---
title: "A SEM user's guide to dagitty for R"
author: "Johannes Textor"
date: "`r Sys.Date()`"
vignette: >
  %\VignetteEngine{knitr::rmarkdown}
  %\VignetteIndexEntry{A SEM user's guide to dagitty for R}
  \usepackage[utf8]{inputenc} 
output:
  knitr:::html_vignette:
    toc: yes
---

```{r, echo = FALSE, message = FALSE}
knitr::opts_chunk$set(comment = "")
library(dagitty)
```

## 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.

```{r}
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
```{r} 
print( impliedConditionalIndependencies( g1 ) )
```

## List adjustment sets for specific path coefficients 

```{r}
print( adjustmentSets( g1, "Z1", "X", effect="direct" ) )
```

```{r}
print( adjustmentSets( g2, "X", "Y", effect="direct" ) )
```

## List path coefficients that are identifiable by regression
```{r}
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=" * " )
		}
	}
}
```

## List adjustment sets for specific total effects

```{r}
print( adjustmentSets( g1, "X", "Y" ) )
```

```{r}
print( adjustmentSets( g2, "X", "Y" ) )
```

## List total effects that are identifiable by regression
```{r}
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=" * " )
		}
	}
}
```

## List path coefficients that are identifiable through instrumental variables
```{r}
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=" * " )
		}
	}
}