Lecture 01: Basics of R

Getting Started

Jihong Zhang*, Ph.D

Educational Statistics and Research Methods (ESRM) Program*

University of Arkansas

2024-10-09

Today’s Class

R objects and prebuilt function
Data types
Vectors
Coercion
Not available (NA)
Sorting
Vector arithmetics
Indexing
Basic Plot

R Object and Pre-built function

Objects

To do data clean, data analysis, or statistics, we need to store some information and manipulate it in R. The information that we can create/change/remove is called R object.
Suppose we want to solve several quadratic equations of the form $x^2 + x - 1 = 0$. We know that the quadratic formula gives us the solutions:

\[ \frac{-b\pm\sqrt{b^2 -4ac}}{2a} \]
The solution depend on the values of a, b, and c. One advantage of programming languages is that we can define variables and write expressions with these variables
```
coef_a <- 1
coef_b <- 1
coef_c <- -1
```
We use <- to assign values to the variables. We can also assign values using = instead of <-, but we recommend against using = to avoid confusion.
To see the value stored in a variable, we simply ask R to evaluate coef_a and it shows the stored value:
```
coef_a
```
```
[1] 1
```
- A more explicit way to ask R to show us the value stored in coef_a is using print function like this (print is a prebuilt function in R, we will explain later):
```
print(coef_a)
```
```
[1] 1
```

Workspace

So we have object, then where they are stored in R. The workspace is the place storing the objects we can use:
You can see all the variables saved in your workspace by typing:
```
ls()
```
```
[1] "coef_a" "coef_b" "coef_c"
```
In RStudio, the Environment tab shows the values:

We should see coef_a, coef_b, and coef_c.
Missing R object in workspace: If you try to recover the value of a variable that is not in your workspace, you receive an error. For example, if you type some_random_object you will receive the following message: Error: object 'some_random_object' not found.
```
print(some_random_object)
```
```
Error in print(some_random_object): object 'some_random_object' not found
```

Now since these values are saved in variables, to obtain a solution to our equation, we use the quadratic formula:

(-coef_b + sqrt(coef_b^2 - 4*coef_a*coef_c))/(2*coef_a)

[1] 0.618034

(-coef_b - sqrt(coef_b^2 - 4*coef_a*coef_c))/(2*coef_a)

[1] -1.618034

Operators

-: is a negative operator which switches the sign of object
+ and * and / : addition, multiplication, and division
sqrt: a prebuilt R function of calculating the squared root of the object
^: exponent operator to calculate the “power” of the “base”; a^3 : a to the 3rd power

Prebuilt functions

Functions: Once we defined the objects, the data analysis process can usually be described as a series of functions applied to the data.
- In other words, we considered “function” as a set of pre-specified operations (e.g., macro in SAS)
- R includes several predefined functions and most of the analysis pipelines we construct make extensive use of these.
- We already used or discussed the install.packages, library, and ls functions. We also used the function sqrt to solve the quadratic equation above.
Evaluation: In general, we need to use parentheses followed by a function name to evaluate a function.
- If you type ls, the function is not evaluated and instead R shows you the code that defines the function. If you type ls() the function is evaluated and, as seen above, we see objects in the workspace.
Function Arguments: Unlike ls, most functions require one or more arguments to specify the settings of the function.
- For example, we assign different object to the argument of the function log. Remember that we earlier defined coef_a to be 1:
```
log(8)
```
```
[1] 2.079442
```
```
log(coef_a) 
```
```
[1] 0
```

Help: You can find out what the function expects and what it does by reviewing the very useful manuals included in R. You can get help by using the help function like this:
```
help("log")
?log
```
- The help page will show you what arguments the function is expecting. For example, log needs x and base to run.
- The base of the function log defaults to base = exp(1) making log the natural log by default.
- You can also use args to look at the arguments
```
args(log)
```
```
function (x, base = exp(1)) 
NULL
```
```
log(x = 8, base = 2)
```
```
[1] 3
```
- If specifying the arguments’ names, then we can include them in whatever order we want:
```
log(base = 2, x = 8)
```
```
[1] 3
```

Prebuilt objects

There are several datasets or values that are included for users to practice and test out functions. For example, you can use $\pi$ in your calculation directly:
```
pi
```
```
[1] 3.141593
```
Or infinity value $\infty$:
```
Inf + 1
```
```
[1] Inf
```
You can see all the available datasets by typing:

data()

For example, if you type iris, it will output the famous (Fisher’s or Anderson’s) iris data set gives the measurements in centimeters of the variables sepal length and width and petal length and width:
```
iris
?iris
```
You can check the detailed help page of iris using ? as we did for functions.

Variable Names

When writing code in R, it’s important to choose variable names that are both meaningful and avoid conflicts with existing functions or reserved words in the language.
- For example, avoid using c as variable name because R has a existing prebuilt function c():
```
c(1, 2)
```
```
[1] 1 2
```
Some basic rules in R are that variable names have to start with a letter, can’t contain spaces, and should not be variables that are predefined in R, such as c.

A nice convention to follow is to use meaningful words that describe what is stored, use only lower case, and use underscores as a substitute for spaces.

r_1 <- (-coef_b + sqrt(coef_b^2 - 4*coef_a*coef_c))/(2*coef_a)
r_2 <- (-coef_b - sqrt(coef_b^2 - 4*coef_a*coef_c))/(2*coef_a)
r_1

[1] 0.618034

r_2

[1] -1.618034

Saving workspace

Objects and functions remain in the workspace until you end your session or erase them with the function rm.
Autosave: Your current workspaces also can be saved for later use.
- In fact, when you quit R, Rstudio asks you if you want to save your workspace as .RData. If you do save it, the next time you start R, the program will restore the workspace.
ManualSave: We actually recommend against saving the workspace this way because, as you start working on different projects, it will become harder to keep track of what is saved.
```
save(file = "project_lecture_2.RData") # Save Workspace as project_lecture_2.RData
load("project_lecture_2.RData") # Load Workspace
```

Commenting your code

If a line of R code starts with the symbol #, it is a comment and is not evaluated.

We can use this to write reminders of why we wrote particular code:

## Code to compute solution to quadratic equation

## Define the variables
coef_a <- 3 
coef_b <- 2
coef_c <- -1

## Now compute the solution
(-coef_b + sqrt(coef_b^2 - 4*coef_a*coef_c))/(2*coef_a)

[1] 0.3333333

(-coef_b - sqrt(coef_b^2 - 4*coef_a*coef_c))/(2*coef_a)

[1] -1

Exercises (30 minutes)

What is the sum of the first 100 positive integers? The formula for the sum of integers 1 through n is $n(n+1)/2$. Define

$n=100$ and then use R to compute the sum of 1 through 100 using the formula. What is the sum?
Now use the same formula to compute the sum of the integers from 1 through 1000.
Look at the result of typing the following code into R:
- Based on the result, what do you think the functions seq and sum do? You can use help.

n <- 1000 
x <- seq(1, n) 
sum(x)

[1] 500500

In math and programming, we say that we evaluate a function when we replace the argument with a given value. So if we type sqrt(4), we evaluate the sqrt function. In R, you can evaluate a function inside another function. The evaluations happen from the inside out. Use one line of code to compute the log, in base 10, of the square root of 100.
Which of the following will always return the numeric value stored in x? You can try out examples and use the help system if you want.

Data types

Check types of object

Variables in R can be of different types.
- For example, we need to distinguish numbers from character strings and tables from simple lists of numbers.

The function class helps us determine what type of object we have:

a <- 2
class(a)

[1] "numeric"

b <- "Jihong"
class(b)

[1] "character"

c <- TRUE
class(c)

[1] "logical"

class(iris)

[1] "data.frame"

To work efficiently in R, it is important to learn the different types of variables and what we can do with these.

Data frames

The most common way of storing a dataset in R is in a data frame.
A data frame is a table with rows representing observations and the different variables reported for each observation defining the columns.

Data frames has multiple informatiom:

We can check the number of rows and number of columns:
```
nrow(iris)
```
```
[1] 150
```
```
ncol(iris)
```
```
[1] 5
```

We can check the columns names

colnames(iris)

[1] "Sepal.Length" "Sepal.Width"  "Petal.Length" "Petal.Width"  "Species"

The function str is useful for finding out more about the structure of an data.frame

str(iris)

'data.frame':   150 obs. of  5 variables:
 $ Sepal.Length: num  5.1 4.9 4.7 4.6 5 5.4 4.6 5 4.4 4.9 ...
 $ Sepal.Width : num  3.5 3 3.2 3.1 3.6 3.9 3.4 3.4 2.9 3.1 ...
 $ Petal.Length: num  1.4 1.4 1.3 1.5 1.4 1.7 1.4 1.5 1.4 1.5 ...
 $ Petal.Width : num  0.2 0.2 0.2 0.2 0.2 0.4 0.3 0.2 0.2 0.1 ...
 $ Species     : Factor w/ 3 levels "setosa","versicolor",..: 1 1 1 1 1 1 1 1 1 1 ...

We can show the first 3 or last 3 lines using the function head and tail

head(iris, n = 3)

  Sepal.Length Sepal.Width Petal.Length Petal.Width Species
1          5.1         3.5          1.4         0.2  setosa
2          4.9         3.0          1.4         0.2  setosa
3          4.7         3.2          1.3         0.2  setosa

tail(iris, n = 3)

    Sepal.Length Sepal.Width Petal.Length Petal.Width   Species
148          6.5         3.0          5.2         2.0 virginica
149          6.2         3.4          5.4         2.3 virginica
150          5.9         3.0          5.1         1.8 virginica

Have access to certain column

we can access the different variables represented by columns included in this data frame using $ or [["column_name"]].
```
head(iris$Sepal.Width)
```
```
[1] 3.5 3.0 3.2 3.1 3.6 3.9
```
```
head(iris[["Sepal.Length"]])
```
```
[1] 5.1 4.9 4.7 4.6 5.0 5.4
```

Note that if we use ["column_name"], it will extract single-column data frame
```
class(iris["Sepal.Length"])
```
```
[1] "data.frame"
```
```
ncol(iris["Sepal.Length"])
```
```
[1] 1
```

Vectors

The object iris$Sepal.Width is not one number but several. We call these types of objects vectors.
We use the term vectors to refer to objects with several entries. The function length tells you how many entries are in the vector:
```
Sepal.Width_values <- iris$Sepal.Width
class(Sepal.Width_values)
```
```
[1] "numeric"
```
```
length(Sepal.Width_values)
```
```
[1] 150
```

We can also calculate some descriptive statistics using max, min, sd if the vector contains numeric values only

max(Sepal.Width_values)

[1] 4.4

min(Sepal.Width_values)

[1] 2

mean(Sepal.Width_values)

[1] 3.057333

sd(Sepal.Width_values)

[1] 0.4358663

Vector also can have multiple types: numeric, character (string), logistic, factor

You cannot calculate min/max/mean for the factor vector containing string values. It will return not applied (NA)

Species_names <- iris$Species
head(Species_names)

[1] setosa setosa setosa setosa setosa setosa
Levels: setosa versicolor virginica

class(Species_names)

[1] "factor"

mean(Species_names)

[1] NA

or the character vector

student_names <- c("Tom", "Jimmy", "Emily")
class(student_names)

[1] "character"

mean(student_names)

[1] NA

You can calculate the mean of the logical vector, which is the proportion of TRUE values in the vector:

is_student_male <- c(TRUE, TRUE, FALSE)
class(is_student_male)

[1] "logical"

mean(is_student_male)

[1] 0.6666667

You can also calculate the distribution of the factor vector using table function:

table(Species_names)

Species_names
    setosa versicolor  virginica 
        50         50         50

Factor

Factors are useful for storing categorical data
```
class(iris$Species)
```
```
[1] "factor"
```
We can see that there are only 3 types of iris by using the levels function:
```
levels(iris$Species)
```
```
[1] "setosa"     "versicolor" "virginica" 
```
In the background, R stores these levels as integers and keeps a map to keep track of the labels. This is more memory efficient than storing all the characters.

Stop at https://rafalab.dfci.harvard.edu/dsbook-part-1/R/R-basics.html#sec-factors