(
"00000000000000000000000000000000",
"01010101010101010101010101010101",
"00110011001100110011001100110011",
"00001111000011110000111100001111",
"00000000111111110000000011111111",
"00000000000000001111111111111111",
"11111111111111111111111111111111" ))
make_model("A -> Y; B ->Y; C->Y; D->Y; E->Y",
nodal_types = nodal_types) |>
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
#>
#>
#> snippet (use grab() to access full 17 x 8 object):
#>
#> param_names node gen param_set nodal_type given param_value priors
#> 1 A.0 A 1 A 0 0.5 1
#> 2 A.1 A 1 A 1 0.5 1
#> 3 B.0 B 2 B 0 0.5 1
#> 4 B.1 B 2 B 1 0.5 1
#> 5 C.0 C 3 C 0 0.5 1
#> 6 C.1 C 3 C 1 0.5 1
#> 7 D.0 D 4 D 0 0.5 1
#> 8 D.1 D 4 D 1 0.5 1
#> 9 E.0 E 5 E 0 0.5 1
#> 10 E.1 E 5 E 1 0.5 1
nodal_types = list(Y = c("01", "10"), Z = c("0", "1"))
make_model("Z -> Y", nodal_types = nodal_types) |>
inspect("parameters_df")
#> Ordering of provided nodal types is being altered to match generation
#>
#> 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 Z.0 Z 1 Z 0 0.5 1
#> 2 Z.1 Z 1 Z 1 0.5 1
#> 3 Y.01 Y 2 Y 01 0.5 1
#> 4 Y.10 Y 2 Y 10 0.5 1