Vectors

here are some useful commands for vectors:

x <- c(1, 2, 3, 4, 5, 6)
x

## [1] 1 2 3 4 5 6

length(x)

## [1] 6

names(x) <- LETTERS[1:6]
x

## A B C D E F 
## 1 2 3 4 5 6

If we have several vectors of the same type and length which belong together we can put them in a

Matrix

x <- c(1, 2, 3, 4, 5, 6)
y <- c(4, 2, 3, 5, 3, 4)
z <- c(3, 4, 2, 3, 4, 2)
cbind(x, y, x)

##      x y x
## [1,] 1 4 1
## [2,] 2 2 2
## [3,] 3 3 3
## [4,] 4 5 4
## [5,] 5 3 5
## [6,] 6 4 6

rbind(x, y, z)

##   [,1] [,2] [,3] [,4] [,5] [,6]
## x    1    2    3    4    5    6
## y    4    2    3    5    3    4
## z    3    4    2    3    4    2

here are several other ways to make a matrix:

matrix(x, 2, 3)

##      [,1] [,2] [,3]
## [1,]    1    3    5
## [2,]    2    4    6

matrix(x, ncol=2)

##      [,1] [,2]
## [1,]    1    4
## [2,]    2    5
## [3,]    3    6

matrix(0, 3, 3)

##      [,1] [,2] [,3]
## [1,]    0    0    0
## [2,]    0    0    0
## [3,]    0    0    0

diag(3)

##      [,1] [,2] [,3]
## [1,]    1    0    0
## [2,]    0    1    0
## [3,]    0    0    1

we can control how the matrix is filled in:

matrix(1:8, nrow=2)

##      [,1] [,2] [,3] [,4]
## [1,]    1    3    5    7
## [2,]    2    4    6    8

matrix(1:8, nrow=2, byrow = TRUE)

##      [,1] [,2] [,3] [,4]
## [1,]    1    2    3    4
## [2,]    5    6    7    8

just like vectors a matrix is all of the same type, with R doing type conversion if necessary:

matrix(c(1, 2, "A", 3), 2, 2)

##      [,1] [,2]
## [1,] "1"  "A" 
## [2,] "2"  "3"

useful commands for R matrices are:

x <- matrix(c(1, 2, 3, 4, 5, 6), 2, 3)
x

##      [,1] [,2] [,3]
## [1,]    1    3    5
## [2,]    2    4    6

dim(x)

## [1] 2 3

nrow(x)

## [1] 2

ncol(x)

## [1] 3

dimnames(x) <- list(c("A", "B"), c("a", "b", "c"))
x

##   a b c
## A 1 3 5
## B 2 4 6

colnames(x)

## [1] "a" "b" "c"

rownames(x)

## [1] "A" "B"

colnames(x) <- c("Height", "Age 1", "Age 2")
x

##   Height Age 1 Age 2
## A      1     3     5
## B      2     4     6

Actually I would recommend

colnames(x) <- c("Height", "Age.1", "Age.2")
x

##   Height Age.1 Age.2
## A      1     3     5
## B      2     4     6

empty spaces in names are allowed but can on occasion lead to problems, so avoiding them is a good idea. Of course they are not nice as labels in graphs or as titles in tables, but it is usually easy to change those.

Sometimes a matrix is created by a function and given row and column names automatically, but we don’t want it to have them. They can be removed with

rownames(x) <- NULL
x

##      Height Age.1 Age.2
## [1,]      1     3     5
## [2,]      2     4     6

Here is a strange way to make a matrix:

x <- 1:6
x

## [1] 1 2 3 4 5 6

dim(x) <- c(2, 3)
x

##      [,1] [,2] [,3]
## [1,]    1    3    5
## [2,]    2    4    6

Why does this work? dim is an attribute of an object, by changing this attribute we are changing the object.

What happens if we try to make a matrix out of a vector that doesn’t have the right number of entries?

matrix(1:5, 2, 2)

## Warning in matrix(1:5, 2, 2): data length [5] is not a sub-multiple or
## multiple of the number of rows [2]

##      [,1] [,2]
## [1,]    1    3
## [2,]    2    4

not surprisingly it just uses the elements needed.

matrix(1:3, 2, 2)

## Warning in matrix(1:3, 2, 2): data length [3] is not a sub-multiple or
## multiple of the number of rows [2]

##      [,1] [,2]
## [1,]    1    3
## [2,]    2    1

In this case R just starts all over again. This behavior is called recycling (in computer science, not just R)

In either case R gives a warning. Except in rare cases you should try to avoid these things, they are usually the consequence of bad programming.

Arrays

an array is a k-dimensional matrix. For example

array(1:8, dim=c(2, 2, 2))

## , , 1
## 
##      [,1] [,2]
## [1,]    1    3
## [2,]    2    4
## 
## , , 2
## 
##      [,1] [,2]
## [1,]    5    7
## [2,]    6    8

Often these come about as a 3-way table:

x <- sample(1:3, size=20, replace=T)
y <- sample(c("F", "M"), size=20, replace = T)
z <- sample(c("a", "b", "c"), size=20, replace = T)
xyz <- table(x,y,z)
xyz

## , , z = a
## 
##    y
## x   F M
##   1 1 2
##   2 1 0
##   3 0 1
## 
## , , z = b
## 
##    y
## x   F M
##   1 1 0
##   2 4 2
##   3 1 0
## 
## , , z = c
## 
##    y
## x   F M
##   1 4 0
##   2 0 0
##   3 1 2

The commands for arrays are similar to those for matrices:

dim(xyz)

## [1] 3 2 3

dimnames(xyz)

## $x
## [1] "1" "2" "3"
## 
## $y
## [1] "F" "M"
## 
## $z
## [1] "a" "b" "c"

Data Frames

sometimes we have several vectors of the same length but of different types, then we can put them together as a data frame:

x <- c(1, 2, 3, 4, 5, 6)
y <- c("a", "a", "b", "c", "a", "c")
z <- c(T, T, F, T, F, T)
xyz <- data.frame(x, y, z)
xyz

##   x y     z
## 1 1 a  TRUE
## 2 2 a  TRUE
## 3 3 b FALSE
## 4 4 c  TRUE
## 5 5 a FALSE
## 6 6 c  TRUE

This type of data is very common in Statistics, and data frames have been the standard data type from its beginning. In general when you get data from a source like the internet it will be as a data frame.

The same commands as for matrices work for data frames as well:

dim(xyz)

## [1] 6 3

nrow(xyz)

## [1] 6

ncol(xyz)

## [1] 3

dimnames(xyz) <- list(letters[1:6], c("a", "b", "c"))
xyz

##   a b     c
## a 1 a  TRUE
## b 2 a  TRUE
## c 3 b FALSE
## d 4 c  TRUE
## e 5 a FALSE
## f 6 c  TRUE

colnames(xyz)

## [1] "a" "b" "c"

rownames(xyz)

## [1] "a" "b" "c" "d" "e" "f"

Say we want to add another column (variable) to the data frame:

xyz[[4]] <- (1:6)^2
colnames(xyz)[4] <- "squares"
xyz

##   a b     c squares
## a 1 a  TRUE       1
## b 2 a  TRUE       4
## c 3 b FALSE       9
## d 4 c  TRUE      16
## e 5 a FALSE      25
## f 6 c  TRUE      36

If we want to get rid of a column:

xyz[[4]] <- NULL

There is a strange default behavior of data frames: they turn strings into factors:

df <- data.frame(x=1:5, y=letters[1:5])
str(df)

## 'data.frame':    5 obs. of  2 variables:
##  $ x: int  1 2 3 4 5
##  $ y: Factor w/ 5 levels "a","b","c","d",..: 1 2 3 4 5

You can prevent this from happening, though:

df <- data.frame(x = 1:5, 
                 y = letters[1:5],
                 stringsAsFactors = FALSE)
str(df)

## 'data.frame':    5 obs. of  2 variables:
##  $ x: int  1 2 3 4 5
##  $ y: chr  "a" "b" "c" "d" ...

In fact, this is what I want to happen almost all the time. So I change that option globally whenever I run R or RStudio. I will show you how to do that at some point.

If a data frame is all of the same type we can use as.matrix to turn it into a matrix.

Exercise

what does as.matrix() do when it is applied to a data frame with columns of different types?

Finally, if the vectors aren’t even of the same lengths we have

Lists

x <- c(1, 2, 3, 4, 5, 6)
y <- c("a", "a", "b")
z <- c(T, T)
xyz <- list(x, y, z)
xyz

## [[1]]
## [1] 1 2 3 4 5 6
## 
## [[2]]
## [1] "a" "a" "b"
## 
## [[3]]
## [1] TRUE TRUE

lists are displayed quite differently from the other formats. Here are a number of commands:

length(xyz)

## [1] 3

names(xyz) <- c("Count", "Letter", "Married?")
xyz

## $Count
## [1] 1 2 3 4 5 6
## 
## $Letter
## [1] "a" "a" "b"
## 
## $`Married?`
## [1] TRUE TRUE

Often we want to use a list inside a function to record various values. So we need to create an “empty” list of a certain length:

x <- as.list(1:3)
x

## [[1]]
## [1] 1
## 
## [[2]]
## [1] 2
## 
## [[3]]
## [1] 3

and if we run out of space:

x[[4]] <- "a"
x

## [[1]]
## [1] 1
## 
## [[2]]
## [1] 2
## 
## [[3]]
## [1] 3
## 
## [[4]]
## [1] "a"

Internally R stores all data as lists. In fact anything can be an element of a list:

kable.nice(wine)

attach(wine)
plot(Wine.Consumption, Heart.Disease.Deaths,
      xlab = "Wine Consumption",
      ylab = "Heart Disease per 100000")

fit <- lm(Heart.Disease.Deaths~Wine.Consumption)
plot(Wine.Consumption, Heart.Disease.Deaths,
      xlab = "Wine Consumption",
      ylab = "Heart Disease per 100000")
abline(fit)

wine.all <- list(data=wine, fit=fit)
length(wine.all)

## [1] 2

z <- list(fit, fit, fit)
length(z)

## [1] 3

df <- data.frame(x=1:3, y=letters[1:3])
df$z <- z
dim(df)

## [1] 3 3

results

## $`Experiment 1`
##     A     B     C     D     E 
## 102.5 110.9  96.3  96.5  88.4 
## 
## $`Experiment 2`
##    A    B    C    D    E 
## 64.6 96.0 94.2 64.3 79.6 
## 
## $`Experiment 3`
##     A     B     C     D     E 
## 120.2 116.4 138.7 100.8 104.1 
## 
## $`Experiment 4`
##     A     B     C     D     E 
##  67.7 113.4  93.3  89.6  90.2 
## 
## $`Experiment 5`
##     A     B     C     D     E 
## 135.5  88.8 105.1  57.1  89.0 
## 
## $`Experiment 6`
##     A     B     C     D     E 
##  98.5 101.0 117.3  83.2 116.4 
## 
## $`Experiment 7`
##     A     B     C     D     E 
##  56.9  98.3 118.9 104.1  86.5 
## 
## $`Experiment 8`
##     A     B     C     D     E 
##  95.3  81.3  94.3  93.4 108.0 
## 
## $`Experiment 9`
##     A     B     C     D     E 
## 127.1  95.1 125.0  98.5 108.5 
## 
## $`Experiment 10`
##     A     B     C     D     E 
##  87.7 103.2  85.9 120.7  84.5

Reduce(`+`, results)/length(results)

##      A      B      C      D      E 
##  95.60 100.44 106.90  90.82  95.52