Regression equation font face for long variable names

Question

I'm writing a paper for a journal that contains several regression equations (a first for me). Some of the models have long variables names (between 2-7 characters in length). I'm wondering what the best practice is for formatting such text, both inline and in display mode?

Variables are usually in italic face, but for long names this looks odd. Using \mathrm{} looks good within display equations, but for inline equations and descriptions of variables embedded in text it blurs the line between the two so much that it often isn't immediately clear which are variables. I've also tried using \textsubscript{} for inline variables, but this seems the same as \mathrm{}. Any suggestions are most welcome. I've provided a self-contained example of some of the above:

\documentclass[twocolumn]{article}

\usepackage{amsthm,amsmath,amssymb}
\usepackage{lipsum}
\usepackage[utf8]{inputenc} %unicode support
\usepackage{fixltx2e}

\DeclareMathOperator{\E}{\mathbb{E}}%


\begin{document}

\lipsum[2]
%
\begin{equation}
    \E \biggl[ \frac{M_5KV}{M_2KV} \biggm\vert \mathbf{X} \biggr] = \beta_0 + \beta_1 \biggl[ \frac{M_6}{M_2} \biggr] + \mathbf{Z_1u_1} + \mathbf{Z_2u_2}, 
\end{equation}
%
where $M_5KV / M_2KV$ is the ratio of blah blah and $ \mathbf{Z_iu_i}$ are matrices of random effects. 
%
\begin{equation}
    \E \biggl[ \mathrm{\frac{M_5KV}{M_2KV}} \biggm\vert \mathbf{X} \biggr] = \beta_0 + \beta_1 \biggl[ \mathrm{\frac{M_6}{M_2}} \biggr] + \mathbf{Z_1u_1} + \mathbf{Z_2u_2}, 
\end{equation}
%
where $\mathrm{M_5KV / M_2KV}$ is the ratio of blah blah and $ \mathbf{Z_iu_i}$ are matrices of random effects. Where M\textsubscript{5}KV/M\textsubscript{2}KV is the ratio of blah blah and $ \mathbf{Z_iu_i}$ are matrices of random effects. 

\lipsum[2]
%
\begin{subequations}
\begin{align} 
    \begin{split}
    \E \bigl[ M_5Area \mid \mathbf{X} \bigr] &= \beta_0 + \beta_1 M_2Area + \beta_2 M_6Area \\
        &\quad + \mathbf{Z_1u_1} + \mathbf{Z_2u_2}, \label{eqn:YXM}
     \end{split}  \\
     \begin{split}
    \E \bigl[ M_6Area \mid \mathbf{X} \bigr] &= \beta_0' + \beta_1' M_2Area \\
        &\quad + \mathbf{Z_1u_1} + \mathbf{Z_2u_2}, \label{eqn:MX}
     \end{split}  \\
    \E \bigl[ ab \bigr] &= \frac{1}{n} \sum_{n=1}^{n} \beta_2 \, \beta_1'. 
\end{align}
\end{subequations}
%
where $M_5Area$ is blah blah $M_2Area$ is blah blah blah and $ \mathbf{Z_iu_i}$ are matrices of random effects.
%
\begin{subequations}
\begin{align} 
    \begin{split}
    \E \bigl[ \mathrm{M_5Area} \mid \mathbf{X} \bigr] &= \beta_0 + \beta_1 \mathrm{M_2Area} + \beta_2 \mathrm{M_6Area} \\
        &\quad + \mathbf{Z_1u_1} + \mathbf{Z_2u_2}, \label{eqn:YXM}
     \end{split}  \\
     \begin{split}
    \E \bigl[ \mathrm{M_6Area} \mid \mathbf{X} \bigr] &= \beta_0' + \beta_1' \mathrm{M_2Area} \\
        &\quad + \mathbf{Z_1u_1} + \mathbf{Z_2u_2}, \label{eqn:MX}
     \end{split}  \\
    \E \bigl[ ab \bigr] &= \frac{1}{n} \sum_{n=1}^{n} \beta_2 \, \beta_1'. 
\end{align}
\end{subequations}
%
where $\mathrm{M_5Area}$ is blah blah $\mathrm{M_2Area}$ is blah blah blah blah and $ \mathbf{Z_iu_i}$ are matrices of random effects. Where M\textsubscript{5}Area is blah blah blah M\textsubscript{2}Area is blah blah blah. Solving for area:  $CA = RA(x) + EA(1-x)$. Solving for area:  $\mathrm{CA = RA(x) + EA(1-x)}$.

\lipsum[1-2]


\end{document}

Answer 1

multi-letter identifiers should never be set in math italic which is specifically designed with wide sidebearings to separate the letters to not look like a word but a product of variables.

You can use \mathrm or \mathbf or \mathit` according to taste but I'd typically use it around each identifier not the whole expression.

So

\mathbf{Z}_2\mathbf{u}_2}

or

\mathbf{Z}_{\mathbf{2}}\mathbf{u}_{\mathbf{2}}

not

\mathbf{Z_2u_2}

Certainly never

 M_6Area

but

M_{6}\mathit{Area}

Rather than use \mathxxx commands directly of course you can use

\vbl{Area}

and then choose the font as a global setting

\newcommand\vbl{\mathit}

which makes it easy to change to different fonts if you change your mind which is best.

Answer 2

Whatever you eventually decide, be careful to define macros for the constructs you use frequently.

For instance, a global macro for expectation is certainly needed, with the ability to specify a size for the brackets. Also a macro for the multiletter variables and one for denoting matrices.

The code \mathbf{Z_1u_1} is wrong in several ways. First, it emboldens also the subscripts, which is probably not wanted as they are numeric indices; second, it hides the fact you have two matrices; third, it violates the recommendation I made at the start.

For the multiletter variables you can choose between upright or italic shape at the very last moment if you do

\newcommand{\vr}[1]{\mathit{#1}} % or \mathrm
\newcommand{\KV}{\vr{KV}}
\newcommand{\Area}{\vr{Area}}

and use \KV and \Area throughout. I similarly defined a macro \mb for matrices and an extended \E command: it doesn't just print the blackboard bold ‘E’, but takes as optional argument a size (\bigg, for instance) and as mandatory argument the material to be in brackets; the conditional is simply denoted by | (if missing there's no problem).

Finally, note the trick in the split environments for better aligning the +.

\documentclass[twocolumn]{article}

\usepackage[utf8]{inputenc} %unicode support
\usepackage{fixltx2e}
\usepackage{amsthm,amsmath,amssymb,mathtools}

\usepackage{lipsum}

\newcommand{\vr}[1]{\mathit{#1}}
\newcommand{\KV}{\vr{KV}}
\newcommand{\Area}{\vr{Area}}

\newcommand{\mb}[1]{\mathbf{#1}}
\DeclarePairedDelimiter{\br}{[}{]}

% see http://tex.stackexchange.com/a/187363/4427
\newcommand{\E}{\operatorname{\mathbb{E}}\expectarg}
\DeclarePairedDelimiterX{\expectarg}[1]{[}{]}{%
  \ifnum\currentgrouptype=16 \else\begingroup\fi
  \activatebar#1
  \ifnum\currentgrouptype=16 \else\endgroup\fi
}
\newcommand{\innermid}{\nonscript\;\delimsize\vert\nonscript\;}
\newcommand{\activatebar}{%
  \begingroup\lccode`\~=`\|
  \lowercase{\endgroup\let~}\innermid 
  \mathcode`|=\string"8000
}

\begin{document}

\lipsum*[2]
\begin{equation}
\E[\bigg]{\frac{M_5KV}{M_2KV} | \mb{X}} = 
  \beta_0 + \beta_1 \br*{\frac{M_6}{M_2}} + \mb{Z}_1\mb{u}_1 + \mb{Z}_2\mb{u}_2, 
\end{equation}
where $M_5\KV / M_2\KV$ is the ratio of blah blah and $\mb{Z}_i\mb{u}_i$ 
are matrices of random effects.
\begin{equation}
\E[\bigg]{\frac{M_5\KV}{M_2\KV} | \mathbf{X}} =
  \beta_0 + \beta_1 \br*{\frac{M_6}{M_2}} + \mb{Z}_1\mb{u}_1 + \mb{Z}_2\mb{u}_2,
\end{equation}
where $M_5\KV / M_2\KV$ is the ratio of blah blah and $\mb{Z}_i\mb{u}_i$ are matrices 
of random effects.

\lipsum*[2]
\begin{subequations}
\begin{align} 
  \begin{split}
  \E{M_5\Area | \mathbf{X}}
     &= \beta_0 + \beta_1 M_2Area \\
     &\hphantom{{}=\beta_0} + \beta_2 M_6Area \\
     &\hphantom{{}=\beta_0} + \mb{Z}_1\mb{u}_1 + \mb{Z}_2\mb{u}_2,
  \end{split}\label{eqn:YXM}
\\
  \begin{split}
  \E{M_6Area | \mathbf{X}}
    &= \beta_0' + \beta_1' M_2Area \\
    &\hphantom{{}=\beta_0'} + \mb{Z}_1\mb{u}_1 + \mb{Z}_2\mb{u}_2,
  \end{split} \label{eqn:MX}
\\
  \E{ab} &= \frac{1}{n} \sum_{n=1}^{n} \beta_2\beta_1'. 
\end{align}
\end{subequations}

\end{document}

If M₂Area is a single object, you can define

\newcommand{\M}[2]{M_{#1}\mathit{#2}}

and use \M{2}{Area}. Or decide for a handier syntax.