Introduction to R: Day 2 September 20, 2017

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1 Introduction to R: Day 2 September 20, 2017 Outline RStudio projects Base R graphics plotting one or two continuous variables customizable elements of plots saving plots to a file Create a new project for today First, let s see how RStudio projects work in practice. We saw in Part 1 how they let you divide your work into self-contained contexts, since each project has its own working directory, workspace, history, and source documents. Exercise: Projects 1. create a new RStudio project 2. create a couple of variables and plot them, e.g.: X <- rnorm(20, 3, 2) Y <- rnorm(20, X/2+2.5, 1.5) 3. quit RStudio ( yes to save) and start again. 4. switch back to the project we used on Day 1 5. switch back to today s project so we can work. Note the following happens in RStudio when switching to an existing project: restore the environment and history set the current working directory to the project directory. restore documents that were open in the editor tabs arrange panels where they were when the project was last open Environment/workspace Objects that you create by assignment make up your R workspace. The workspace is shown in the Environment tab in RStudio, and so the term environment is sometimes used, even though strictly speaking that s not [what environment means][r-environment] in the R programming language itself. But the meaning is usually clear from the context, and the latter won t normally be something you have to deal with. It s important to remember that the workspace exists only in your computer s memory: unless you save it to the disk, it will be gone once the R application exits (or you turn off the computer). Luckily, saving the workspace is simple, because R gives us the option to save it to disk when quitting or switching projects. When you choose to save the workspace, all objects in it are stored in a file named.rdata in R s current working directory. When starting R (or opening an RStudio project), the saved workspace is automatically restored from the.rdata file in the starting directory. So for the most part this is not something you need 1

2 to worry about just don t delete the.rdata file, unless you know how to recreate all the important objects in it. (And you should know, either from the history or because you saved your analysis code into an R script file.) Working Directory R has a notion of the working directory, which is the location where it will look for files to read or write if then don t contain the full directory information. (Kind of like the current directory in a terminal shell.) Initially, this is the location where R was started from, and if you re using RStudio projects, it s inside the project directory. So unless you choose to change your working directory, all your files will be stored in the project, which is exactly what you want. (You can set the working directory from the File pane, but avoid do so until you re more comfortable with R. You can always load a file from directories other than the working one by giving the correct path in the file name.) Switching the working directories, and more generally managing files from R, is a more advanced topic that we will cover in one of the later workshops on reproducible computing practices. Graphics Let s revisit the mtcars dataset from last session. mtcars ## mpg cyl disp hp drat wt qsec vs am gear carb ## Mazda RX ## Mazda RX4 Wag ## Datsun ## Hornet 4 Drive ## Hornet Sportabout ## Valiant ## Duster ## Merc 240D ## Merc ## Merc ## Merc 280C ## Merc 450SE ## Merc 450SL ## Merc 450SLC ## Cadillac Fleetwood ## Lincoln Continental ## Chrysler Imperial ## Fiat ## Honda Civic ## Toyota Corolla ## Toyota Corona ## Dodge Challenger ## AMC Javelin ## Camaro Z ## Pontiac Firebird ## Fiat X ## Porsche ## Lotus Europa ## Ford Pantera L ## Ferrari Dino

3 ## Maserati Bora ## Volvo 142E This is a data.frame object, a table are rectangular objects where each column is a variable and each row is an observed unit. Data frames are particularly well suited to representing data being analyzed, and as such are the most common type of data used in functions used for statistical analysis. We saw on Monday many functions that can be used to learn about the shape and size of the data in the data frame: dim(mtcars) ## [1] str(mtcars) ## 'data.frame': 32 obs. of 11 variables: ## $ mpg : num ## $ cyl : num ## $ disp: num ## $ hp : num ## $ drat: num ## $ wt : num ## $ qsec: num ## $ vs : num ## $ am : num ## $ gear: num ## $ carb: num summary(mtcars) ## mpg cyl disp hp ## Min. :10.40 Min. :4.000 Min. : 71.1 Min. : 52.0 ## 1st Qu.: st Qu.: st Qu.: st Qu.: 96.5 ## Median :19.20 Median :6.000 Median :196.3 Median :123.0 ## Mean :20.09 Mean :6.188 Mean :230.7 Mean :146.7 ## 3rd Qu.: rd Qu.: rd Qu.: rd Qu.:180.0 ## Max. :33.90 Max. :8.000 Max. :472.0 Max. :335.0 ## drat wt qsec vs ## Min. :2.760 Min. :1.513 Min. :14.50 Min. : ## 1st Qu.: st Qu.: st Qu.: st Qu.: ## Median :3.695 Median :3.325 Median :17.71 Median : ## Mean :3.597 Mean :3.217 Mean :17.85 Mean : ## 3rd Qu.: rd Qu.: rd Qu.: rd Qu.: ## Max. :4.930 Max. :5.424 Max. :22.90 Max. : ## am gear carb ## Min. : Min. :3.000 Min. :1.000 ## 1st Qu.: st Qu.: st Qu.:2.000 ## Median : Median :4.000 Median :2.000 ## Mean : Mean :3.688 Mean :2.812 ## 3rd Qu.: rd Qu.: rd Qu.:4.000 ## Max. : Max. :5.000 Max. :8.000 head(mtcars) ## mpg cyl disp hp drat wt qsec vs am gear carb ## Mazda RX ## Mazda RX4 Wag

4 ## Datsun ## Hornet 4 Drive ## Hornet Sportabout ## Valiant Then there are the functions that calculate various descriptive statistics, like the mean and standard deviation of the variables, either individually or all at once: mean(mtcars$mpg) ## [1] apply(mtcars, 2, sd) ## mpg cyl disp hp drat wt ## ## qsec vs am gear carb ## median(mtcars$mpg) ## [1] 19.2 Just as importantly, the early stages of data exploration should also involve a lot of graphing, because our visual system can very quickly process the information displayed in a way that is just not possible in a tabular form. We saw already how to create a boxplot in R. Let s try it on the mpg variable from the mtcars dataset: boxplot(mtcars$mpg)

5 Recall that the dollar sign $ can be used to access individual variables in a data frame, so mtcars$mpg is how I get the value of the mpg variable. This particular plot gives us some sense of the shape of the mpg values, but boxplots really come into their own when comparing different groups. There are two ways this can be done: by having the values for each group in a different argument, for example Xs and Ys from the first exercise: boxplot(x, Y) However, we can also use a more concise notation when the grouping variable is already part of the dataset. With mtcars, we have such a grouping variable in cyl, indicating the number of cylinders in the engine. In this case, we can write: boxplot(mpg ~ cyl, data = mtcars) 5

6 Notice the mpg ~ cyl. This is called a formula in R, and is used by many functions in a (fairly) consistent way. Just remember that to the right side of tilde are the X variables (i.e., predictors aka independent variables), while the left-hand side is the Y (response, or dependent variable). I think you ll agree that the formula notation makes it easier to see what is being plotted, since it focuses on looking at your data as variables playing a certain role in the statistical model. We will stick with it whenever possible. Exercise: Boxplots Create a boxplot of fuel efficiency (mpg) vs. transmission type (am), using the data in mtcars. Customizing the plot This is not a terribly pretty graphic, and certainly not good enough for a publication. We briefly saw on Monday that various aspects of the plot can be modified by specifying optional arguments. There are many such arguments in the R graphing system, but we will focus on only the most common ones. These graphics parameters are shared by the various plotting functions, so you only have to learn them once. Most commonly, we label the plot to make it more informative to the reader: boxplot(mpg ~ cyl, data = mtcars, ylab = "Cylinders", main = "Fuel efficiency by engine cylinders") 6

7 Fuel efficiency by engine cylinders Cylinders We can also change the size of the font used to annotate the plot ( cex. plus the element being annotated, such as main for the title): boxplot(mpg ~ cyl, data = mtcars, ylab = "Cylinders", main = "Fuel efficiency by engine cylinders", cex.lab = 1.5, cex.main = 2, cex.axis =.8) 7

8 Fuel efficiency by engine cylinders Cylinders There are also several arguments that control specifically the way the boxplot is drawn: the length of the whiskers ( range ), whether the outliers are drawn ( outline ), whether to notch the side of the boxes at median ( notch ). Example: boxplot(mpg ~ cyl, data = mtcars, outline = FALSE, range = 1) 8

9 Lastly, we can make the boxplot extend horizontally, with the horizontal argument: boxplot(mpg ~ cyl, data = mtcars, horizontal = TRUE) 9

10 Note that in this case you may also want to rotate the axis tick labes so that they re horizontal (with las = 1 ): boxplot(mpg ~ cyl, data = mtcars, horizontal = TRUE, las = 1) 10

11 Exercise: Modifying boxplots Add the plot title and both axis labels to the boxplot you produced in our last exercise. Increase the size of the plot title, and make the whiskers extend the full range of the data. Histograms To get a fuller picture of the distribution of observed values, we use histograms. This plot type divides the entire range of values into a series of intervals, and then shows the count of how many values fall into each interval by the height of the interval s bar. We create histograms using the hist functions. Unfortunately, this function doesn t accept a formula as input; you have to give it a vector of observations: hist(mtcars$mpg) 11

12 Histogram of mtcars$mpg Frequency mtcars$mpg By default, R uses equally spaced breaks to divide the data into bins and plot the counts of points falling into each bin. (If not specified by the user, the number of bins is determined by one of a number of available algorithms, and depends on various aspects of the input data. The default calculation uses only the number of observations to determine the number of breaks.) One thing to keep in mind with histograms is that the choice of the number of bins can greatly determine the overall shape of the histogram and potentially mask important aspects of the data. So it s always good to try plotting the histograms with a couple of different numbers of bins. For the hist function, this is done with the argument breaks : hist(mtcars$mpg, breaks=10) 12

13 Histogram of mtcars$mpg Frequency mtcars$mpg Exercise: Histograms Plot a histogram of engine size (displacement) for data in mtcars. Try varying the number of bins. What do you see? Note that if the number of breaks given doesn t allow the breakpoints to fall nicely on on pretty values (for some R-defined notion of nice and pretty ), you may end up with fewer bins than requested: hist(mtcars$mpg, breaks=8) 13

14 Histogram of mtcars$mpg Frequency mtcars$mpg If you really want to have 8 bins in this case, you will have to specify the breakpoints explicitly: hist(mtcars$mpg, breaks=c(10, 14, 16, 18, 21, 24, 28, 30, 34)) 14

15 Histogram of mtcars$mpg Density mtcars$mpg Notice that you don t have to have evenly spaced breaks, although they usually are. If you need to use the exact number of evenly-spaced bins (let s say 8), you can use the seq function, giving one more than the desired number of bins in the length argument: hist(mtcars$mpg, breaks = seq(10, 35, length=9)) 15

16 Histogram of mtcars$mpg Frequency mtcars$mpg If it bothers you that the tails of the histogram hang outside the drawn X-axis, you can control the axis s range with the xlim argument. Just give it the pair of the lower and upper endpoint of the axis: hist(mtcars$mpg, breaks=10, xlim=c(0, 35)) 16

17 Histogram of mtcars$mpg Frequency mtcars$mpg Also, all the usual ways to annotate the plot are available, main, xlab, ylab, etc. (You cannot make the histogram draw horizontally, unfortunately.) hist(mtcars$mpg, main="fuel efficiency (mpg)") 17

18 Fuel efficiency (mpg) Frequency mtcars$mpg Dot charts If you want to plot a single variable but see all the individual cases, a dot chart is a good option: dotchart(mtcars$mpg) 18

19 Usually, you will want to label the cases: dotchart(mtcars$mpg, rownames(mtcars)) 19

20 Mazda Mazda Datsun Hornet Hornet Valiant Duster Merc Merc Merc Merc Merc Merc Merc Cadillac Lincoln Chrysler Fiat Honda Toyota Toyota Dodge AMC Camaro Pontiac Fiat Porsche Lotus Ford Ferrari Maserati Volvo 142E Pantera Dino Bora Europa L X Firebird Javelin Z28 Corolla Corona Challenger 128 Civic Continental Imperial 240D C 450SE 450SL 450SLC Fleetwood Sportabout RX4 RX4 710 Drive Wag If the labels don t look right, you know how to modify them: with the cex.axis argument! Except that here it is called cex. (Base graphics is sometimes inconsistent, as you may have noticed.) dotchart(mtcars$mpg, rownames(mtcars), cex =.8) 20

21 Volvo 142E Maserati Bora Ferrari Dino Ford Pantera L Lotus Europa Porsche Fiat X1 9 Pontiac Firebird Camaro Z28 AMC Javelin Dodge Challenger Toyota Corona Toyota Corolla Honda Civic Fiat 128 Chrysler Imperial Lincoln Continental Cadillac Fleetwood Merc 450SLC Merc 450SL Merc 450SE Merc 280C Merc 280 Merc 230 Merc 240D Duster 360 Valiant Hornet Sportabout Hornet 4 Drive Datsun 710 Mazda RX4 Wag Mazda RX Breaking the cases into groups is also possible, with the groups argument: dotchart(mtcars$mpg, rownames(mtcars), groups = mtcars$cyl, cex =.6) 21

22 Volvo 142E Lotus Europa Porsche Fiat X1 9 Toyota Corona Toyota Corolla Honda Civic Fiat 128 Merc 230 Merc 240D Datsun 710 Ferrari Dino Merc 280C Merc 280 Valiant Hornet 4 Drive Mazda RX4 Wag Mazda RX4 Maserati Bora Ford Pantera L Pontiac Firebird Camaro Z28 AMC Javelin Dodge Challenger Chrysler Imperial Lincoln Continental Cadillac Fleetwood Merc 450SLC Merc 450SL Merc 450SE Duster 360 Hornet Sportabout Why can t this be done with a formula? Good question. Most likely, this function was created before the formula interface was introduced, and in a way that makes it very difficult to add the formula support at this point. But there are alternatives in other packages that do just that. (There almost always are, with R. For example, see dotplot in package lattice, although it does involve a whole new graphics framework, which is very different to work with from base graphics that we re exploring here. Or wait until the workshop on ggplot2 in November, which is very flexible and currently the most popular way to produce graphics in R.) lattice::dotplot(rownames(mtcars)~mpg, data=mtcars, groups=cyl) 22

23 Volvo 142E Valiant Toyota Corona Toyota Corolla Porsche Pontiac Firebird Merc 450SLC Merc 450SL Merc 450SE Merc 280C Merc 280 Merc 240D Merc 230 Mazda RX4 Wag Mazda RX4 Maserati Bora Lotus Europa Lincoln Continental Hornet Sportabout Hornet 4 Drive Honda Civic Ford Pantera L Fiat X1 9 Fiat 128 Ferrari Dino Duster 360 Dodge Challenger Datsun 710 Chrysler Imperial Camaro Z28 Cadillac Fleetwood AMC Javelin mpg Exercise: Dot charts Create a dot chart of weights (wt) for mtcars, grouped by number of cylinders. Add labels for the x axis and title. Scatterplots When you want to plot two continuous variables, you probably want to use a scatterplot. In base R graphics, this is done with the plot function: plot(mpg~disp, data = mtcars) 23

24 mpg disp Exercise: Customizing scatterplot labels Create a scatterplot of fuel consumption (mpg) vs. car weight (wt) from mtcars. Add title and axis labels to the plot. In addition, there is a range of plotting parameters that you may want to modify. The style of the points and their colour are the most common, and are controlled with the pch and col argument to plot. This can be useful to distinguish different groups in the single plot. plot(mpg~disp, data = mtcars, col = cyl) 24

25 mpg disp The coding of pch is very contra-intuitive. For instance, the value of 19 will produce a solid circle, while 9 is an asterisk. See the help page for points for different values, or consult this cheat sheet. Creating a matrix of scatterplots When dealing with multi-dimensional data, you may wish to explore relationships between many pairs of variables. With R, you can do so for many variables at once using the pairs function. The function accepts a formula interface, where on the right-hand side you include all the variables you re interested in, joined with + signs: pairs(~mpg+wt+disp, data=mtcars) 25

26 mpg wt disp Line plot Often, the data contain repeated measurements, or even a time series. BOD ## Time demand ## ## ## ## ## ## plot(demand ~ Time, data = BOD) 26

27 demand Time In those cases, we may want to emphasize the continuity by connecting the data points with a line. This is done by giving argument type = "l" to plot: plot(demand ~ Time, data = BOD, type = "l") 27

28 demand Time Similarly to scatter plots, we can control the colour and type of the line being drawn with arguments to plot: plot(demand ~ Time, data = BOD, type = "l", lty=2, lwd = 3.5, col='red') 28

29 demand Time Combining multiple line plots in a single graph Calling lines multiple times simply adds another line to the current plot for each call. Here is an example where repeated measurements of multiple subjects are drawn as a scatterplot showing all the data at once. Then, lines connecting the measurements of four subjects are drawn one at a time ( subset = Subject == 1 ), each in a different colour: plot(conc~time, data = Theoph) lines(conc~time, data = Theoph, subset = Subject == 1) lines(conc~time, data = Theoph, subset = Subject == 2, col='red') lines(conc~time, data = Theoph, subset = Subject == 3, col='blue') lines(conc~time, data = Theoph, subset = Subject == 4, col='darkgreen') 29

30 conc Time Adding straight lines to the plot Often time, we want to add to the plot one or more straight lines to provide some kind of comparison with or reference to the plotted/observed points. For instance: coordinate axes, mean value of cases in particular groups, or the line of best fit. While this can be done by providing the precise coordinates for lines, there is a simpler way with abline. This function can draw horizontal and vertical lines by providing a single argument: plot(mpg ~ disp, data = mtcars) abline(h = 20) # mean fuel consumption abline(v = median(mtcars$disp)) 30

31 mpg disp Two other arguments, a and b, are used to draw angled lines, by giving the intercept (a) and slope (b) of the line. Exercise: adding a line Draw a scatterplot of fuel consumption (mpg) vs. weight (wt) for mtcars, and add a red line for the least squares estimate with slope of and intercept at Legends When plotting different groups, it can be useful to include the legend to help the reader match the plotted colours/symbols with the groups. With base graphics, we do this with the legend function, which takes in the X and Y coordinate of the top-left corner of the legend, the text of each of the legend s items, as well as a symbol/colour matching it with the plot. For instance: boxplot(mpg~cyl, data=mtcars, col=c('steelblue', 'darkgreen', 'darkred')) legend(3, 35, c('4 cyl', '6 cyl', '8 cyl'), fill=c('steelblue', 'darkgreen', 'darkred')) 31

32 cyl 6 cyl 8 cyl (The X-coordinate is 3, because the boxes for the three groups are drawn at one-unit increments along the X-axis i.e., 1, 2, and 3 despite the axis tick labels saying 4, 6, and 8. A different plot type, say a scatterplot, uses the actual range of the data values.) Exercise: Legends Add a legend to the scatterplot from the last exercise to provide the explanation of what the red line is. In this case, we have just a single item in the legend, but we want to provide an additional symbol matching the label with the red line in the plot. We do this by specifying the color (i.e., red: col="red" ) and the style of the symbol (i.e., a line: lwd=1). plot(mpg ~ wt, data = mtcars) abline(a=37.285, b=-5.34, col="red") legend(4.5, 33, "Best fit", col="red", lwd=1) 32

33 mpg Best fit wt 33