R Markdown
Devin Judge-Lord
02 February, 2019
*This is why don’t copy and paste numbers, table, or figures into a paper.
R Markdown
Markdown is just plain text that can be rendered as HTML, PDF, or even Microsoft Word. Rstudio’s “Knit” button will make the selected document.
We can use various syntaxes, like \(\LaTeX\) and R as needed inline with the rest of our text, which we write in markdown syntax. For example, typing “$y = \alpha + X\beta$” gives us “\(y = \alpha + X\beta\)” and typing “{r nchar("hello world")}” gives us “11”—pretty cool. For more, see http://rmarkdown.rstudio.com, especially this cheatsheet.
We can embed a chunk of R code like this:
# a dataset built into R
head(pressure)## temperature pressure
## 1 0 0.0002
## 2 20 0.0012
## 3 40 0.0060
## 4 60 0.0300
## 5 80 0.0900
## 6 100 0.2700In the .Rmd file, you’ll see that the above chunk of R code begins with “```{r pressure}”, which tells the computer that this chunk is r code and names this chunk “pressure.”
Give code chunks informative names! If your chunk produces figures, they will be saved with this name.
If we don’t want our code chunk in the output, only the results, we add echo = FALSE to the header:
## temperature pressure
## 1 0 0.0002
## 2 20 0.0012
## 3 40 0.0060
## 4 60 0.0300
## 5 80 0.0900
## 6 100 0.2700We can set defaults for the whole document (e.g. knitr::opts_chunk$set(echo = TRUE)). See the above “setup” chunk in this .Rmd file.
Problem sets and papers will use echo = FALSE to display just the output. For notes, we may want to see our code echo = TRUE. Or, if our output is HTML, hide our code; try knitting to HTML after adding code_folding: hide to the YAML header in this .Rmd file like this:
html_document:
latex_engine: pdflatex
code_folding: hideTo display code we don’t want to run, we add eval = FALSE.
This code will not run. For example, if you want to share code that does not work on your 811 page, use eval = FALSE.
It is safer to use cache = FALSE, which re-computes all results each time and will thus update if your data have changed. If computing is taking a long time, you can use cache = TRUE to knit faster, but this will only run chunks where the code has changed.
Including Plots
We can also embed plots. For example:
library(ggplot2);
ggplot(data = pressure, aes(x = temperature, y = pressure)) +
geom_point() +
geom_line()
Note that we needed to load the library ggplot2 because knitting uses a new R session. Your .Rmd file must load any required libraries, functions, and data. The upshot of this is that knitting is self-contained. It starts fresh; not depending on whatever you may have done in R previously.
We can adjust the size by adding fig.width = 3, fig.height= 2 to get a \(4\times3\) inch figure.
Let us also center fig.align='center and add a caption, fig.cap = "Plotting Temperature vs. Pressure":
Plotting Temperature vs. Pressure
Two ways to code
1. Get code working in a .R file (e.g. in your /scratchpad subfolder), then copy the final code into .Rmd file chunks.
2. Workshop code in .Rmd file chunks.
Writing Math
We can use MathJax and/or \(\LaTeX\) to write nice-looking math. For example, we can write out a regression equation as \(y = \alpha + X\beta + \varepsilon\), without having to copy, paste, or insert special symbols. To write out anything math related, we enclose it in dollar signs \(\$\)math\(\$\). The regression equasion above, for example, is \(\$\) y = \alpha + X\beta + \varepsilon \(\$\). If we want to index something by adding subscripts \(x_{1}, x_{2}\) etc, the code is \(\$\)x_{1}, x_{2}\(\$\). Fractions are written such that \(\$\)\frac{1}{2}\(\$\) is \(\frac{1}{2}\), and exponents (\(2^{2}\)) are written \(\$\)2^{2}\(\$\).
The Greek letters have a slash before them which tells \(\LaTeX\) or MathJax to print that as a Greek letter. Similarly \(2 \times 2\) is written \(\$\) 2 \times 2 \(\$\). See guides to special characters and formatting in \(\LaTeX\) here and MathJax here. I regularly google symbols.
Matrices
To write a matrix: \[ \left[ \begin{array}{ccc} 1 & 2 & 3 \\ 4 & 5 & 6\\ 7 & 8 & 0 \end{array} \right] \] we write:
$$
\left[
\begin{array}{ccc}
1 & 2 & 3 \\
4 & 5 & 6\\
7 & 8 & 0
\end{array}
\right]
$$where:
$$ % start Latex mode
\left[ %creates the left bracket, the "\left" command scales the bracket "["
\begin{array}{ccc} % Creates the "array" (matrix), {ccc} defines the number of columns
1 & 2 & 3 \\ % "&" divides the columns, "\\" creates a new line
4 & 5 & 6\\
7 & 8 & 0
\end{array} % ends the matrix
\right] %creates the left bracket, the "\right" command scales the bracket "]"
$$ % ends LaTeX modeMatrix multiplication
\[ \left[ \begin{array}{ccc} 1 & 2 & 3 \\ 4 & 5 & 6\\ 7 & 8 & 0 \end{array} \right] \times \left[ \begin{array}{ccc} 1 \\ 1 \\ 1 \end{array} \right] = \left[ \begin{array}{ccc} 1 + 2 + 3 \\ 4 + 5 + 6\\ 7 + 8 + 0 \end{array} \right] = \left[ \begin{array}{ccc} 5 \\ 15\\ 15 \end{array} \right] \]
\[ \left[ \begin{array}{ccc} 1 & 1 & 1 \end{array} \right] \times \left[ \begin{array}{ccc} 1 & 2 & 3 \\ 4 & 5 & 6\\ 7 & 8 & 0 \end{array} \right] = \left[ \begin{array}{ccc} 1 + 4 + 7 & 2 + 5 + 8 & 3 + 6 + 0 \end{array} \right] = \left[ \begin{array}{ccc} 12 & 15 & 9 \end{array} \right] \]
Example Notes
Linear regression with fixed effects:
\[ y_{i} = \alpha_{0} + \alpha_{j} + x_{i} \beta + \varepsilon \] Where \(\alpha_{0}\) is the intercept,
\(\alpha_{j}\) are fixed effects (effects that do not vary by \(x\), i.e. intercept shifts) for each group \(j\),
\(x\) and \(y\) are vectors of observations, and
\(\varepsilon\) is the error.
OLS estimation
Data: \[ X = \left[ \begin{array}{cc} x_{1, 1} & x_{1, 2} \\ x_{2, 1} & x_{2, 2} \\ \end{array} \right], \\ y = \left[ \begin{array}{cc} y_{1}\\ y_{2}\\ \end{array} \right] \]
OLS equation \[ \hat{\beta} = (X'X)^{-1}(X'y) \]
Logistic link function:
\[ Pr(y_{i} = 1) = \frac{1}{1 + e^{-x_{i} \beta}} \]
Poisson PMF:
\[ \frac{\lambda^k}{k!} e^{-\lambda} \]
Gaussian (normal) PDF:
\[ \frac{1}{\sigma\sqrt{2\pi}}\, e^{-\frac{(x - \mu)^2}{2 \sigma^2}} \]