Introduction to R. Stat Statistical Computing - Summer Dr. Junvie Pailden. July 5, Southern Illinois University Edwardsville

Transcription

1 Introduction to R Stat Statistical Computing - Summer 2016 Dr. Junvie Pailden Southern Illinois University Edwardsville July 5, 2016

2 Why R R offers a powerful and appealing interactive environment for exploring data, running simulations, etc. R is platform independent meaning it is available on Windows, Mac, and Linux. R has the best help resources both online (just google any issue/question) and using help(...), e.g. help(lm). R is not a black box software, i.e., you can trace how a function or package works by following the R script, e.g. lm() Many more!!!

3 Install R and RStudio on Windows 1 Download R from (click on "Download R for Windows" > "base" > "Download R 3.x.x for Windows") 2 Install R. Leave all default settings in the installation options. 3 Download RStudio from and install it. Leave all default settings in the installation options. 4 Open RStudio.

4 Commands on R Console > # create an integer sequence > 3:7 [1] > # create an sequence from 0 to 3 with 0.5 increment > seq(0,3,by=0.5) [1] > # create a repeated sequence > rep(pi,4) [1] > # Basic Operations > (2-3)*(3/4) [1] -0.75

5 Concatenate operator Concatenate operator > c(6,20,-3) # numbers [1] > c("words","are","wind") # strings [1] "words" "are" "wind" > # Operations > c(1,2,3,4) + 1 [1] > 1/ c(1,2,3,4) [1] > c(1,2,3,4)^2 [1]

6 Variable assignment > x <- 3 > # is the same as > 3 -> x > # and x = 3 Be careful with = because it does not mean equals. For that, you need == operator > one <- 1 ; two <- 2 > one = two # Assign the value of "two" to "one" > one [1] 2 > two [1] 2 Let s start again > one <- 1 ; two <- 2 > one == two [1] FALSE

7 Commonly Used Operators Scalar addition and multiplication > a <- sqrt(2); b <- 1:3; c <- 2:4 > a + b [1] > a * b [1] Entrywise multiplication > b * c [1] x modulus y > 17 %% 5 [1] 2 Integer Division > 17 %/% 5 [1] 3

8 Some built-in functions in R General Form f(argument1, argument2,...) > b <- c(1,2,3) > sum(b) [1] 6 > exp(1) [1] > cos( ) [1] -1 > log(x=64,base=4) [1] 3

9 Simple Summaries > height <- 58:72 > weight <- c(115,117,120,123,126,129,132,135,139, + 142,146,150,154,159,164) > hbar <- mean(height) # mean of height > hbar [1] 65 > hvar <- var(height) # variance of height > hvar [1] 20 > n <- length(height) > sum(height)/n [1] 65 > sum((height-hbar)^2)/(n-1) [1] 20

10 Correlation: Your turn Find the correlation of height and weight? > # size > n <- length(height) > # mean > hbar <- mean(height) > wbar <- mean(weight) > # standard deviation > sdh <- sd(height) > sdw <- sd(weight) > # correlation coefficient > r <- sum((height-hbar)*(weight-wbar))/(sdh*sdw*(n-1)) > r [1]

11 Writing Functions in R General Form function(arglist) expr return(value) > my_fun <- function(x,y){ + x + y + } > my_fun(1,2) [1] 3 Body of the function does not need to be in separate lines. If the body of the function is only one line, then braces aren t necessary. > my_fun2 <- function(x,y) x + y > my_fun2(1,2) [1] 3

12 More on functions in R I can set default values, say y=5 > my_fun2 <- function(x,y=5) x + y > my_fun2(1) [1] 6 The sapply() function accepts a list and a function, then applies the function to every element of that list and returns the result. Because functions are also objects, I can pass a function into another function as the argument. > l <- 1:5 > sapply(l, my_fun2) [1]

13 Special Values There are a few special values that are used in R The NA values are used to represent missing values. You may encounter NA values in text loaded in R or in data loaded from databases (to replace Null values). > v <- c(1,2,3) > length(v) <- 4 > v [1] NA If a computation results in a number that is too big, R will return Inf for a positive and -Inf for a negative. > 2^1024 [1] Inf > -2^1024 [1] -Inf > 1/0 [1] Inf > Inf-Inf # will return `NaN`

14 Lists A list, in R use list(), is an ordered collection of objects of possibly different types. Lists are frequently used to return several results of a function in a single object. > arya <- list(name='arya of Winterfell',age=11,northman=TRUE) > arya $name [1] "Arya of Winterfell" $age [1] 11 $northman [1] TRUE You can see that the name of each item is preceded by a $. You can then reference each item in the list by its position or its name.

15 Matrices A matrix is a two-dimensional array. Matrices (same as vectors) can hold elements only of the same type. > # 2 by 4 matrix > m <- matrix(1:8,nrow=2,ncol=4) > m [,1] [,2] [,3] [,4] [1,] [2,] By default, the matrix is populated by column. To populate the matrix by row, add byrow=true in the argument. To access the matrix, use square brackets. > m[2,1] # entry on 2nd row, 1s column [1] 2 > m[2:3] # 2rd to 3th entry columnwise [1] 2 3

16 Matrices (con t) You can also give names to each row and each column using dimnames(). > dimnames(m) <- list(c('a','b'),c('p','q','r','s')) > m p q r s a b Combine objects by rows rbind() or columns cbind() > S <- rbind(rep(false,5),rep(na,5)) > rownames(s) <- c('all False','All NA') > S [,1] [,2] [,3] [,4] [,5] All False FALSE FALSE FALSE FALSE FALSE All NA NA NA NA NA NA

17 Arrays An array is an extention of the vector to more than two dimensions. > # 2 by 3 by 2 array > A <- array(1:12,c(2,3,2)) > A,, 1 [,1] [,2] [,3] [1,] [2,] 2 4 6,, 2 [,1] [,2] [,3] [1,] [2,]

18 Arrays (Con t) Interchange the first two subscripts on a 3-way array A > At <- aperm(a, c(2,1,3)) > At,, 1 [,1] [,2] [1,] 1 2 [2,] 3 4 [3,] 5 6,, 2 [,1] [,2] [1,] 7 8 [2,] 9 10 [3,] 11 12

19 Factors in R Values can be nominal, ordinal, or continuous. In R, nominal and ordinal values are represented by factor(). > trident <- c('a','a','b','b','b','c') > factor(trident) [1] a a b b b c Levels: a b c By default, factor levels are created in alphabetical order. > saltpans <- c('c','b','a') > factor(trident,order=true,levels=saltpans) [1] a a b b b c Levels: c < b < a

20 Functions as Arguments Many of R functions require functions as arguments (e.g. integrate). Suppose we need to compute the beta function 1 B(a,b) = x a 1 (1 x) b 1 dx, a > 0,b > 0. 0 First we write a function that returns the integrand evaluated at a point x. The additional arguments a and b specify the exponents. > f <- function(x, a=1, b=1){ + x^(a-1)*(1-x)^(b-1) + } > x <- seq(0, 1,.2) # seq from 0 to 1 with steps of.2 > f(x, a=2, b=2) [1] > integrate(f, lower=0, upper=1, a=2, b=2) with absolute error < 1.9e-15

21 Apply function in R Applies a function to sections of an array (or matrix) and returns the results in an array (or matrix). apply(array, margin, function,...) The margin argument is used to specify which margin we want to apply the function to and which margin we wish to keep. > #row sums of matrix m from previous slide, margin is 1 > apply(m, 1, sum) a b > #column sums of m, margin is 2 > apply(m, 2, sum) p q r s

22 Data Frames A data frame is a list that contains multiple named vectors of the same length. Whereas we usually use spreadsheet or database table by row, data frames are constructed by columns. > # Recall correlation coeff from previous slide > data.frame(hbar,wbar,sdh,sdw,r) hbar wbar sdh sdw r > # can also be used in functions > myfun_df <- function(x) data.frame(mean = mean(x), + variance = var(x)) > myfun_df(1:20) mean variance

23 Conditionals if (arglist is satisfied) { \ \ do this one } else { \ \ do this two } Create a function that tells you whether a variable is greater than 20. > my_cond <- function(x){ if (x > 20) { + print("x is greater than 20") + } else { + print("x is less than 20") + } + } > x <- 10 > my_cond(x) [1] "x is less than 20"

24 Repeat Loops in R R has three forms of loops. The first is repeat w/c repeats a particular expression until it hits a break keyword. > x <- 0 > repeat{if (x>4) break + else {print(x); x <- x+1} } [1] 0 [1] 1 [1] 2 [1] 3 [1] 4 Within the outermost braces is an if-else expression: if (x>4) break else print(x); x <- x+1. The inner set of braces is part of the else clause: print(x); x <- x+1. The semicolon separates the clause into two parts. The first is print statement, and the second increments x so that the condition that termintes the loop, x>4, is eventually satisfied.

25 While and For Loops in R > x <- 0 > while (x < 5) {print (x); x <- x + 1} [1] 0 [1] 1 [1] 2 [1] 3 [1] 4 For loops iterate through each item in a vector or a list: > for (x in 0:4) print(x) [1] 0 [1] 1 [1] 2 [1] 3 [1] 4 The colon creates a vector, passing each integer from 0 to 4 to the loop.

26 Fibonacci Sequence Find the first 10 Finonacci numbers. > len <- 10 > fibvals <- numeric(len) # creates a vector of 0's > fibvals[1] <- 1 > fibvals[2] <- 1 > for (i in 3:len) { + fibvals[i] <- fibvals[i-1]+fibvals[i-2] + } > fibvals [1]

27 Your Turn - Seatwork time! 1 Create the vector (20,19,...,2,1) and call it myvec. 2 Create the identity matrix I 3 3 Create the matrix with rows (2,1,2) and (1,0, 1). Multiply the resulting matrix with I 3. 4 Write a function norm that will compute the Euclidean norm of a numeric vector x = (x 1,...,x n ) given by n x = xi 2. Try this function on the vectors (0,0,0,1) and (2,5,2,4) to check that your function result is correct. i=1

28 Package.R An R package is a set of related functions and help files, bundled together. It is similar to libraries in C or toolbox in Matlab. * Normally, all functions within a single package are related: for example, the stats package contains functions for statistical analysis. There are few public repositories of packages: the largest is CRAN hosted by the R foundation with more than 4000 packages, and is mirrored in many sites worldwide. Of course, you need internet connection to do this. To use a package, you first need to install it into R. If you re using the R console user interface, you can use the package installer from the menu. You can also install R packages directly through R console using install.packages(). To load up an R package, use the library().