Drawing DAGs: LaTeX Solution

Directed acyclic graphs (DAGs) are commonly used to represent causal relationships between variables across a wide variety of disciplines. For an excellent (and quite accessible) textbook on the topic, please see the book Causal Inference by Miguel Hernan and Jamie Robins.

In this post, I briefly explore how you can draw DAGs in LaTeX. In the subsequent post, I will show how to draw DAGs using R.

The first example of DAG is the common instrumental variable (IV) setup:

We seek to identify the effect of treatment T on outcome Y. However, this is confounded by an unmeasured variable U. The IV is denoted as Z. Technically, we do not need to put in the crossed out red edges between U and Z and Z and Y - absence of edges encodes independence relations. However, I included them to reinforce (and make explicit) the assumptions needed for identification of causal effects using IVs:

• (Quasi)-exogeneity of the instrument (no path from U to Z)
• Exclusion restriction (no direct path from Z to Y)

This was made using the TikZ package in LaTeX. I used the \usepackage{pgf,tikz} command at the beginning of my document.

The code to create the DAG above is:

\begin{tikzpicture}
% nodes %
\node[text centered] (z) {$Z$};
\node[right = 1.5 of z, text centered] (t) {$T$};
\node[right=1.5 of t, text centered] (y) {$Y$};
\node[draw, rectangle, dashed, above = 1 of t, text centered] (u) {$U$};

% edges %
\draw[->, line width= 1] (z) --  (t);
\draw [->, line width= 1] (t) -- (y);
\draw[->,red, line width= 1,dashed] (u) --node {X} (z);
\draw[->,line width= 1] (u) --(t);
\draw[->,line width= 1] (u) -- (y);
\draw[->, red, line width=1,dashed] (z) to  [out=270,in=270, looseness=0.5] node{X} (y);
\end{tikzpicture}

Note that I first create the nodes (corresponding to variables in the DAG), and then draw the directed edges between the nodes.

Another example of a DAG is a simple structural equation model where we want each edge to be marked with the parameter signifying the causal effect. For example:

In LaTeX:

\begin{tikzpicture}
% nodes %
\node[text centered] (t) {$T$};
\node[right = 1.5 of t, text centered] (m) {$M$};
\node[right=1.5 of m, text centered] (y) {$Y$};

% edges %
\draw[->, line width= 1] (t) -- node[above,font=\footnotesize]{$\beta$}  (m);
\draw [->, line width= 1] (m) -- node[above,font=\footnotesize]{$\gamma$}  (y);
\draw[->, line width=1] (t) to  [out=270,in=270, looseness=0.5] node[below,font=\footnotesize]{$\delta$} (y);
\end{tikzpicture}

Installing MinionPro font for LaTeX on Mac OS X

This tutorial shows how to install the MinionPro font for LaTeX. Following these instructions should insure that you can compile LaTeX documents with the \usepackage{MinionPro} command (instead of using XeTeX). Throughout this explanation, the TeX tree that I refer to is located at: /Library/TeX/Root/texmf/. Note that this is equivalent to /usr/local/texlive/2012/texmf/ for my 2012 TeX distribution.

In Terminal, I created a variable for the TeX tree directory:

texmf_folder=/Library/TeX/Root/texmf/

Part 1: Install MnSymbol

1) Download MnSymbol package, which provides mathematical symbol font for Adobe MinionPro, from CRAN in the form of a zip file. Unzip the file to form a temporary directory (I just created a mnsymbol directory in ~/Downloads temporarily).

2) Using Terminal:

cd ~/Downloads/mnsymbol/tex
latex MnSymbol.ins 

3) Move contents from MnSymbol directory to appropriate locations of TeX tree:

First create the new directories in TeX tree:

sudo mkdir -p $texmf_folder/tex/latex/MnSymbol/
sudo mkdir -p $texmf_folder/fonts/source/public/MnSymbol/
sudo mkdir -p $texmf_folder/doc/latex/MnSymbol

Move MnSymbol.sty to /usr/local/texlive/2012/texmf/tex/latex/MnSymbol.sty:

sudo cp MnSymbol.sty $texmf_folder/tex/latex/MnSymbol/MnSymbol.sty 

Move all contents of directory source to /texmf/fonts/source/public/MnSymbol/:

cd ..
sudo cp source/* $texmf_folder/fonts/source/public/MnSymbol/

Move documentation:

sudo cp MnSymbol.pdf README $texmf_folder/doc/latex/MnSymbol/

4) To install the PostScript fonts into TeX tree:

sudo mkdir -p $texmf_folder/fonts/map/dvips/MnSymbol
sudo mkdir -p $texmf_folder/fonts/enc/dvips/MnSymbol
sudo mkdir -p $texmf_folder/fonts/type1/public/MnSymbol
sudo mkdir -p $texmf_folder/fonts/tfm/public/MnSymbol

sudo cp enc/MnSymbol.map $texmf_folder/fonts/map/dvips/MnSymbol/
sudo cp enc/*.enc $texmf_folder/fonts/enc/dvips/MnSymbol/
sudo cp pfb/*.pfb $texmf_folder/fonts/type1/public/MnSymbol/
sudo cp tfm/* $texmf_folder/fonts/tfm/public/MnSymbol/

5) Regenerate TeX tree file database:

sudo mktexlsr
sudo updmap-sys --enable MixedMap MnSymbol.map

The following file should now compile: mnsymbol-test.tex



Part 2: Install MinionPro

1) Locate MinionPro OpenType font files. On Mac OS X, fonts are generally located under /Library/Fonts/. However, on my computer the Adobe fonts are under /Applications/Adobe Reader.app/Contents/Resources/Resource/Font/ (alternatively sometimes /Library/Application Support/Adobe/Fonts).

Note that before proceeding, double-check that you have a working installation of lcdf-typetools, needed to convert the OpenType fonts. On my system, LCDF Typetools were already installed (can check in Terminal if otfinfo --help command works).

Figure out version of fonts using following command in Terminal:

otfinfo -v MinionPro-Regular.otf

Output for my fonts:

Version 2.015;PS 002.000;Core 1.0.38;makeotf.lib1.7.9032

2) Go to CTAN directory for MinionPro.

• Download scripts.zip. This will contains convert.sh, a Unix script. Unzip as a temporary directory wherever you want (I placed in ~/Downloads).
• Download the appropriate encoding file, corresponding to the version of the MinionPro font you are using. My MinionPro font is of version 2.000, so I downloaded enc-v2.000.zip. I left the zipfile in ~/Downloads.
• Download metrics-base.zip (contains metrics for Regular, It, Bold, and BoldIt fonts) and, optionally, metrics-full.zip (contains additional metrics for Medium, Medium Italic, Semibold, and SemiboldItalic fonts). I left the zipfiles in ~/Downloads.

3) We need to convert the OpenType font files (.otf) to PostScript files (.pfb). In order to do this, copy the MinionPro OpenType files (MinionPro-Regular.otf, MinionPro-Bold.otf, MinionPro-It.otf, and MinionPro-BoldIt.otf) from pre-identified directory to ~Downloads/scripts/otf. 

Then in Terminal: 

cd ~/Downloads/scripts
./convert.sh

4) Copy PostScript fonts to TeX tree:

sudo mkdir -p $texmf_folder/fonts/type1/adobe/MinionPro/
sudo cp pfb/*.pfb $texmf_folder/fonts/type1/adobe/MinionPro/

5) Unzip enc-2.000.zip, metrics-base.zip, and metrics-full.zip files into the TeX directory:

cd $texmf_folder
sudo unzip ~/Downloads/enc-2.000.zip
sudo unzip ~/Downloads/metrics-base.zip
sudo unzip ~/Downloads/metrics-full.zip

6) Regenerate TeX tree file database:

sudo mktexlsr
sudo updmap-sys --enable MixedMap MinionPro.map

The following file should now compile: minionpro-test.tex

I would like to thank the following tutorials for help in figuring this out:

http://carlo-hamalainen.net/blog/2007/12/11/installing-minion-pro-fonts/

http://jklukas.blogspot.com/2010/02/installing-minionpro-tex-package.html