Week 5: Factor Variables

POP88162 Introduction to Quantitative Research Methods

Tom Paskhalis

Department of Political Science, Trinity College Dublin

So Far

  • Vector is the core data structure in R.
  • Vectors can be one of the main data types (character, numeric, logical).
  • As opposed to homogeneous vectors, lists allow to combine data of different types.
  • Matrices are vectors with an added class and dimensionality attribute.
  • Data frames are lists of equal-sized vectors.
  • When subsetting data frames the techniques of subsetting matrices and lists are combined.

Topics for Today

  • Attributes
  • Factors
  • Crosstabulation

Review: Data Structures

Structure Description Dimensionality Data Type
vector Atomic vector (scalar) 1d homogenous
matrix Matrix 2d homogenous
array One-, two or n-dimensional array 1d/2d/nd homogenous
list List 1d heterogeneous
data.frame Rectangular data 2d heterogeneous

Review: Data Frame Subsetting

  • In subsetting data frames the techniques of subsetting matrices and lists are combined
  • If you subset with a single vector, it behaves as a list
  • If you subset with two vectors, it behaves as a matrix
data_frame[row_indices, column_indices]
data_frame[row_indices, column_name(s)]
data_frame[column_indices]
data_frame[column_name(s)]
data_frame$column_name

Attributes

  • All R objects can have attributes that contain metadata about them.
  • Attributes can be thought of as named lists.
  • Names, dimensions and class are common examples of attributes.
  • They (and some other) have special functions for getting and setting them.

Names Attribute

v <- c(0, 1, 1, 0)
# To set names for vector elements we can use names() function
names(v) <- c("Housing Bill", "Pension Bill", "Health Bill", "EU Bill")
v
Housing Bill Pension Bill  Health Bill      EU Bill 
           0            1            1            0 
# Names of vector elements can be used for subsetting
v[c("Housing Bill", "Health Bill")]
Housing Bill  Health Bill 
           0            1 
# This is still a numeric vector, don't let the presence of names mislead you
v + 1
Housing Bill Pension Bill  Health Bill      EU Bill 
           1            2            2            1

Factors

  • Factors form the basis of categorical data analysis in R.
  • Values of nominal (categorical) variables represent categories rather than numeric data.
  • Internally, in R factor variables are represented by integer vectors.
  • With 2 additional attributes:
    • class() attribute which is set to factor
    • levels() attribute which defines allowed values

Factors Example

parties <- c("Labour", "Conservative", "Conservative", "Labour", "LibDem")
parties
[1] "Labour"       "Conservative" "Conservative" "Labour"       "LibDem"      
typeof(parties)
[1] "character"
class(parties)
[1] "character"
# We use factor() function to convert character vector into factor
# Only unique elements of character vector are considered as a level
parties_factor <- factor(parties)
parties_factor
[1] Labour       Conservative Conservative Labour       LibDem      
Levels: Conservative Labour LibDem

Factors Example Continued

parties_factor
[1] Labour       Conservative Conservative Labour       LibDem      
Levels: Conservative Labour LibDem
class(parties_factor)
[1] "factor"
# Note that the data type of this vector is integer 
typeof(parties_factor)
[1] "integer"
# and not character
is.character(parties_factor)
[1] FALSE

Factors Example Continued

# Note that R automatically sorted the categories alphabetically
levels(parties_factor)
[1] "Conservative" "Labour"       "LibDem"      
# You can change the reference category using relevel() function
parties_factor <- relevel(parties_factor, ref = "Labour")
levels(parties_factor)
[1] "Labour"       "Conservative" "LibDem"      
# Or define an arbitrary ordering of levels
# using levels argument in factor() function
parties_factor <- factor(
  parties_factor,
  levels = c("Labour", "LibDem", "Conservative")
)
levels(parties_factor)
[1] "Labour"       "LibDem"       "Conservative"

Factors Example Continued

# Note that there is no meaningful way of converting the original character vector
# into numeric, so NAs are introduced when we try to do so
as.numeric(parties)
[1] NA NA NA NA NA
# But this is a perfectly doable operation for factor, even though
# we loose some information in the form of level labels
as.numeric(parties_factor)
[1] 1 3 3 1 2

Crosstabulation

We can use table() function for tabulating a single variable as well as creating contingency tables (crosstabs).

df <- data.frame(
  party = sample(c("left", "right", "centre"), size = 50, replace = TRUE),
  vote = sample(c(0, 1), size = 50, replace = TRUE)
)
table(df$party, df$vote)
        
          0  1
  centre 11  7
  left    6  6
  right   8 12
table(df$vote, df$party)
   
    centre left right
  0     11    6     8
  1      7    6    12

Factors in Crosstabs

Implicitly, R treats variables (vectors) that are tabulated as factors.

df$party <- factor(
  df$party,
  levels = c("left", "right", "centre")
)
table(df$party, df$vote)
        
          0  1
  left    6  6
  right   8 12
  centre 11  7
table(df$vote, df$party)
   
    left right centre
  0    6     8     11
  1    6    12      7

Next

  • Tutorial:
    • Cross Tabulation
  • R Assignment 2 due:
    • 08:59 Tuesday, 25 February
  • Next week:
    • Visualisations