--- language: R contributors: - ["e99n09", "http://github.com/e99n09"] - ["isomorphismes", "http://twitter.com/isomorphisms"] - ["kalinn", "http://github.com/kalinn"] filename: learnr.r --- R is a statistical computing language. It has lots of libraries for uploading and cleaning data sets, running statistical procedures, and making graphs. You can also run `R` commands within a LaTeX document. ```r # Comments start with number symbols. # You can't make multi-line comments, # but you can stack multiple comments like so. # in Windows or Mac, hit COMMAND-ENTER to execute a line ############################################################################# # Stuff you can do without understanding anything about programming ############################################################################# # In this section, we show off some of the cool stuff you can do in # R without understanding anything about programming. Do not worry # about understanding everything the code does. Just enjoy! data() # browse pre-loaded data sets data(rivers) # get this one: "Lengths of Major North American Rivers" ls() # notice that "rivers" now appears in the workspace head(rivers) # peek at the data set # 735 320 325 392 524 450 length(rivers) # how many rivers were measured? # 141 summary(rivers) # what are some summary statistics? # Min. 1st Qu. Median Mean 3rd Qu. Max. # 135.0 310.0 425.0 591.2 680.0 3710.0 # make a stem-and-leaf plot (a histogram-like data visualization) stem(rivers) # The decimal point is 2 digit(s) to the right of the | # # 0 | 4 # 2 | 011223334555566667778888899900001111223333344455555666688888999 # 4 | 111222333445566779001233344567 # 6 | 000112233578012234468 # 8 | 045790018 # 10 | 04507 # 12 | 1471 # 14 | 56 # 16 | 7 # 18 | 9 # 20 | # 22 | 25 # 24 | 3 # 26 | # 28 | # 30 | # 32 | # 34 | # 36 | 1 stem(log(rivers)) # Notice that the data are neither normal nor log-normal! # Take that, Bell curve fundamentalists. # The decimal point is 1 digit(s) to the left of the | # # 48 | 1 # 50 | # 52 | 15578 # 54 | 44571222466689 # 56 | 023334677000124455789 # 58 | 00122366666999933445777 # 60 | 122445567800133459 # 62 | 112666799035 # 64 | 00011334581257889 # 66 | 003683579 # 68 | 0019156 # 70 | 079357 # 72 | 89 # 74 | 84 # 76 | 56 # 78 | 4 # 80 | # 82 | 2 # make a histogram: hist(rivers, col="#333333", border="white", breaks=25) # play around with these parameters hist(log(rivers), col="#333333", border="white", breaks=25) # you'll do more plotting later # Here's another neat data set that comes pre-loaded. R has tons of these. data(discoveries) plot(discoveries, col="#333333", lwd=3, xlab="Year", main="Number of important discoveries per year") plot(discoveries, col="#333333", lwd=3, type = "h", xlab="Year", main="Number of important discoveries per year") # Rather than leaving the default ordering (by year), # we could also sort to see what's typical: sort(discoveries) # [1] 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 2 2 2 2 # [26] 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 3 3 3 # [51] 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 4 4 4 4 4 4 4 4 # [76] 4 4 4 4 5 5 5 5 5 5 5 6 6 6 6 6 6 7 7 7 7 8 9 10 12 stem(discoveries, scale=2) # # The decimal point is at the | # # 0 | 000000000 # 1 | 000000000000 # 2 | 00000000000000000000000000 # 3 | 00000000000000000000 # 4 | 000000000000 # 5 | 0000000 # 6 | 000000 # 7 | 0000 # 8 | 0 # 9 | 0 # 10 | 0 # 11 | # 12 | 0 max(discoveries) # 12 summary(discoveries) # Min. 1st Qu. Median Mean 3rd Qu. Max. # 0.0 2.0 3.0 3.1 4.0 12.0 # Roll a die a few times round(runif(7, min=.5, max=6.5)) # 1 4 6 1 4 6 4 # Your numbers will differ from mine unless we set the same random.seed(31337) # Draw from a standard Gaussian 9 times rnorm(9) # [1] 0.07528471 1.03499859 1.34809556 -0.82356087 0.61638975 -1.88757271 # [7] -0.59975593 0.57629164 1.08455362 ################################################## # Data types and basic arithmetic ################################################## # Now for the programming-oriented part of the tutorial. # In this section you will meet the important data types of R: # integers, numerics, characters, logicals, and factors. # There are others, but these are the bare minimum you need to # get started. # INTEGERS # Long-storage integers are written with L 5L # 5 class(5L) # "integer" # (Try ?class for more information on the class() function.) # In R, every single value, like 5L, is considered a vector of length 1 length(5L) # 1 # You can have an integer vector with length > 1 too: c(4L, 5L, 8L, 3L) # 4 5 8 3 length(c(4L, 5L, 8L, 3L)) # 4 class(c(4L, 5L, 8L, 3L)) # "integer" # NUMERICS # A "numeric" is a double-precision floating-point number 5 # 5 class(5) # "numeric" # Again, everything in R is a vector; # you can make a numeric vector with more than one element c(3,3,3,2,2,1) # 3 3 3 2 2 1 # You can use scientific notation too 5e4 # 50000 6.02e23 # Avogadro's number 1.6e-35 # Planck length # You can also have infinitely large or small numbers class(Inf) # "numeric" class(-Inf) # "numeric" # You might use "Inf", for example, in integrate(dnorm, 3, Inf); # this obviates Z-score tables. # BASIC ARITHMETIC # You can do arithmetic with numbers # Doing arithmetic on a mix of integers and numerics gives you another numeric 10L + 66L # 76 # integer plus integer gives integer 53.2 - 4 # 49.2 # numeric minus numeric gives numeric 2.0 * 2L # 4 # numeric times integer gives numeric 3L / 4 # 0.75 # integer over numeric gives numeric 3 %% 2 # 1 # the remainder of two numerics is another numeric # Illegal arithmetic yeilds you a "not-a-number": 0 / 0 # NaN class(NaN) # "numeric" # You can do arithmetic on two vectors with length greater than 1, # so long as the larger vector's length is an integer multiple of the smaller c(1,2,3) + c(1,2,3) # 2 4 6 # Since a single number is a vector of length one, scalars are applied # elementwise to vectors (4 * c(1,2,3) - 2) / 2 # 1 3 5 # Except for scalars, use caution when performing arithmetic on vectors with # different lengths. Although it can be done, c(1,2,3,1,2,3) * c(1,2) # 1 4 3 2 2 6 # Matching lengths is better practice and easier to read c(1,2,3,1,2,3) * c(1,2,1,2,1,2) # CHARACTERS # There's no difference between strings and characters in R "Horatio" # "Horatio" class("Horatio") # "character" class('H') # "character" # Those were both character vectors of length 1 # Here is a longer one: c('alef', 'bet', 'gimmel', 'dalet', 'he') # => # "alef" "bet" "gimmel" "dalet" "he" length(c("Call","me","Ishmael")) # 3 # You can do regex operations on character vectors: substr("Fortuna multis dat nimis, nulli satis.", 9, 15) # "multis " gsub('u', 'ø', "Fortuna multis dat nimis, nulli satis.") # "Fortøna møltis dat nimis, nølli satis." # R has several built-in character vectors: letters # => # [1] "a" "b" "c" "d" "e" "f" "g" "h" "i" "j" "k" "l" "m" "n" "o" "p" "q" "r" "s" # [20] "t" "u" "v" "w" "x" "y" "z" month.abb # "Jan" "Feb" "Mar" "Apr" "May" "Jun" "Jul" "Aug" "Sep" "Oct" "Nov" "Dec" # LOGICALS # In R, a "logical" is a boolean class(TRUE) # "logical" class(FALSE) # "logical" # Their behavior is normal TRUE == TRUE # TRUE TRUE == FALSE # FALSE FALSE != FALSE # FALSE FALSE != TRUE # TRUE # Missing data (NA) is logical, too class(NA) # "logical" # Use | and & for logic operations. # OR TRUE | FALSE # TRUE # AND TRUE & FALSE # FALSE # Applying | and & to vectors returns elementwise logic operations c(TRUE,FALSE,FALSE) | c(FALSE,TRUE,FALSE) # TRUE TRUE FALSE c(TRUE,FALSE,TRUE) & c(FALSE,TRUE,TRUE) # FALSE FALSE TRUE # You can test if x is TRUE isTRUE(TRUE) # TRUE # Here we get a logical vector with many elements: c('Z', 'o', 'r', 'r', 'o') == "Zorro" # FALSE FALSE FALSE FALSE FALSE c('Z', 'o', 'r', 'r', 'o') == "Z" # TRUE FALSE FALSE FALSE FALSE # FACTORS # The factor class is for categorical data # Factors can be ordered (like childrens' grade levels) or unordered (like gender) factor(c("female", "female", "male", NA, "female")) # female female male female # Levels: female male # The "levels" are the values the categorical data can take # Note that missing data does not enter the levels levels(factor(c("male", "male", "female", NA, "female"))) # "female" "male" # If a factor vector has length 1, its levels will have length 1, too length(factor("male")) # 1 length(levels(factor("male"))) # 1 # Factors are commonly seen in data frames, a data structure we will cover later data(infert) # "Infertility after Spontaneous and Induced Abortion" levels(infert$education) # "0-5yrs" "6-11yrs" "12+ yrs" # NULL # "NULL" is a weird one; use it to "blank out" a vector class(NULL) # NULL parakeet = c("beak", "feathers", "wings", "eyes") parakeet # => # [1] "beak" "feathers" "wings" "eyes" parakeet <- NULL parakeet # => # NULL # TYPE COERCION # Type-coercion is when you force a value to take on a different type as.character(c(6, 8)) # "6" "8" as.logical(c(1,0,1,1)) # TRUE FALSE TRUE TRUE # If you put elements of different types into a vector, weird coercions happen: c(TRUE, 4) # 1 4 c("dog", TRUE, 4) # "dog" "TRUE" "4" as.numeric("Bilbo") # => # [1] NA # Warning message: # NAs introduced by coercion # Also note: those were just the basic data types # There are many more data types, such as for dates, time series, etc. ################################################## # Variables, loops, if/else ################################################## # A variable is like a box you store a value in for later use. # We call this "assigning" the value to the variable. # Having variables lets us write loops, functions, and if/else statements # VARIABLES # Lots of way to assign stuff: x = 5 # this is possible y <- "1" # this is preferred TRUE -> z # this works but is weird # LOOPS # We've got for loops for (i in 1:4) { print(i) } # We've got while loops a <- 10 while (a > 4) { cat(a, "...", sep = "") a <- a - 1 } # Keep in mind that for and while loops run slowly in R # Operations on entire vectors (i.e. a whole row, a whole column) # or apply()-type functions (we'll discuss later) are preferred # IF/ELSE # Again, pretty standard if (4 > 3) { print("4 is greater than 3") } else { print("4 is not greater than 3") } # => # [1] "4 is greater than 3" # FUNCTIONS # Defined like so: jiggle <- function(x) { x = x + rnorm(1, sd=.1) #add in a bit of (controlled) noise return(x) } # Called like any other R function: jiggle(5) # 5±ε. After set.seed(2716057), jiggle(5)==5.005043 ########################################################################### # Data structures: Vectors, matrices, data frames, and arrays ########################################################################### # ONE-DIMENSIONAL # Let's start from the very beginning, and with something you already know: vectors. vec <- c(8, 9, 10, 11) vec # 8 9 10 11 # We ask for specific elements by subsetting with square brackets # (Note that R starts counting from 1) vec[1] # 8 letters[18] # "r" LETTERS[13] # "M" month.name[9] # "September" c(6, 8, 7, 5, 3, 0, 9)[3] # 7 # We can also search for the indices of specific components, which(vec %% 2 == 0) # 1 3 # grab just the first or last few entries in the vector, head(vec, 1) # 8 tail(vec, 2) # 10 11 # or figure out if a certain value is in the vector any(vec == 10) # TRUE # If an index "goes over" you'll get NA: vec[6] # NA # You can find the length of your vector with length() length(vec) # 4 # You can perform operations on entire vectors or subsets of vectors vec * 4 # 16 20 24 28 vec[2:3] * 5 # 25 30 any(vec[2:3] == 8) # FALSE # and R has many built-in functions to summarize vectors mean(vec) # 9.5 var(vec) # 1.666667 sd(vec) # 1.290994 max(vec) # 11 min(vec) # 8 sum(vec) # 38 # Some more nice built-ins: 5:15 # 5 6 7 8 9 10 11 12 13 14 15 seq(from=0, to=31337, by=1337) # => # [1] 0 1337 2674 4011 5348 6685 8022 9359 10696 12033 13370 14707 # [13] 16044 17381 18718 20055 21392 22729 24066 25403 26740 28077 29414 30751 # TWO-DIMENSIONAL (ALL ONE CLASS) # You can make a matrix out of entries all of the same type like so: mat <- matrix(nrow = 3, ncol = 2, c(1,2,3,4,5,6)) mat # => # [,1] [,2] # [1,] 1 4 # [2,] 2 5 # [3,] 3 6 # Unlike a vector, the class of a matrix is "matrix", no matter what's in it class(mat) # => "matrix" # Ask for the first row mat[1,] # 1 4 # Perform operation on the first column 3 * mat[,1] # 3 6 9 # Ask for a specific cell mat[3,2] # 6 # Transpose the whole matrix t(mat) # => # [,1] [,2] [,3] # [1,] 1 2 3 # [2,] 4 5 6 # Matrix multiplication mat %*% t(mat) # => # [,1] [,2] [,3] # [1,] 17 22 27 # [2,] 22 29 36 # [3,] 27 36 45 # cbind() sticks vectors together column-wise to make a matrix mat2 <- cbind(1:4, c("dog", "cat", "bird", "dog")) mat2 # => # [,1] [,2] # [1,] "1" "dog" # [2,] "2" "cat" # [3,] "3" "bird" # [4,] "4" "dog" class(mat2) # matrix # Again, note what happened! # Because matrices must contain entries all of the same class, # everything got converted to the character class c(class(mat2[,1]), class(mat2[,2])) # rbind() sticks vectors together row-wise to make a matrix mat3 <- rbind(c(1,2,4,5), c(6,7,0,4)) mat3 # => # [,1] [,2] [,3] [,4] # [1,] 1 2 4 5 # [2,] 6 7 0 4 # Ah, everything of the same class. No coercions. Much better. # TWO-DIMENSIONAL (DIFFERENT CLASSES) # For columns of different types, use a data frame # This data structure is so useful for statistical programming, # a version of it was added to Python in the package "pandas". students <- data.frame(c("Cedric","Fred","George","Cho","Draco","Ginny"), c(3,2,2,1,0,-1), c("H", "G", "G", "R", "S", "G")) names(students) <- c("name", "year", "house") # name the columns class(students) # "data.frame" students # => # name year house # 1 Cedric 3 H # 2 Fred 2 G # 3 George 2 G # 4 Cho 1 R # 5 Draco 0 S # 6 Ginny -1 G class(students$year) # "numeric" class(students[,3]) # "factor" # find the dimensions nrow(students) # 6 ncol(students) # 3 dim(students) # 6 3 # The data.frame() function converts character vectors to factor vectors # by default; turn this off by setting stringsAsFactors = FALSE when # you create the data.frame ?data.frame # There are many twisty ways to subset data frames, all subtly unalike students$year # 3 2 2 1 0 -1 students[,2] # 3 2 2 1 0 -1 students[,"year"] # 3 2 2 1 0 -1 # An augmented version of the data.frame structure is the data.table # If you're working with huge or panel data, or need to merge a few data # sets, data.table can be a good choice. Here's a whirlwind tour: install.packages("data.table") # download the package from CRAN require(data.table) # load it students <- as.data.table(students) students # note the slightly different print-out # => # name year house # 1: Cedric 3 H # 2: Fred 2 G # 3: George 2 G # 4: Cho 1 R # 5: Draco 0 S # 6: Ginny -1 G students[name=="Ginny"] # get rows with name == "Ginny" # => # name year house # 1: Ginny -1 G students[year==2] # get rows with year == 2 # => # name year house # 1: Fred 2 G # 2: George 2 G # data.table makes merging two data sets easy # let's make another data.table to merge with students founders <- data.table(house=c("G","H","R","S"), founder=c("Godric","Helga","Rowena","Salazar")) founders # => # house founder # 1: G Godric # 2: H Helga # 3: R Rowena # 4: S Salazar setkey(students, house) setkey(founders, house) students <- founders[students] # merge the two data sets by matching "house" setnames(students, c("house","houseFounderName","studentName","year")) students[,order(c("name","year","house","houseFounderName")), with=F] # => # studentName year house houseFounderName # 1: Fred 2 G Godric # 2: George 2 G Godric # 3: Ginny -1 G Godric # 4: Cedric 3 H Helga # 5: Cho 1 R Rowena # 6: Draco 0 S Salazar # data.table makes summary tables easy students[,sum(year),by=house] # => # house V1 # 1: G 3 # 2: H 3 # 3: R 1 # 4: S 0 # To drop a column from a data.frame or data.table, # assign it the NULL value students$houseFounderName <- NULL students # => # studentName year house # 1: Fred 2 G # 2: George 2 G # 3: Ginny -1 G # 4: Cedric 3 H # 5: Cho 1 R # 6: Draco 0 S # Drop a row by subsetting # Using data.table: students[studentName != "Draco"] # => # house studentName year # 1: G Fred 2 # 2: G George 2 # 3: G Ginny -1 # 4: H Cedric 3 # 5: R Cho 1 # Using data.frame: students <- as.data.frame(students) students[students$house != "G",] # => # house houseFounderName studentName year # 4 H Helga Cedric 3 # 5 R Rowena Cho 1 # 6 S Salazar Draco 0 # MULTI-DIMENSIONAL (ALL ELEMENTS OF ONE TYPE) # Arrays creates n-dimensional tables # All elements must be of the same type # You can make a two-dimensional table (sort of like a matrix) array(c(c(1,2,4,5),c(8,9,3,6)), dim=c(2,4)) # => # [,1] [,2] [,3] [,4] # [1,] 1 4 8 3 # [2,] 2 5 9 6 # You can use array to make three-dimensional matrices too array(c(c(c(2,300,4),c(8,9,0)),c(c(5,60,0),c(66,7,847))), dim=c(3,2,2)) # => # , , 1 # # [,1] [,2] # [1,] 2 8 # [2,] 300 9 # [3,] 4 0 # # , , 2 # # [,1] [,2] # [1,] 5 66 # [2,] 60 7 # [3,] 0 847 # LISTS (MULTI-DIMENSIONAL, POSSIBLY RAGGED, OF DIFFERENT TYPES) # Finally, R has lists (of vectors) list1 <- list(time = 1:40) list1$price = c(rnorm(40,.5*list1$time,4)) # random list1 # You can get items in the list like so list1$time # one way list1[["time"]] # another way list1[[1]] # yet another way # => # [1] 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 # [34] 34 35 36 37 38 39 40 # You can subset list items like any other vector list1$price[4] # Lists are not the most efficient data structure to work with in R; # unless you have a very good reason, you should stick to data.frames # Lists are often returned by functions that perform linear regressions ################################################## # The apply() family of functions ################################################## # Remember mat? mat # => # [,1] [,2] # [1,] 1 4 # [2,] 2 5 # [3,] 3 6 # Use apply(X, MARGIN, FUN) to apply function FUN to a matrix X # over rows (MAR = 1) or columns (MAR = 2) # That is, R does FUN to each row (or column) of X, much faster than a # for or while loop would do apply(mat, MAR = 2, jiggle) # => # [,1] [,2] # [1,] 3 15 # [2,] 7 19 # [3,] 11 23 # Other functions: ?lapply, ?sapply # Don't feel too intimidated; everyone agrees they are rather confusing # The plyr package aims to replace (and improve upon!) the *apply() family. install.packages("plyr") require(plyr) ?plyr ######################### # Loading data ######################### # "pets.csv" is a file on the internet # (but it could just as easily be be a file on your own computer) pets <- read.csv("http://learnxinyminutes.com/docs/pets.csv") pets head(pets, 2) # first two rows tail(pets, 1) # last row # To save a data frame or matrix as a .csv file write.csv(pets, "pets2.csv") # to make a new .csv file # set working directory with setwd(), look it up with getwd() # Try ?read.csv and ?write.csv for more information ######################### # Statistical Analysis ######################### # Linear regression! linearModel <- lm(price ~ time, data = list1) linearModel # outputs result of regression # => # Call: # lm(formula = price ~ time, data = list1) # # Coefficients: # (Intercept) time # 0.1453 0.4943 summary(linearModel) # more verbose output from the regression # => # Call: # lm(formula = price ~ time, data = list1) # # Residuals: # Min 1Q Median 3Q Max # -8.3134 -3.0131 -0.3606 2.8016 10.3992 # # Coefficients: # Estimate Std. Error t value Pr(>|t|) # (Intercept) 0.14527 1.50084 0.097 0.923 # time 0.49435 0.06379 7.749 2.44e-09 *** # --- # Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 # # Residual standard error: 4.657 on 38 degrees of freedom # Multiple R-squared: 0.6124, Adjusted R-squared: 0.6022 # F-statistic: 60.05 on 1 and 38 DF, p-value: 2.44e-09 coef(linearModel) # extract estimated parameters # => # (Intercept) time # 0.1452662 0.4943490 summary(linearModel)$coefficients # another way to extract results # => # Estimate Std. Error t value Pr(>|t|) # (Intercept) 0.1452662 1.50084246 0.09678975 9.234021e-01 # time 0.4943490 0.06379348 7.74920901 2.440008e-09 summary(linearModel)$coefficients[,4] # the p-values # => # (Intercept) time # 9.234021e-01 2.440008e-09 # GENERAL LINEAR MODELS # Logistic regression set.seed(1) list1$success = rbinom(length(list1$time), 1, .5) # random binary glModel <- glm(success ~ time, data = list1, family=binomial(link="logit")) glModel # outputs result of logistic regression # => # Call: glm(formula = success ~ time, # family = binomial(link = "logit"), data = list1) # # Coefficients: # (Intercept) time # 0.17018 -0.01321 # # Degrees of Freedom: 39 Total (i.e. Null); 38 Residual # Null Deviance: 55.35 # Residual Deviance: 55.12 AIC: 59.12 summary(glModel) # more verbose output from the regression # => # Call: # glm(formula = success ~ time, # family = binomial(link = "logit"), data = list1) # Deviance Residuals: # Min 1Q Median 3Q Max # -1.245 -1.118 -1.035 1.202 1.327 # # Coefficients: # Estimate Std. Error z value Pr(>|z|) # (Intercept) 0.17018 0.64621 0.263 0.792 # time -0.01321 0.02757 -0.479 0.632 # # (Dispersion parameter for binomial family taken to be 1) # # Null deviance: 55.352 on 39 degrees of freedom # Residual deviance: 55.121 on 38 degrees of freedom # AIC: 59.121 # # Number of Fisher Scoring iterations: 3 ######################### # Plots ######################### # BUILT-IN PLOTTING FUNCTIONS # Scatterplots! plot(list1$time, list1$price, main = "fake data") # Plot regression line on existing plot abline(linearModel, col = "red") # Get a variety of nice diagnostics plot(linearModel) # Histograms! hist(rpois(n = 10000, lambda = 5), col = "thistle") # Barplots! barplot(c(1,4,5,1,2), names.arg = c("red","blue","purple","green","yellow")) # GGPLOT2 # But these are not even the prettiest of R's plots # Try the ggplot2 package for more and better graphics install.packages("ggplot2") require(ggplot2) ?ggplot2 pp <- ggplot(students, aes(x=house)) pp + geom_histogram() ll <- as.data.table(list1) pp <- ggplot(ll, aes(x=time,price)) pp + geom_point() # ggplot2 has excellent documentation (available http://docs.ggplot2.org/current/) ``` ## How do I get R? * Get R and the R GUI from [http://www.r-project.org/](http://www.r-project.org/) * [RStudio](http://www.rstudio.com/ide/) is another GUI