21.3: R Functions
- Page ID
- 57819
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\(\newcommand{\avec}{\mathbf a}\) \(\newcommand{\bvec}{\mathbf b}\) \(\newcommand{\cvec}{\mathbf c}\) \(\newcommand{\dvec}{\mathbf d}\) \(\newcommand{\dtil}{\widetilde{\mathbf d}}\) \(\newcommand{\evec}{\mathbf e}\) \(\newcommand{\fvec}{\mathbf f}\) \(\newcommand{\nvec}{\mathbf n}\) \(\newcommand{\pvec}{\mathbf p}\) \(\newcommand{\qvec}{\mathbf q}\) \(\newcommand{\svec}{\mathbf s}\) \(\newcommand{\tvec}{\mathbf t}\) \(\newcommand{\uvec}{\mathbf u}\) \(\newcommand{\vvec}{\mathbf v}\) \(\newcommand{\wvec}{\mathbf w}\) \(\newcommand{\xvec}{\mathbf x}\) \(\newcommand{\yvec}{\mathbf y}\) \(\newcommand{\zvec}{\mathbf z}\) \(\newcommand{\rvec}{\mathbf r}\) \(\newcommand{\mvec}{\mathbf m}\) \(\newcommand{\zerovec}{\mathbf 0}\) \(\newcommand{\onevec}{\mathbf 1}\) \(\newcommand{\real}{\mathbb R}\) \(\newcommand{\twovec}[2]{\left[\begin{array}{r}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\ctwovec}[2]{\left[\begin{array}{c}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\threevec}[3]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\cthreevec}[3]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\fourvec}[4]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\cfourvec}[4]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\fivevec}[5]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\cfivevec}[5]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\mattwo}[4]{\left[\begin{array}{rr}#1 \amp #2 \\ #3 \amp #4 \\ \end{array}\right]}\) \(\newcommand{\laspan}[1]{\text{Span}\{#1\}}\) \(\newcommand{\bcal}{\cal B}\) \(\newcommand{\ccal}{\cal C}\) \(\newcommand{\scal}{\cal S}\) \(\newcommand{\wcal}{\cal W}\) \(\newcommand{\ecal}{\cal E}\) \(\newcommand{\coords}[2]{\left\{#1\right\}_{#2}}\) \(\newcommand{\gray}[1]{\color{gray}{#1}}\) \(\newcommand{\lgray}[1]{\color{lightgray}{#1}}\) \(\newcommand{\rank}{\operatorname{rank}}\) \(\newcommand{\row}{\text{Row}}\) \(\newcommand{\col}{\text{Col}}\) \(\renewcommand{\row}{\text{Row}}\) \(\newcommand{\nul}{\text{Nul}}\) \(\newcommand{\var}{\text{Var}}\) \(\newcommand{\corr}{\text{corr}}\) \(\newcommand{\len}[1]{\left|#1\right|}\) \(\newcommand{\bbar}{\overline{\bvec}}\) \(\newcommand{\bhat}{\widehat{\bvec}}\) \(\newcommand{\bperp}{\bvec^\perp}\) \(\newcommand{\xhat}{\widehat{\xvec}}\) \(\newcommand{\vhat}{\widehat{\vvec}}\) \(\newcommand{\uhat}{\widehat{\uvec}}\) \(\newcommand{\what}{\widehat{\wvec}}\) \(\newcommand{\Sighat}{\widehat{\Sigma}}\) \(\newcommand{\lt}{<}\) \(\newcommand{\gt}{>}\) \(\newcommand{\amp}{&}\) \(\definecolor{fillinmathshade}{gray}{0.9}\)There are a plethora of functions available in R. The key is to use functions to become familiar with them. Also, because you will always need to use new functions, it is very important to be familiar with the R help files for the functions.
Basic Functions
The following are basic functions in R. You will use these frequently.
| Function | Description |
|---|---|
| source() | Run an external R script |
| head() | Show the first six elements in the vector |
| tail() | Show the last six elements in the vector |
| length() | Calculate the length of the vector |
| seq() | Create a sequence of values |
| summary() | Print the six-number summary |
| mean() | Calculate the arithmetic mean |
| median() | Calculate the median |
| sum() | Calculate the sum of the elements in the vector |
| sd() | Calculate the standard deviation |
| var() | Calculate the variance |
Please know what each does. If necessary, use the help file for the given function. The more you familiarize yourself with the help files, the more they will tell you.
Matrix Functions
R can also do arithmetic on matrices. Since the internal computer calculations are all based on matrices, it is important to be familiar with matrix operations to make sure you know what \R\ is doing (can check the output).
Element-wise Functions
| + | usual matrix addition |
| * | Hadamard product |
| ^ | exponentiation |
Additional Matrix Functions
| %*% | usual matrix product |
| t() | transpose |
| solve() | matrix inverse |
Probability Functions
At the core of statistics is probability and probability distributions. These will be important in helping you better understand the effects of randomness on the estimates... and the effects of violating procedure requirements on those estimates.
Generic Functions
| set.seed() | set the specified random number seed |
| sample() | randomly sample from a vector. This can also be used to sample from a discrete Uniform distribution |
Probability Function Naming Logic
Each named probability function in R can be parsed into two parts, the stem and the prefix. The stem specifies the probability distribution, whereas the prefix specifies what aspect of the distribution you wish to access.
This is an exhaustive list of the standard prefixes:
| d | specifies the likelihood value. If the distribution is discrete, then this will also be the probability, otherwise it is the density. |
| p | specifies the cumulative probability, P[X ≤ x]. This prefix will rarely be available for multivariate functions. |
| q | specifies the quantile, the value of x that produces the probability. This prefix will rarely be available for multivariate functions. |
| r | specifies a random value. In simulation, this is the most important prefix, as it produces a random sample of a given size from the specified distribution. |
The second part is the stem. This specifies the distribution involved. Here is a list of some of the more interesting stems available:
| binom | Binomial distribution. One needs to specify the number of trials, size, and the success probability, prob. |
| cauchy | Cauchy distribution. Optionally, one can specify the location and the spread. The default is the standard Cauchy with location of 0 and scale of 1. |
| chisq | Chi-squared distribution. One needs to specify the number of degrees of freedom, df. |
| exp | Exponential distribution. One needs to specify the rate, λ. |
| f | Snedecor's F distribution. One needs to specify both degrees of freedom, with the numerator preceding the denominator degrees of freedom, df1 and df2. |
| gamma | Gamma distribution. One must specify the shape parameter, α, since there is no default. The rate parameter has a default value of β = 1. |
| norm | Normal (Gaussian) distribution. Optionally, one can specify the mean m and standard deviation s of the Normal. This defaults to a standard Normal distribution. |
| pois | Poisson distribution. One needs to specify the expected value, lambda, λ. |
| t | Student's t distribution. One needs to also specify the number of degrees of freedom, df. |
| unif | Continuous Uniform distribution. Optionally, one can specify the minimum and maximum value. The default is the standard Uniform with min of 0 and max of 1. |
Testing Functions
Because R is a statistical program, it is able to perform all of the basic statistical tests and procedures. These are the related functions.
| aov | Analysis of Variance procedure |
| lm | OLS regression |
| summary.aov | ANOVA table of a linear model |
| summary.lm | Regression table of a linear model |
| residuals | calculated residuals from a model |
| confint | confidence interval for estimated parameters |
| predict | estimation and prediction of a value |
Non-Base Testing Functions
| runs.test | KnoxStats | the runs test |
| hetero.test | KnoxStats | univariate test of heteroskedasticity |
| fligner.test | stats | test of heteroskedasticity across groups |
| bptest | lmtest | Breusch-Pagan test of heteroskedasticity |
Control Functions
| for | for-loops |
| if | if-then statements |
| ifelse | triary operator |
| numeric | creates a vector in memory |
Graphical Functions
R is a full-fledged graphical system. In fact, this is what set R apart from its competitors (and still does!). Every pixel of a graphic can be modified in R. This book relies on the basic R graphic engine. There are two other graphical engines (metaphors): grid and ggplot2. Base-R graphics will always serve you. With that being said, ggplot2 is the modern graphics engine for R. It serves as a wrapper for the basic graphics, making some graphics much easier to create.
| qqnorm | Q-Q plot for a Normal target |
| qqline | plots the diagonal line in a normal Q-Q plot |
| barplot | bar chart |
| boxplot | box-and-whiskers plot |
| hist | histogram |
| histogram | histogram* |
| overlay | histogram with a distribution overlaying it* |
| plot | plots a basic graphic |
| par | sets the parameters for the future graphic |
| plot.new | starts a new graphic |
| plot.window | sets the size of a new window |
| axis | creates axes |
| title | plots a title on the specified axis |
| points | plots points on the graphic |
| lines | plots lines on the graphic |
* Those graphical functions marked with an asterisk are found in the KnoxStats package.