Visualizing Nominal Distributions with nomiShape
Data can be measured on different scales, which fundamentally affects
how they can be analyzed and visualized (Table 1). Four commonly
recognized measurement scales are nominal, ordinal, interval, and ratio.
Variables measured on continuous scales can take any value within a
range and are often modeled using continuous probability distributions,
whereas variables with a finite set of possible values follow discrete
distributions.
Among discrete and qualitative variables, nominal
variables are unique in that they classify observations into
categories without any inherent order, ranking, or numerical meaning.
Nominal categories indicate membership only: an observation either
belongs to a category or it does not. No information about magnitude,
distance, or direction is implied. Common examples of nominal variables
include species identities in an ecological community, political
attitudes or party affiliation in social surveys, behavioral categories
in ethological or psychological studies (e.g. play, aggression,
vigilance), word types in a linguistic corpus, or thematic codes in
qualitative research.
Although nominal variables lack intrinsic numeric structure, the
frequency with which categories occur provides rich
information about the organization of the system under study. Count data
derived from nominal variables can reveal patterns of dominance, rarity,
symmetry, and tail structure—features that are rarely formalized but are
often visually apparent. The nomiShape package is designed
to make these distributional properties explicit by combining centered
visualizations with quantitative indices and model-based comparisons
tailored specifically to nominal data.
Table 1. Summary of Nominal Data Characteristics and
Visualization and Analysis Tools in the nomiShape
package
| Variable Type |
Nominal (categorical, unordered) |
| Core Properties |
Discrete categories with no intrinsic order or numeric meaning |
| Typical Examples |
Species in a biological community; political attitudes
(e.g. conservative, liberal, undecided); behavioral categories
(e.g. play, aggression, grooming); word types in a text corpus;
qualitative themes or codes |
| What Can Be Counted |
Frequencies, proportions, dominance, rarity |
| What Cannot Be Computed |
Means, medians, variances, distances, or ranks derived from numeric
magnitude |
| Common Visualizations |
Standard bar plots (unordered or frequency-ranked) |
| Often-Ignored Distributional Structure |
Dominance, symmetry, central concentration, tail heaviness |
| Main Analytical Challenge |
Distributional “shape” exists but is difficult to formalize for
nominal data |
Visual Tools in nomiShape |
Centered Bar Plot, Centered Dot Plot, Ranked Bar Plot, Ranked Dot
Plot, Pareto Chart |
Analytical Tools in nomiShape |
Pielou’s evenness, Dominance index, Central concentration, Tail
index |
| Model-Based Shape Comparison |
AIC-based comparison of uniform, triangular, normal-like, and
exponential (Pareto-like) shapes |
| Design Philosophy |
Reveal latent distributional structure visually (via centering and
ranking), then formalize it analytically |
Handling nominal (categorical) data is an essential part of data
analysis. Almost every data science project involves working with such
variables, and students and practitioners alike should know how to
store, summarize, visualize, and manipulate them. Traditional
visualizations of nominal variables often use unordered bar plots or
frequency-sorted bar plots (from high to low), which emphasize category
counts but rarely provide insight into distributional structure. As a
result, concepts like symmetry, skewness, dominance, or tail
behaviour—commonly discussed for numerical variables—are seldom
considered for nominal data. However, exceptions include Pareto charts
and other ranked visualizations, which can highlight the “vital few”
categories following the 80:20 rule or reveal long-tailed distributions,
such as rank-abundance plots in ecology where typically most species are
relatively rare and a few are common. These visualizations allow
insights into categorical dominance and rarity patterns even for nominal
variables.
The nomiShape package is designed to further explore the
shape of nominal distributions. It offers multiple plotting functions,
including classic visualizations such as Pareto charts and ranked bar
plots, as well as novel centered bar and dot plots. These functions help
users understand frequency structures, dominance patterns, and
distributional characteristics of nominal variables, facilitating more
nuanced analysis of categorical data.
Plotting Shapes of Nominal Distributions
Ranked Bar Plots
Ranked bar plots order categories from the most frequent to the least
frequent, providing a clear view of category dominance and
distribution.
# Example usage of ranked_barplot
ranked_barplot(categories, "animal")
# Example usage of ranked_barplot
ranked_barplot(categories2, "animal")
# Example usage of ranked_barplot
ranked_barplot(categories3, "animal")
Ranked Dot Plots
Ranked dot plots display categories as points ordered from the most
frequent to the least frequent, allowing for easy comparison of category
frequencies.
# Example usage of ranked_dotplot
ranked_dotplot(categories, "animal", connect = TRUE)
# Example usage of ranked_dotplot
ranked_dotplot(categories2, "animal", connect = TRUE, shade = TRUE)
# Example usage of ranked_dotplot
ranked_dotplot(categories3, "animal", connect = FALSE, shade = TRUE)
Pareto Charts
Pareto charts combine bar plots and line graphs to highlight the most
significant categories in a nominal variable. They help identify the
“vital few” categories that contribute most to the overall
distribution.
# Example usage of pareto
pareto(categories3, "animal")
#> Category Freq cumulative cumulative_percentage
#> 1 Sea sponge 110 110 44.0
#> 2 Starfish 75 185 74.0
#> 3 Octopus 20 205 82.0
#> 4 Crab 12 217 86.8
#> 5 Squirrel 9 226 90.4
#> 6 Copepod 7 233 93.2
#> 7 Snail 6 239 95.6
#> 8 Pufferfish 5 244 97.6
#> 9 Whale 3 247 98.8
#> 10 Lobster 2 249 99.6
#> 11 Sea god 1 250 100.0
Centered Bar Plots
Centered bar plots arrange categories symmetrically around the
center, with the most frequent categories in the middle and less
frequent ones towards the edges. This layout helps to visualize the
distribution shape effectively.
# Example usage of centered_barplot
centered_barplot(categories, "animal")
# Example usage of centered_barplot
centered_barplot(categories2, "animal",scale = "percent")
# Example usage of centered_barplot
centered_barplot(categories3, "animal")
Centered Dot Plots
Centered dot plots display categories as points arranged
symmetrically around the center, with the most frequent categories in
the middle. Optionally, points can be connected with lines to highlight
trends.
# Example usage of centered_dotplot
centered_dotplot(categories, "animal",connect = TRUE,shade = TRUE)
# Example usage of centered_dotplot
centered_dotplot(categories2, "animal",connect = TRUE,shade = TRUE)
# Example usage of centered_dotplot
centered_dotplot(categories3, "animal",connect = TRUE,shade = TRUE)
Measuring Shapes of Nominal Distributions
Evenness
Pielou’s evenness quantifies how evenly individuals are distributed
across categories in a nominal variable.
# Example usage of pielou_evenness
pielou_evenness(categories, "animal")
#> [1] 0.9981314
# Example usage of pielou_evenness
pielou_evenness(categories2, "animal")
#> [1] 0.9462875
# Example usage of pielou_evenness
pielou_evenness(categories3, "animal")
#> [1] 0.6553931
Dominance Index
The dominance index quantifies the degree to which a few categories
dominate the distribution of a nominal variable.
# Example usage of dominance_index
dominance_index(categories, "animal")
#> [1] 0.091712
# Example usage of dominance_index
dominance_index(categories2, "animal")
#> [1] 0.113056
# Example usage of dominance_index
dominance_index(categories3, "animal")
#> [1] 0.295584
Central Concentration
The central concentration quantifies how concentrated the
distribution of a nominal variable is around its most frequent
categories.
# Example usage of central_concentration
central_concentration(categories, "animal")
#> [1] 0.3
# Example usage of central_concentration
central_concentration(categories2, "animal")
#> [1] 0.448
# Example usage of central_concentration
central_concentration(categories3, "animal")
#> [1] 0.82
Tail Index
The tail index quantifies the proportion of categories contributing
to the lower part of the distribution, useful for identifying long-tail
structures in nominal data. By default, it uses a threshold of 0.8,
following the Pareto principle, but this can be adjusted as needed.
# Example usage of tail_index
tail_index(categories, "animal")
#> [1] 0.1818182
# Example usage of tail_index
tail_index(categories2, "animal", threshold = 0.9)
#> [1] 0.1818182
# Example usage of tail_index
tail_index(categories3, "animal", threshold = 0.75)
#> [1] 0.7272727
