## What is dagitty

Dagitty is a software to analyze causal diagrams, also known as directed acyclic graphs (DAGs). Structural equation models (SEMs) can be viewed as a parametric form of DAGs, which encode linear functions instead of arbitrary nonlinear functions.

Because every SEM is a DAG, much of the methodology developed for DAGs is of potentially great interest for SEM users as well. In this vignette, I am going to show some possibilities. This follows the structure of Kyono's “Commentator” program (http://ftp.cs.ucla.edu/pub/stat_ser/r364.pdf), and thereby also shows how the tasks implemented in that program can be solved using the dagitty package.

``````g1 <- dagitty( "dag {
W1 -> Z1 -> X -> Y
Z1 <- V -> Z2
W2 -> Z2 -> Y
X <-> W1 <-> W2 <-> Y
}")

g2 <- dagitty( "dag {
Y <- X <- Z1 <- V -> Z2 -> Y
Z1 <- W1 <-> W2 -> Z2
X <- W1 -> Y
X <- W2 -> Y
}")

plot(graphLayout(g1))
``````

## List testable implications of a structural equation model

``````print( impliedConditionalIndependencies( g1 ) )
``````
``````V _||_ W1
V _||_ W2
V _||_ X | W1, Z1
V _||_ Y | W1, W2, Z1, Z2
W1 _||_ Z2 | W2
W2 _||_ Z1 | W1
X _||_ Z2 | V, W2
X _||_ Z2 | W1, W2, Z1
Z1 _||_ Z2 | V, W2
Z1 _||_ Z2 | V, W1
``````

## List adjustment sets for specific path coefficients

``````print( adjustmentSets( g1, "Z1", "X", effect="direct" ) )
``````
``````{ W1 }
``````
``````print( adjustmentSets( g2, "X", "Y", effect="direct" ) )
``````
``````{ W1, W2, Z2 }
{ V, W1, W2 }
{ W1, W2, Z1 }
``````

## List path coefficients that are identifiable by regression

``````for( n in names(g1) ){
for( m in children(g1,n) ){
a <- adjustmentSets( g1, n, m, effect="direct" )
if( length(a) > 0 ){
cat("The coefficient on ",n,"->",m,
" is identifiable controlling for:\n",sep="")
print( a, prefix=" * " )
}
}
}
``````
``````The coefficient on V->Z1 is identifiable controlling for:
*  {}
The coefficient on V->Z2 is identifiable controlling for:
*  {}
The coefficient on W1->Z1 is identifiable controlling for:
*  {}
The coefficient on W2->Z2 is identifiable controlling for:
*  {}
The coefficient on Z1->X is identifiable controlling for:
{ W1 }
The coefficient on Z2->Y is identifiable controlling for:
{ W1, W2, Z1 }
{ V, W2 }
``````

## List adjustment sets for specific total effects

``````print( adjustmentSets( g1, "X", "Y" ) )
``````
``````print( adjustmentSets( g2, "X", "Y" ) )
``````
``````{ W1, W2, Z2 }
{ V, W1, W2 }
{ W1, W2, Z1 }
``````

## List total effects that are identifiable by regression

``````for( n in names(g1) ){
for( m in setdiff( descendants( g1, n ), n ) ){
a <- adjustmentSets( g1, n, m )
if( length(a) > 0 ){
cat("The total effect of ",n," on ",m,
" is identifiable controlling for:\n",sep="")
print( a, prefix=" * " )
}
}
}
``````
``````The total effect of V on Z2 is identifiable controlling for:
*  {}
The total effect of V on Y is identifiable controlling for:
*  {}
The total effect of V on Z1 is identifiable controlling for:
*  {}
The total effect of V on X is identifiable controlling for:
*  {}
The total effect of W1 on Z1 is identifiable controlling for:
*  {}
The total effect of W2 on Z2 is identifiable controlling for:
*  {}
The total effect of Z1 on X is identifiable controlling for:
{ W1 }
The total effect of Z1 on Y is identifiable controlling for:
{ W1, W2, Z2 }
{ V, W1 }
The total effect of Z2 on Y is identifiable controlling for:
{ W1, W2, Z1 }
{ V, W2 }
``````

## List path coefficients that are identifiable through instrumental variables

``````for( n in names(g1) ){
for( m in children(g1,n) ){
iv <- instrumentalVariables( g1, n, m )
if( length( iv ) > 0 ){
cat( n, m, "\n" )
print( iv , prefix=" * " )
}
}
}
``````
``````V Z1
*  Z2 |  W1
V Z2
*  X |  W2
*  Z1 |  W2
W1 Z1
*  W2
*  Z2 |  V
W2 Z2
*  W1
*  X |  V
*  Z1 |  V
X Y
*  V |  W2, Z2
*  Z1 |  W1, W2, Z2
Z1 X
*  V
*  W2
*  Z2
Z2 Y
*  V |  X
*  W1 |  X
*  Z1 |  X
``````