The Art of R Programming

R informed us here that, from a vector-indexing point of view, elements

1, 3, 5, and 6 ofmare larger than 2. For example, element 5 is the element in

row 2, column 2 ofm, which we see has the value 10, which is indeed greater

than 2.

3.2.5 Extended Example: Generating a Covariance Matrix...............

This example demonstrates R’srow()andcol()functions, whose arguments

are matrices. For example, for a matrixa,row(a[2,8])will return the row

number of that element ofa, which is 2. Well, we knewrow(a[2,8])is in row

2, didn’t we? So why would this function be useful?

Let’s consider an example. When writing simulation code for multi-

variate normal distributions—for instance, usingmvrnorm()from theMASS

library—we need to specify a covariance matrix. The key point for our pur-

poses here is that the matrix is symmetric; for example, the element in row

1, column 2 is equal to the element in row 2, column 1.

Suppose that we are working with ann-variate normal distribution. Our

matrix will havenrows andncolumns, and we wish each of thenvariables

to have variance 1, with correlationrhobetween pairs of variables. Forn=3

andrho = 0.2, for example, the desired matrix is as follows:

⎛

⎝

10. 20. 2

0. 210. 2

0. 20. 21

⎞

⎠

Here is code to generate this kind of matrix:

1 makecov <- function(rho,n) {
2 m <- matrix(nrow=n,ncol=n)
3 m <- ifelse(row(m) == col(m),1,rho)
4 return(m)
5 }

Let’s see how this works. First, as you probably guessed,col()returns

the column number of its argument, just asrow()does for the row num-

ber. Then the expressionrow(m)in line 3 returns a matrix of integer values,

each one showing the row number of the corresponding element ofm. For

instance,

>z

[,1] [,2]

[1,] 3 6

[2,] 4 7

[3,] 5 8

> row(z)

[,1] [,2]

[1,] 1 1

[2,] 2 2

[3,] 3 3

Matrices and Arrays 69