Factors in R

Introduction

A factor is a data structure in R used to represent categorical data. Categorical data consists of a limited number of distinct values called levels. Factors are widely used in statistical analysis, machine learning, and data analysis.

Examples of categorical variables are:

• Gender (Male, Female)
• Blood Group (A, B, AB, O)
• Grade (A, B, C, D)
• Department (CSE, ECE, ME)
• Marital Status (Single, Married)

Unlike character vectors, factors store the categories internally as integers and maintain a set of corresponding labels called levels.

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Why Use Factors?

Factors provide:

• Efficient storage of repeated categorical values.
• Information about the categories (levels).
• Easy statistical analysis.
• Support for ordered categories.
• Compatibility with modeling functions in R.

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Creating Factors

Factors are created using the factor() function.

Syntax

factor(x)

where x is a vector containing categorical values.

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Example 1: Gender

gender <- c("Male", "Female", "Male", "Male", "Female")

f <- factor(gender)

print(f)

Output

[1] Male   Female Male   Male   Female
Levels: Female Male

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Internal Representation

as.numeric(f)

Output

[1] 2 1 2 2 1

Internally:

Category	Code
Female	1
Male	2

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Determining Factor Properties

class()

class(f)

Output

[1] "factor"

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levels()

Returns the categories.

levels(f)

Output

[1] "Female" "Male"

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length()

Returns the number of elements.

length(f)

Output

[1] 5

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nlevels()

Returns the number of categories.

nlevels(f)

Output

[1] 2

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Creating Factors with Specified Levels

blood <- factor(
    c("B","A","O","AB","A"),
    levels=c("A","B","AB","O")
)

print(blood)

Output

[1] B  A  O  AB A
Levels: A B AB O

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Frequency Table

table(blood)

Output

A  B AB  O
2  1  1  1

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Accessing Factor Elements

blood[3]

Output

[1] O
Levels: A B AB O

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Modifying Factor Elements

gender[1] <- "Female"

print(gender)

Output

[1] "Female" "Female" "Male" "Male" "Female"

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Adding Levels

Suppose

gender <- factor(c("Male","Female","Male"))

Current levels:

Female Male

Add a new level:

levels(gender) <- c(levels(gender), "Other")

Now

gender[1] <- "Other"

print(gender)

Output

[1] Other Female Male
Levels: Female Male Other

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Renaming Levels

levels(gender) <- c("F","M","O")

print(gender)

Output

[1] O F M
Levels: F M O

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Ordered Factors

Some categories have a natural order.

Examples:

• Small < Medium < Large
• Poor < Average < Good < Excellent

Such factors are called ordered factors.

Example

grade <- factor(
    c("Good","Excellent","Average","Good"),
    levels=c("Poor","Average","Good","Excellent"),
    ordered=TRUE
)

print(grade)

Output

[1] Good Excellent Average Good
Levels: Poor < Average < Good < Excellent

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Comparing Ordered Factors

grade[1] > grade[3]

Output

[1] TRUE

because

Good > Average

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Converting Character Vector to Factor

dept <- c("CSE","ECE","ME","CSE")

f <- factor(dept)

print(f)

Output

[1] CSE ECE ME CSE
Levels: CSE ECE ME

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Converting Factor to Character

as.character(f)

Output

[1] "CSE" "ECE" "ME" "CSE"

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Converting Factor to Numeric

Suppose

x <- factor(c("10","20","30"))

Incorrect

as.numeric(x)

Output

[1] 1 2 3

These are level numbers, not actual values.

Correct

as.numeric(as.character(x))

Output

[1] 10 20 30

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Using Factors in Data Frames

student <- data.frame(
    Name=c("John","Mary","Alex"),
    Gender=factor(c("Male","Female","Male"))
)

print(student)

Output

  Name Gender
1 John   Male
2 Mary Female
3 Alex   Male

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Counting Categories

gender <- factor(c("Male","Female","Male","Male"))

table(gender)

Output

Female Male
     1    3

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Summary of Factor Values

summary(gender)

Output

Female Male
     1    3

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Useful Functions

Function	Purpose
factor()	Create factor
levels()	Display levels
nlevels()	Number of levels
table()	Frequency of levels
summary()	Summary of factor
as.character()	Convert factor to character
as.numeric()	Convert to numeric codes
class()	Determine class

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Difference Between Character Vectors and Factors

Character Vector	Factor
Stores text directly	Stores categories as integers
No levels	Has levels
Less efficient	More memory efficient
No ordering	Can be ordered
Used for text	Used for categorical data

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Applications of Factors

Gender Classification

Male, Female

Student Grades

A, B, C, D

Blood Groups

A, B, AB, O

Shirt Sizes

Small, Medium, Large

Customer Categories

Silver, Gold, Platinum

Disease Severity

Mild, Moderate, Severe

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Example: Student Grade Analysis

grades <- factor(
    c("A","B","A","C","B","A")
)

print(table(grades))

Output

A B C
3 2 1

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Conclusion

Factors are specialized data structures used to represent categorical data. They store categories efficiently using integer codes and maintain a set of levels corresponding to the categories. Factors play a crucial role in statistical analysis, machine learning, and data modeling, making them one of the most important data structures in R.