Download R Programming Tutorial for Econ 520: Vectors, Logical Vectors, and Indexing - Prof. Hiran and more Exams Economics in PDF only on Docsity! R Tutorial 2 Econ 520, Fall 2008 1. Vectors In R, a variable can hold a vector of numbers. (You can also define matrices and arrays, as we'll see later on.) This is very handy because we can do a set of operations simultaneously on a large set of numbers. An easy way to construct a vector is to use the "c" command. This "concatenates" numbers into a vector: > x<- c(1,3,5,10) This defines a vector (1,3,5,10) and stores the entire vector in x. If you just type "x" at the prompt, you will see the entire vector: > x [1] 1 3 5 10 Many arithmetic operations work element-by-element on vectors. For example: > x [1] 1 3 5 10 > x+1 [1] 2 4 6 11 > 3*x [1] 3 9 15 30 Also some functions work element-by-element on vectors: > exp(x) [1] 2.718282 20.085537 148.413159 22026.465795 > log(x) [1] 0.000000 1.098612 1.609438 2.302585 > sin(x) [1] 0.8414710 0.1411200 -0.9589243 -0.5440211 Some functions in R work directly on a vector to return a scalar. For example: > sum(x) [1] 19 > mean(x) [1] 4.75 > sd(x) [1] 3.86221 These calculate the sum of the elements in x, the mean (average) of the elements, and the (sample) standard deviation. Another useful type of calculation involves logical vectors. A logical vector is a vector where each element can be either "TRUE" or "FALSE." Logical vectors can be constructed using the concatenation function: > lv1 <- c(FALSE, TRUE, FALSE, TRUE) > lv1 [1] FALSE TRUE FALSE TRUE or by applying a logical test to a vector, for example: > x [1] 1 3 5 10 > lv2 <- x > 4 > lv2 [1] FALSE FALSE TRUE TRUE Here, lv2 is a vector of the same size as x, with FALSE indicating that the corresponding element of x is not strictly greater than 4. (For weak inequality, you can use <= and >=) Two logical vectors of the same length can be combined using logical operators (& for "and", | for "or"): > lv1 [1] FALSE TRUE FALSE TRUE > lv2 [1] FALSE FALSE TRUE TRUE > lv1 & lv2 [1] FALSE FALSE FALSE TRUE > lv1 | lv2 [1] FALSE TRUE TRUE TRUE Some numerical functions can be applied to logical vectors: > sum(lv2) [1] 2 2. Indexing vectors Recall that we defined: > x [1] 1 3 5 10 We can access elements of the vector individually, by using x[n], where n is the position of the element in the vector: > x[1] [1] 1 > x[2] [1] 3 > x[4] [1] 10 Notice that x[1] is the first element in the vector x. (In some programming languages, vector indices start at 0, but in R, they start at 1.) We can take subvectors using the ":" notation: > x[1:3] [1] 1 3 5 We can also reorder the elements. Here, "reverseindex" is a vector containing the numbers 1 through 4, but in reverse sequence. Writing x[reverseindex] asks R to construct the vector (x[4], x [3], x[2], x[1]): > reverseindex <- c(4,3,2,1) > x[reverseindex] [1] 10 5 3 1 Another way to extract subvectors is using a logical index vector: > logindex <- x > 4 > logindex [1] FALSE FALSE TRUE TRUE > x[logindex] [1] 5 10 This creates a vector of those elements of x that are greater than 4. 3. Random Numbers R has extensive facilities for working with random numbers and probability distributions. Suppose we are interested in the Uniform(0,4) distribution. The function dunif(x,min,max) gives the PDF of a uniform distribution with lower bound equal to min, upper bound equal to max, evaluated at x: > dunif(.5, min=0, max=4) [1] 0.25 The function punif(x, min, max) gives the probability of being less than or equal to x (i.e., the CDF): > punif(.5, min=0, max=4) [1] 0.125 Finally, the function runif(n, min, max) generates n (independent) random draws from the Uniform (min,max) distribution. Since we don't necessarily want to view all of them on the screen, we can store them in a vector variable for later use:
