An Introductory Guide to R

Transcription

1 An Introductory Guide to R By Claudia Mahler

2 1 Contents Installing and Operating R 2 Basics 4 Importing Data 5 Types of Data 6 Basic Operations 8 Selecting and Specifying Data 9 Matrices 11 Simple Statistics 12 Correlation 14 Regression 15 T-tests 18 Basic Graphics 19 Please note: Everything in this guide is presented as I learned it or figured it out on my own. For many operations listed, there may be other techniques that might be easier or more intuitive to use. Please note that I am writing this as someone who had previously used SAS and has used R for a little over two years now. As titled, this is a very introductory guide, and as such there are many things not covered. Other operations can easily be found in other guides, but I hope that what I provide here will be enough to get you started with R. Enjoy!

3 2 Installing and Operating R The main website for R is You can find links for download as well as links to manuals and other documentations. Once you ve installed it, operating R is simple. The window into which you will type commands, the R Console, is the only window open once you start up the program* (if you ve used SAS, you will notice the difference between the three windows used in that program and the one window used in this). The only other windows that appear are the graphics window when you create a plot and a help window when you look something up. *Note: you can also choose the built-in script editor (File New Script) into which you can type commands and send them to the workspace via Ctrl + R, but I find that once you get to a level where you re comfortable enough with R to start using this, an additional code editor works better and is easier to use. For more info, see the Optional R Editors section). Basic Operations R essentially runs what you type. What you type is displayed in red, and what is output by R is blue. I ll use these colors throughout the rest of the guide to help show you what s going on when I use R examples. The drop-down menus are mainly for locating help, finding additional libraries, and customizing the layout of the R window. In this respect, it s pretty different from SPSS. If you ever want to clear the window of all the commands typed so far, simply press Ctrl + L, or right click in the command space and select clear window. Though everything typed so far will be cleared from your screen, pressing the up and down arrows will allow you to scroll line by line through what has been previously typed in your R session. When you quit R, you will be asked whether or not you would like to save your workspace. I ve never found it especially helpful to do this; if I want to retrieve code, I either copy it into a Notepad file for later use or save it in an editor (to be discussed later). Saving a workspace allows you to re-access everything you had typed in that workspace. When you restore a workspace in later sessions, you should see previous workspace restored when you open R again. Downloading libraries Many useful statistical operations in R require the installation of additional libraries, or packages. For example, in order to perform more complex linear regression analyses, you will need to install the faraway library. To install specific libraries, open R, go to the Packages menu at the top of the screen, then click on Install Package(s). You will need to select a mirror off of which to download the package. After this, you will be directed to a list of all available packages. Since many of the names are not self-explanatory, it helps to know what specific library you need. Once you found the library you want, double click it and the download will automatically begin. It is important to remember that in order to utilize a downloaded library, you will have to load it in your R session. Suppose I had just downloaded the library sem (a library used for structural equation modeling), I would type library(sem) or

4 3 require(sem). This has to be done every time you start a new R session and want to use that library, but it only has to be done once per session. Built-In Datasets R has quite a few built-in datasets available. I often use them to test out new functions or to practice creating graphics. I will use several of the built-in datasets in this guide, mainly for the convenience as well as to allow anyone who wants to replicate results to have easy access to the data used. If you ever want to view a list and brief descriptions of these built-in datasets, type?datasets. This will bring up a new help window in which you can view the descriptions of these datasets. Optional R Editors If you choose to use R as your primary tool for analyses, it could be beneficial to download a supported code editor to make things easier for yourself. Code editors essentially function as a notepad in which you can enter and modify R code before actually running any analyses in the R workspace. Many editors color-code what you enter as well, so they can make it easy for you to better decipher and read your own code. My editor of choice is Tinn-R, which runs on Windows. It is free and is available at as well as many other places. Once it is installed and running, you can directly open the R workspace from the editor, and send code line-by-line from Tinn-R to the workspace. I highly recommend using an editor if you re going to be working with R frequently. Other editors for both Windows and Mac are available as well.

5 4 Basics Now we get into the basics of how to actually use R. Named storage, or assigning variable names to data, is the way R stores data and the results of calculations. For example: > x <- 36 > x [1] 36 Unless you reassign x to mean something else, every time you type x, it will represent 36. > x + 73 [1] 109 You can also assign variable names to characters (for example, if you want to create a vector of names). To do this, simply put the characters in quotes. > y <- "This is a character variable" > y [1] "This is a character variable" Named storage isn t necessary if you re doing simple and non-stored calculations (such as addition, subtraction, multiplication, etc.), but if you have variables or a matrix of variables, it is best to assign a variable name to it. While R supports both <- and = to assign variable names, it is recommended to use <- and reserve = for stating a relation, to eliminate confusion when code gets a little more complicated. This distinction will be more apparent later. Reminders: R is case sensitive. X and x are two different names. Variable names can contain periods and underscores, but cannot contain spaces. Anything to which do don t assign a variable name is non-retrievable in the workspace. In other words, if you wish to save a calculation and make it easily accessible later on during your work session, it s best to assign it a variable name. Sometimes you may be performing multiple operations in one line such that you might be using parentheses around certain components (example: 4 + 7*(3/.6)). If you return this equation and get a + at the start of the next line rather than an actual output, this means that you forgot to close a parentheses statement. Double check your statement to make sure you close all parenthetical components!

6 5 Importing Data Clipboard Importing data using the clipboard is an easy and fast way to get data into R, but is less optimal than importing using a data file if you plan on using your data set more than once. To import using the clipboard, simply highlight the whole of your data from wherever you re getting it (a page on the internet, an excel file, Notepad, etc.) and copy it to the clipboard. In R, type the following: > read.table('clipboard') [your data will appear after hitting ENTER ] If you wish you save your data, don t forget to assign it a name. > x <- read.table('clipboard') > x [your data will appear here] Suppose, in the file you re importing, that the columns of data are named. For example: Subject Height Weight If you try the above method, you ll get an error, since R will read the first line as data instead of as the names of the columns. To fix this, you have to specify that there is a header for your data. > x <- read.table('clipboard', header = TRUE) > x Subject Height Weight Data File Importing data from a data file ensures that, if you save your R code, you will easily be able to load the data file again, assuming you keep your data in the same place. Importing data this way is slightly different than the way you import from the clipboard. x <- read.table(file("c:\\....txt ) x [your data will appear here] The header command works with this type of data import as well. This is also the more preferred way of importing data over using the clipboard.

7 6 Types of Data Data Frame Data frames in R are the most convenient ways to store data, as they are compatible with most types of operations. R views data frame rows as cases and data frame columns as variables. Data frames are also able to include columns of different types, such as both numerical and character, and support column names (which can be included using the header command as above). > x <- read.table("clipboard", header = TRUE) > x Height Weight Gender Female Female Female Male Male Male This is a data frame. If a data set you import has both numerical and character columns, it is automatically imported as a data frame. Matrix Unlike a data frame, a matrix must consist of either all numerical or all character components. However, the matrix specification for a table of data is ideal if the data you re examining requires matrix operations to be performed. More will be said on this later. > as.matrix(x) Height Weight Gender [1,] "60" "104" "Female" [2,] "62" "113" "Female" [3,] "64" "130" "Female" [4,] "66" "150" "Male" [5,] "68" "155" "Male" [6,] "70" "167" "Male" As you can see, if we try to convert our x data into a matrix, all the data gets converted into character data, since there is a mixture of both character and numerical. However, if we import a set of data that is all numerical: > as.matrix(y) Height Weight [1,] [2,] [3,] [4,] [5,] [6,] All the data remain numerical. Viewing data Suppose you have a large dataset that you want to make sure has been imported correctly. Rather than having to view the entire dataset, you can either view the first

8 7 few observations of the set or the last few observations of the set. You can do this with head( ) or tail( ). For example, the built-in dataset beaver1 has 114 observations. What if I wanted to check if the column names were in the correct places? > x <- beaver1 > head(x) day time temp activ What if I wanted to make sure that there were 114 observations? > tail(x) day time temp activ You can also get a quick summary of a dataset using dim( ). > dim(x) [1] This tells you the number of rows and the number of columns in a dataset. These commands become even more useful as you start working with larger and larger datasets.

9 8 Basic Operations R can perform many basic operations, including addition, subtraction, multiplication, division, exponentiation, square root, and logarithms. > [1] 10 > 6-4 [1] 2 > 6 * 4 [1] 24 > 6 / 4 [1] 1.5 > 6^4 [1] 1296 > sqrt(6) [1] > log(10) [1] > 6*pi [1] Note that pi is a built-in number in R, so that you don t have to define it, but the name pi WILL become a different value if you assign it something other than

10 9 Selecting and Specifying Data Unfortunately, the selection of specific data out of data frames and matrices in R is not necessarily intuitive. For these examples, I ll be using the x data frame of height, weight, and gender that was used in the above section. > x Height Weight Gender Female Female Female Male Male Male Columns and rows can be selected using the standard formula dataframename[,column] or dataframename[row,]. Note the placement of the commas. For example: To select the first column of the x data set: > x[,1] [1] To select the first row of the x data set: > x[1,] Height Weight Gender Female If the data frame you re working with has column names, you can specify columns using them as well: > x$weight [1] To select a specific point in a data frame, specify the row and the column. > x[3,2] [1] 130 Don t forget that you can select a row or column and give them a separate name if you want to use that specific row or column multiple times and don t want to keep typing a long command. > y <- x[,1] > y [1] You can also select subsets of data if you want to break a large data frame into two or more parts. Suppose we wanted to select only the data from the females in the data frame above. To do so, we would use the command subset( ). > sub1 <- subset(x, Gender == "Female") > sub1 Height Weight Gender Female Female Female

11 10 What if you only wanted the height data for the females? > sub2 <- subset(x, Gender == "Female", select = Height) > sub2 Height This is another command you ll be using a lot once you start working with larger datasets in R. Reminders: It s dataframename[row,column]. Type the column names exactly as they appear in the data frame, otherwise you ll get an error (e.g., if I had typed x$weight instead of x$weight, R would have returned an error). When using the subset( ) command, be sure to type the column names and the categorical variables (if that s what you re using to create the subset) exactly as they appear in the data frame. Also, remember the double equals sign.

12 11 Matrices Matrix operations are performed quite easily in R. I will use the same matrix z for all operations. > z <- matrix(data = 1:9, nrow = 3, ncol = 3, byrow = FALSE) > z [,1] [,2] [,3] [1,] [2,] [3,] > t(z) [,1] [,2] [,3] [1,] [2,] [3,] This transposes a matrix. This can also be performed on vectors. > sum(diag(z)) [1] 15 This gives you the trace of a matrix. > det(z) [1] 0 This calculates the determinant of a matrix. Anyone who has had to do this by hand knows how convenient this command is! > q <- matrix(data = 10:18, nrow = 3, ncol = 3, byrow = FALSE) > q [,1] [,2] [,3] [1,] [2,] [3,] To multiply matrices, you have to remember that matrices must be of compatible dimensions to be multiplied (if they are not, R will give you an error message). > z%*%q [,1] [,2] [,3] [1,] [2,] [3,] > z%*%t(q) [,1] [,2] [,3] [1,] [2,] [3,] Reminders: When multiplying matrices, order matters!

13 12 Simple Statistics R can perform many simple statistics, including calculation of means, standard deviations, sums, and medians, with a single command. For this section, I will use the built-in dataset attitude, which includes the survey responses of 30 individuals who are clerical employees of a large financial organization. > x <- attitude I will select the column of ratings to use as an example. > w <- x$rating Commands for the mean, median, standard deviation, variance, sum, and range are as follows: > mean(w) [1] > median(w) [1] 65.5 > sd(w) [1] > var(w) [1] > sum(w) [1] 1939 > range(w) [1] These commands are most useful if you only need to find the mean of a set of data, or the sum of a set of data, etc. However, if you want a general statistical summary, you can do that as well and save yourself a few lines of commands. > summary(w) Min. 1st Qu. Median Mean 3rd Qu. Max You can also perform these commands on entire data frames of information. > mean(x) rating complaints privileges learning raises critical advance > sd(x) rating complaints privileges learning raises critical advance > summary(x) rating complaints privileges learning raises Min. :40.00 Min. :37.0 Min. :30.00 Min. :34.00 Min. : st Qu.: st Qu.:58.5 1st Qu.: st Qu.: st Qu.:58.25 Median :65.50 Median :65.0 Median :51.50 Median :56.50 Median :63.50 Mean :64.63 Mean :66.6 Mean :53.13 Mean :56.37 Mean : rd Qu.: rd Qu.:77.0 3rd Qu.: rd Qu.: rd Qu.:71.00

14 13 Max. :85.00 Max. :90.0 Max. :83.00 Max. :75.00 Max. :88.00 critical advance Min. :49.00 Min. : st Qu.: st Qu.:35.00 Median :77.50 Median :41.00 Mean :74.77 Mean : rd Qu.: rd Qu.:47.75 Max. :92.00 Max. :72.00 Obviously, many more statistical procedures can be performed with R, some of which will be discussed in the following pages. Also remember that many of these basic summary statistics can be better described and understood using graphics. Methods for creating basic graphics in R will be discussed at the end of this guide.

15 14 Correlation For this section, I will use the included faithful data. R can perform several different types of correlation. Pearson Product Moment Correlation r > cor(faithful) eruptions waiting eruptions waiting This creates a correlation matrix for the two vectors. This short command is especially useful if you want to create a correlation matrix for a longer list of variables. You can also specify different vectors if you want to compute a correlation between two vectors in any given data set. > cor(faithful$eruptions, faithful$waiting) [1] This will just give you the single correlation, not a correlation matrix. Polychoric Correlation Polychoric correlations are used to correlate two sets of forced polychotomous data. In order to perform this type of correlation in R, you first need to download the polycor library. > polychor(x, y) This will give you a polychoric correlation. Polyserial Correlation Polyserial correlations are used to correlate a polychotomous variable with a continuous variable. In R, this correlation requires the polycor library. > polyserial(x, y) This will give you a polyserial correlation.

16 15 Regression R can perform multiple forms of regression, including basic and multiple linear regressions, logistic regression, and Poisson regression. I will use the built-in dataset attitude again for the first two examples. Linear Regression Linear regression can be performed with the lm command. > q <- lm(x$rating ~ x$learning) Here, I m predicting the rating score based on the learning score. R reads regression input as lm(predictor variable ~ criterion variable(s)). > summary(q) Call: lm(formula = x$rating ~ x$learning) Residuals: Min 1Q Median 3Q Max Coefficients: Estimate Std. Error t value Pr(> t ) (Intercept) ** x$learning *** --- Signif. codes: 0 *** ** 0.01 * Residual standard error: on 28 degrees of freedom Multiple R-squared: 0.389, Adjusted R-squared: F-statistic: on 1 and 28 DF, p-value: Multiple Linear Regression Multiple linear regression follows from simple linear regression. > q <- lm(x$rating ~ x$learning + x$raises + x$critical) > summary(q) Call: lm(formula = x$rating ~ x$learning + x$raises + x$critical) Residuals: Min 1Q Median 3Q Max Coefficients: Estimate Std. Error t value Pr(> t ) (Intercept) x$learning * x$raises x$critical Signif. codes: 0 *** ** 0.01 * Residual standard error: on 26 degrees of freedom

17 16 Multiple R-squared: , Adjusted R-squared: F-statistic: on 3 and 26 DF, p-value: Logistic Regression Logistic regression is appropriate when the variable you re predicting is binary. To perform this type of regression in R, you will need to install and load the faraway library. q <- glm(y ~ x1 + x2 + x3, data = x, family = binomial) Note the differences between this and linear regression. You have to use the function glm as well as have to specify that you are drawing from the binomial family of distributions. summary(q) will display a similar result layout to that of linear regression. Diagnostic Plots Four essential diagnostic plots can be displayed by typing one command. > plot(q)

18 17 Reminders: For the diagnostic plots, plot the name of the regression analysis, not the dataset itself!

19 18 T-Tests Several types of t-tests can also be performed in R. I will be using the built-in dataset Puromycin for these examples. First, I split the data into treated and untreated so that I have two groups. x <- Puromycin sub1 <- subset(x, state == "treated", select = conc) sub2 <- subset(x, state == "untreated", select = conc) If you examine the dataset, you will see that I m just looking at the conc variable. Now I have two sets of data whose means on the conc variable can be compared. T-tests are performed with the t.test command, which can be modified to perform different types of t-tests based on your data. > t.test(sub1, sub2, alternative = "greater", mu = 0, paired = FALSE, var.equal = TRUE, conf.level = 0.95) Two Sample t-test data: sub1 and sub2 t = , df = 21, p-value = alternative hypothesis: true difference in means is greater than 0 95 percent confidence interval: Inf sample estimates: mean of x mean of y To better understand this command, it helps to look at the individual components. > t.test(sub1, sub2, alternative = "greater", mu = 0, paired = FALSE, var.equal = TRUE, conf.level = 0.95) These indicate the two samples being tested. If you re only testing one sample against a hypothesized mu, type y = NULL for the second value. > t.test(sub1, sub2, alternative = "greater", mu = 0, paired = FALSE, var.equal = TRUE, conf.level = 0.95) This indicates the alternative test you want: greater, less, or two.tailed. The last four commands are obvious. Mu is your mu value set it to zero when comparing two samples, or to whatever number you hypothesize when doing a onesample t-test. Specify if the values are paired or not, if there is equal variance or not, and specify a confidence interval.

20 19 Basic Graphics Most graphics included here require you to install the graphics library. Assuming you have installed it, to load this library simply type library(graphics) and press enter. Basic Plot For this plot, I will use the cars dataset, which lists a speed and a distance required to stop for 50 cars. Suppose you just want a quick and easy way to visualize your data. A quick way to do so is simply typing: > plot(cars) This will give you this: Notice that the axes labels are automatically set to the column names of the dataset. If you have no column names, the axes will simply be named V1 and V2. Prettying Up the Basic Plot Suppose, instead of creating a graphic that is used for quick visualization of your data, you wanted to create a graphic that looked nice enough to present to others? In base graphics, it s a little less than intuitive to customize your graphics, but what I will show you here can be easily applied to almost every single base graphic. I will give all my examples using a dot/line plot, but the code used is generalizable. I will also be using the built-in dataset Puromycin.

21 Here is the basic plot of conc versus rate (the state will be involved in plotting later). > x <- Puromycin > plot(x$conc, x$rate) 20

22 21 Axes Labels and Titles xlab = changes the x-axis label to whatever you put into the quotes. ylab = changes the y-axis label to whatever you put into the quotes. main = changes the title to whatever you put into the quotes. > plot(x$conc, x$rate, xlab='this is the x-axis', ylab = 'This is the y- axis', main = 'This is the title') Modification of Points col = changes the color of the plotting symbol. A list of acceptable colors that can be put into this specification can be found by typing colors(). However, if you want to actually see what the colors look like, check here: pch = changes the plotting symbol shape. The possible numbers (note that there are no parentheses used) that relate to symbols for this specification are: pch=19: solid circle, pch=20: bullet (smaller circle), pch=21: circle, pch=22: square, pch=23: diamond, pch=24: triangle point-up, pch=25: triangle point down.

23 > plot(x$conc, x$rate, col='red', pch = 19) 22

24 23 Grouping by Class What if you wanted the color of the points to reflect the groups of observations in this case, the two classes? Setting col= to the column containing the class specifications will automatically color the points by group. > plot(x$conc, x$rate, col=x$state)

25 24 Legends When you color code the points by group, it s necessary to add a legend. This can be done by, after creating your plot, using the legend command to superimpose one onto the plot. > plot(x$conc, x$rate, col=x$state) > legend (.8, 75, c("treated","untreated"), col = c("black","red"), pch=21) Note that you don t have to specify what data you re working with if you ve already plotted it and have left the graphics window open the legend will simply appear on the already-existing graphic. The legend command requires some explanation to be understood. > legend (.8, 75, c("treated","untreated"), col = c("black","red"), pch=21) These correspond to the coordinates of the top and left sides of the legend box. Note that they are in terms of the scales of the axes. If I had typed (0, 100), the legend would have been touching the left side of the plot and in the middle of a bunch of points. If I had typed (100, 0), it would have been displayed off the range of the axes of the graph, and you would not have been able to see it.

26 25 > legend (.8, 75, c("treated","untreated"), col = c("black","red"), pch=21) Whatever you put in quotes is what the legend displays as labels. If I had typed c( Black Point, Red Point ), those would be what were listed next to the two points in the legend. You can have as many labels as you require, just remember to put quotations around the words you want displayed and commas in between the quoted statements. > legend (.8, 75, c("treated","untreated"), col = c("black","red"), pch=21) This assigns color to the labels you created above. Putting black first assigns that color to the first label ( Treated ) and putting red second assigns it to the second label. Make sure to have as many different colors as you have labels! > legend (.8, 75, c("treated","untreated"), col = c("black","red"), pch=21) The pch specifies which type of symbol should be used in the legend in this case, the circle symbol, since it was used in the default plot. If your symbol changes, you should match it in the legend. This is what a graph with all of these new components axis labels, color based on categories, and a legend looks like: > plot(x$conc, x$rate, xlab='this is the x-axis', ylab = 'This is the y- axis', main = 'This is the title', pch = 19, col=x$state) > legend (.8, 75, c("treated","untreated"), col = c("black","red"), pch=19)

27 26 Line plots can be constructed very similarly the only addition you need is a command that says you want a line connecting the points. > x <- women > plot(x, xlab='weight', ylab = 'Height', main = 'A Line Plot!', pch = 19, col= "red") > lines (x, type = "l", col = "red", lwd =.5) type = indicates the type of line, but for my purposes, I always just use l, as it just draws the simple line. lty = indicates what type of line you want 1, 2, 3, and 4 for solid, dashed, dotted, and dot-dash-dot, respectively. You can completely leave out this command if you just want a solid line, though, as it defaults to that automatically. lwd = indicates the width of the line. I usually find.5 to 1 to be a good line width. Other Graphs Various other types of graphs can be created as well. Many of these can be customized in similar ways as the ones above, when applicable. For more information on these types of graphs in R, type the name of the command with a? in front of it. hist(x) creates a histogram barplot(x) creates a bar graph plot(density(x)) creates a density plot pie(x) creates a pie chart

28 stripchart(x) creates a univariate scatterplot boxplot(x) creates a boxplot pairs(x) creates pairwise scatterplot matrices 27