---
title: "Types, Marks, and Encodings"
description: | 
  Tying together the introductions to ggplot2 and vega-lite, using the common
  language of encodings.
author:
  - name: Kris Sankaran
    affiliation: UW Madison
date: 01-28-2021
output:
  distill::distill_article:
    self_contained: false
---

_[Reading](https://observablehq.com/@uwdata/data-types-graphical-marks-and-visual-encoding-channels?collection=@uwdata/visualization-curriculum), [Recording](https://mediaspace.wisc.edu/media/1_ooup7c7n), [Rmarkdown](https://raw.githubusercontent.com/krisrs1128/stat479/master/_posts/2021-01-18-week1-4/week1-4.Rmd)_

The reason that the ggplot2 and vega-lite packages feel similar is that they are
based on the same underlying ideas,

* Each observation (row) within a dataset corresponds to a geometric mark in a
visualization.
* Important attributes (columns) of an observation within a dataset can be
encoded by properties of visual marks.

This encoding of rows as marks and columns as properties of the marks is
illustrated in the toy diagram below.

![](assets/encoding_illustration.png)

In fact, we can roughly translate the function names between the two packages,

* `geom_*` →  `mark*`
* `aes` → `vl.encode()`
* `scale_*` → `scale()`
* `labs` → `title()`

A good visualization makes it easy to visually compare the relevant attributes
across observations. A challenge is that there are often many possible marks and
encodings for any given comparison. It's also difficult to know which
comparisons are actually of interest. For these reasons, we're going to want to
build up a vocabulary of marks and encodings.

![](assets/example_encodings.png)

## Field types

To identify good encodings, it can often help to first what the types of each
field are.

* Nominal: These are fields that allow identity comparisons between observations
(is $A = B$?), but don't come with any notion of order.
  - City region, country name, movie genres, file types, ...
* Ordinal: These are fields that allow ordering comparisons between observations
(is $A > B$?), but don't let you quantify the degree of difference.
  - Shirt size, sports team rankings, order of appearance of characters on TV show
* Quantitative: These are field types that let you make distance comparisons
between observations. For interval data, absolute comparisons can be made ($A -
B$), while for ratio data, only relative ones ($\frac{A}{B}$) are possible.
  - Temperature, stock price, number of drinks sold in a coffee shop per day

This is not an exhaustive list, and there are subtleties,

* The same field could be treated as nominal, ordinal, or quantitative depending
on the context. Age could be nominal (underage or overage), ordinal (gen Z,
millenial, ...), or quantitative.
* A given field might be thought of hierarchically. There might be interesting
patterns at the city, county, or region level -- what seems like a single column
can become the source for multiple derived fields.
* Even though temporal fields can be thought of as quantitative, they come with
their own conventions. For example, the hour - week - month hierarchy is a
natural one for temporal data.

It's worth highlighting that, even if a particular encoding *could* be used for
a given data type, different encodings have different effectiveness. When trying
to encoding several data fields at once, a choice of one encoding over another
will implicitly prioritize certain comparisons over others. 

For example, in the figure below (Figure 5.8
[here](https://search.library.wisc.edu/catalog/9911196629502121)), the same two
numbers are encoded using many different visual properties -- position on a
shared $y$-axis, position on distinct $y$-axes, etc. -- and study participants
were asked to gauge the difference in the numbers. People were best at comparing
positions on a common scale, and worst at distinguishing differences in areas.

![](assets/encoding_effectiveness.png)

Here is a similar example. In the left four panels, a nominal field is encoded
using color (left two) and shape (middle two). The red circles are easiest to
find in the left two. In the right two panels, two nominal fields are encoded,
using both shape and color. It's much harder to find the red circle -- you have
to scan over the entire image to find it, which you didn't have to do at all for
the first two panels.

![](assets/encoding_effectiveness_2.png)

Implicit in this discussion is that there is never any "perfect" visualization
for a given dataset -- the quality of a visualization is a function of its
intended purpose. What comparisons do you want to facilitate? The choice of
encoding will strongly affect the types of comparisons that are easy to perform.