make_model uses dagitty syntax and functionality to
specify 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. The default setting for a causal model have flat
(uniform) priors and parameters putting equal weight on each parameter
within each parameter set. These can be adjust with set_priors
and set_parameters
Arguments
- statement
character string. Statement describing causal relations using
dagittysyntax. Only directed relations are permitted. For instance "X -> Y" or "X1 -> Y <- X2; X1 -> X2".- 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
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 types by node:
#> X Y
#> 2 4
#>
#> Number of causal types: 8
modelXKY <- make_model("X -> K -> Y; X -> Y")
# Example where cyclicaly dag 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