3.6 Cross References

3.6.1 Using bookdown

You can number and refer to an equation by adding \begin{equation} along with a label, provided with (\#eq:label).

  • The position of the label matters.

    • For single-lined equations: First write your equation, then append your label (\#eq:label). Otherwise, your equation won’t be rendered.
    • For multi-lined equations: append (\#eq:label) after \end{split}, \end{aligned} …

  • Note that \begin{equation} must NOT be quoted in $$...$$ for the equation to be rendered.

    Otherwise, will cause “Bad math delimiter” error at the time of tex compilation for pdf output. Might be alright for html output though.

    Unexpected consequence: Without the $$...$$, RStudio won’t provide previews for equations.

    • For temporary preview in RStudio at the composing stage, you can enclose the whole math environment in $$...$$. But remember to delete them when you are done editing the equation.
    • See this post by Kenji Sato for a more efficient workaround.

  • You can then refer to the equation in text using \@ref(eq:CJ). Remember to put the label in parentheses ().

    General syntax for other environments: \@ref(type:label) where type is the environment being referenced, and label is the chunk label.

This is an equation redered using bookdown

\begin{equation} (\#eq:CJ)
y=\beta_0 + \beta_1x + e_t
\end{equation}

will render as

\[\begin{equation} y=\beta_0 + \beta_1x + e_t \tag{3.1} \end{equation}\]

You may refer to it using eqn \@ref(eq:CJ), e.g., see eqn (3.1).

Multilined equations.
  
\begin{equation} 
\begin{aligned}
y_i &= f(x_{1i}, x_{2i}, \ldots, x_{Ki}) + \varepsilon_i \\
&= x_{1i} \beta_1 + x_{2i} \beta_2 + \cdots + x_{Ki} \beta_K + \varepsilon_i
\end{aligned}(\#eq:scalar-form)
\end{equation}

will render as

\[\begin{equation} \begin{aligned} y_i &= f(x_{1i}, x_{2i}, \ldots, x_{Ki}) + \varepsilon_i \\ &= x_{1i} \beta_1 + x_{2i} \beta_2 + \cdots + x_{Ki} \beta_K + \varepsilon_i \end{aligned}\tag{3.2} \end{equation}\]

You may refer to it using eqn \@ref(eq:scalar-form), e.g., see eqn (3.2) .

Note that

  • For HTML output, bookdown can only number the equations with labels.

    Please make sure equations without labels are not numbered by either using the equation* environment or adding \nonumber or \notag to your equations.

Troubleshooting

Issue: Bad math environment delimiter on conversion to pdf when using equation or align.

Cause: The error happens because I enclosed \begin{equation} environment in $$. I did this as the dollar sings enable equation rendering and preview in file.

Fix: remove the double signs.

The following equation causes error. Need to remove the dollar signs.
$$
\begin{equation}
y=x+2
\end{equation}
$$

More examples:

  • Headers

    # Introduction {#intro}

This is Chapter \@ref(intro)

    Refer to Markdown: cross references for more examples.

  • Figures

    See Figure \@ref(fig:cars-plot)

```{r cars-plot, fig.cap="A plot caption"}
plot(cars)  # a scatterplot
```

  • Tables

    See Table \@ref(tab:mtcars)

```{r mtcars}
knitr::kable(mtcars[1:5, 1:5], caption = "A caption")
```

  • Theorems

    See Theorem \@ref(thm:boring)

```{theorem, boring}
Here is my theorem.
```

  • Equations

    See equation \@ref(eq:linear)

\begin{equation}
a + bx = c  (\#eq:linear)
\end{equation}

3.6.2 Using the LaTeX Way

The LaTeX way allows you to assign your own labels by \tag. One drawback is that this does not allow preview of equations.

  1. Add the following script at the beginning of your document body:

    <script type="text/x-mathjax-config">
MathJax.Hub.Config({
  TeX: { equationNumbers: { autoNumber: "AMS" } }
});
</script>

    It configures MathJax to automatically number equations. Source.

  2. In the text, use label{eq:label}. If you want to provide a specific number to the equation, you can use \tag{XX.XX}.

    • Note that \begin{equation} is NOT inside $$ ...$$!

  3. Cite using $\ref{eq:label}$ (no parenthesis) or $\eqref{eq:label}$ (with parenthesis). The dollar sign $ here around \ref and \eqref is not essential. Commands work with or without $.

    Without using the bookdown package.

\begin{equation} \label{eq:test} \tag{my custom label}
  Y_i = \beta_0 + \beta_1 x_i + \epsilon_i
\end{equation}

Cite Equation $\eqref{eq:test}$ like this.

    \[\begin{equation} \label{eq:test} \tag{my label} Y_i = \beta_0 + \beta_1 x_i + \epsilon_i \end{equation}\]

    Refer to the eq \(\eqref{eq:test}\)

Reference:

https://bookdown.org/yihui/bookdown/markdown-extensions-by-bookdown.html#equations