# Chapter 10 Visualization14

### Motivation: The Law of the Census

In this module, let's visualize some cross-sectional stats with an actual Census. Then, we'll do an example on time trends with Supreme Court ideal points.

Why care about the Census? The Census is one of the fundamental acts of a government. See the Law Review article by Persily (2011), "The Law of the Census."15 The Census is government's primary tool for apportionment (allocating seats to districts), appropriations (allocating federal funding), and tracking demographic change. See for example Hochschild and Powell (2008) on how the categorizations of race in the Census during 1850-1930.16 Notice also that both of these pieces are not inherently "quantitative" --- the Persily article is a Law Review and the Hochschild and Powell article is on American Historical Development --- but data analysis would be certainly relevant.

Time series data is a common form of data in social science data, and there is growing methodological work on making causal inferences with time series.17 We will use the the ideological estimates of the Supreme court.

### Where are we? Where are we headed?

Up till now, you should have covered:

• The R Visualization and Programming primers at https://rstudio.cloud/primers/
• Reading and handling data
• Matrices and Vectors
• What does : mean in R? What about ==? ,?, != , &, |, %in%
• What does %>% do?

Today we'll cover:

• Visualization
• A bit of data wrangling

### Check your understanding

• How do you make a barplot, in base-R and in ggplot?
• How do you add layers to a ggplot?
• How do you change the axes of a ggplot?
• How do you make a histogram?
• How do you make a graph that looks like this?

## 10.1 Read data

First, the census. Read in a subset of the 2010 Census that we looked at earlier. This time, it is in Rds form.

cen10 <- readRDS("data/input/usc2010_001percent.Rds")

The data comes from IPUMS18, a great source to extract and analyze Census and Census-conducted survey (ACS, CPS) data.

## 10.2 Counting

How many people are in your sample?

nrow(cen10)
## [1] 30871

This and all subsequent tasks involve manipulating and summarizing data, sometimes called "wrangling". As per last time, there are both "base-R" and "tidyverse" approaches.

We have already seen several functions from the tidyverse:

• select selects columns
• filter selects rows based on a logical (boolean) statement
• slice selects rows based on the row number
• arrange reordered the rows in descending order.

In this visualization section, we'll make use of the pair of functions group_by() and summarize().

## 10.3 Tabulating

Summarizing data is the key part of communication; good data viz gets the point across.19 Summaries of data come in two forms: tables and figures.

Here are two ways to count by group, or to tabulate.

In base-R Use the table function, that provides how many rows exist for an unique value of the vector (remember unique from yesterday?)

### 10.4.2 ggplot

A popular alternative a ggplot graphics, that you were introduced to in the tutorial. gg stands for grammar of graphics by Hadley Wickham, and it has a new semantics of explaining graphics in R. Again, first let's set up the data.

Although the tutorial covered making scatter plots as the first cut, often data requires summaries before they made into graphs.

For this example, let's group and count first like we just did. But assign it to a new object.

grp_race <- count(cen10, race)

We will now plot this grouped set of numbers. Recall that the ggplot() function takes two main arguments, data and aes.

1. First enter a single dataframe from which you will draw a plot.
2. Then enter the aes, or aesthetics. This defines which variable in the data the plotting functions should take for pre-set dimensions in graphics. The dimensions x and y are the most important. We will assign race and count to them, respectively,
3. After you close ggplot() .. add layers by the plus sign. A geom is a layer of graphical representation, for example geom_histogram renders a histogram, geom_point renders a scatter plot. For a barplot, we can use geom_col()

What is the right geometry layer to make a barplot? Turns out:

ggplot(data = grp_race, aes(x = race, y = n)) + geom_col()

## 10.5 Improving your graphics

Adjusting your graphics to make the point clear is an important skill. Here is a base-R example of showing the same numbers but with a different design, in a way that aims to maximize the "data-to-ink ratio".

par(oma = c(1, 11, 1, 1))
barplot(sort(table(cen10race)), # sort numbers horiz = TRUE, # flip border = NA, # border is extraneous xlab = "Number in Race Category", bty = "n", # no box las = 1) # alignment of axis labels is horizontal Notice that we applied the sort() function to order the bars in terms of their counts. The default ordering of a categorical variable / factor is alphabetical. Alphabetical ordering is uninformative and almost never the way you should order variables. In ggplot you might do this by: library(forcats) grp_race_ordered <- arrange(grp_race, n) %>% mutate(race = as_factor(race)) ggplot(data = grp_race_ordered, aes(x = race, y = n)) + geom_col() + coord_flip() + labs(y = "Number in Race Category", x = "", caption = "Source: 2010 U.S. Census sample") The data ink ratio was popularized by Ed Tufte (originally a political economy scholar who has recently become well known for his data visualization work). See Tufte (2001), The Visual Display of Quantitative Information and his website https://www.edwardtufte.com/tufte/. For a R and ggplot focused example using social science examples, check out Healy (2018), Data Visualization: A Practical Introduction with a draft at https://socviz.co/20. There are a growing number of excellent books on data visualization. ## 10.6 Cross-tabs Visualizations and Tables each have their strengths. A rule of thumb is that more than a dozen numbers on a table is too much to digest, but less than a dozen is too few for a figure to be worth it. Let's look at a table first. A cross-tab is counting with two types of variables, and is a simple and powerful tool to show the relationship between multiple variables. xtab_race_state <- table(cen10state, cen10\$race)
xtab_race_state
##
##                        American Indian or Alaska Native Black/Negro Chinese
##   Alabama                                             2         128       1
##   Alaska                                             11           6       0
##   Arizona                                            28          23       1
##   Arkansas                                            1          45       0
##   California                                         42         253     141
##   Colorado                                            7          26       3
##   Connecticut                                         1          39       7
##   Delaware                                            3          28       1
##   District of Columbia                                0          35       0
##   Florida                                             9         304       4
##   Georgia                                             2         304       5
##   Hawaii                                              0           0       2
##   Idaho                                               2           0       0
##   Illinois                                            5         194       6
##   Indiana                                             2          66       3
##   Iowa                                                0           9       1
##   Kansas                                              2          24       2
##   Kentucky                                            2          35       2
##   Louisiana                                           3         161       1
##   Maine                                               0           4       1
##   Maryland                                            2         177       4
##   Massachusetts                                       5          38      15
##   Michigan                                            5         147       8
##   Minnesota                                           6          25       5
##   Mississippi                                         1         116       0
##   Missouri                                            4          74       2
##   Montana                                             8           0       0
##   Nebraska                                            2          11       0
##   Nevada                                              6          15       6
##   New Hampshire                                       1           1       1
##   New Jersey                                          0         130      19
##   New Mexico                                         21           3       1
##   New York                                           13         305      55
##   North Carolina                                     12         220       4
##   North Dakota                                        4           1       0
##   Ohio                                                1         122       5
##   Oklahoma                                           21          20       0
##   Oregon                                              5           5       4
##   Pennsylvania                                        2         156      10
##   Rhode Island                                        2           3       0
##   South Carolina                                      2         120       1
##   South Dakota                                        7           1       0
##   Tennessee                                           0          97       0
##   Texas                                              14         316      15
##   Utah                                                8           0       1
##   Vermont                                             0           2       0
##   Virginia                                            0         171       8
##   Washington                                         14          20       9
##   West Virginia                                       0           5       0
##   Wisconsin                                           6          27       0
##   Wyoming                                             1           1       0
##
##                        Japanese Other Asian or Pacific Islander Other race, nec
##   Alabama                     0                               3               8
##   Alaska                      0                               5               2
##   Arizona                     0                              12              74
##   Arkansas                    0                               1              11
##   California                 27                             359             585
##   Colorado                    0                              10              28
##   Connecticut                 0                              16              20
##   Delaware                    0                               4               5
##   District of Columbia        0                               1               1
##   Florida                     1                              24              72
##   Georgia                     0                              35              35
##   Hawaii                     16                              35               0
##   Idaho                       1                               0               8
##   Illinois                    3                              53              75
##   Indiana                     0                               8              20
##   Iowa                        0                               4              10
##   Kansas                      0                               8               6
##   Kentucky                    0                               4               5
##   Louisiana                   0                               5               7
##   Maine                       0                               1               0
##   Maryland                    1                              12              28
##   Massachusetts               2                              28              26
##   Michigan                    1                              23               8
##   Minnesota                   1                              28              13
##   Mississippi                 0                               3               2
##   Missouri                    0                               9               6
##   Montana                     0                               0               1
##   Nebraska                    0                               5               6
##   Nevada                      2                              15              41
##   New Hampshire               1                               3               1
##   New Jersey                  2                              65              69
##   New Mexico                  1                               1              23
##   New York                    3                              68             154
##   North Carolina              1                              12              40
##   North Dakota                0                               0               0
##   Ohio                        2                              17               7
##   Oklahoma                    0                               5              15
##   Oregon                      0                              11              21
##   Pennsylvania                1                              28              30
##   Rhode Island                0                               4               6
##   South Carolina              0                               4               6
##   South Dakota                1                               1               2
##   Tennessee                   0                              13              13
##   Texas                       2                              92             253
##   Utah                        1                               6              14
##   Vermont                     0                               0               1
##   Virginia                    2                              29              29
##   Washington                  4                              46              37
##   West Virginia               0                               0               0
##   Wisconsin                   1                              11              13
##   Wyoming                     0                               2               2
##
##                        Three or more major races Two major races White
##   Alabama                                      1               8   344
##   Alaska                                       0              15    37
##   Arizona                                      2              11   485
##   Arkansas                                     1               2   247
##   California                                  14             174  2168
##   Colorado                                     1              22   401
##   Connecticut                                  1               7   284
##   Delaware                                     1               1    66
##   District of Columbia                         0               2    21
##   Florida                                      2              42  1435
##   Georgia                                      1              21   587
##   Hawaii                                      14              27    39
##   Idaho                                        1               6   129
##   Illinois                                     2              35   856
##   Indiana                                      1               6   514
##   Iowa                                         0               8   287
##   Kansas                                       0               8   237
##   Kentucky                                     1               9   357
##   Louisiana                                    0               6   273
##   Maine                                        0               1   117
##   Maryland                                     1              13   302
##   Massachusetts                                0              18   515
##   Michigan                                     2              23   792
##   Minnesota                                    1              10   483
##   Mississippi                                  2               1   167
##   Missouri                                     2              14   516
##   Montana                                      0               0    88
##   Nebraska                                     0               5   155
##   Nevada                                       1              16   171
##   New Hampshire                                0               1   129
##   New Jersey                                   3              25   589
##   New Mexico                                   1               6   146
##   New York                                     8              51  1220
##   North Carolina                               2              20   648
##   North Dakota                                 0               1    46
##   Ohio                                         3              20   931
##   Oklahoma                                     3              24   266
##   Oregon                                       4               9   279
##   Pennsylvania                                 1              27  1045
##   Rhode Island                                 1               4    74
##   South Carolina                               1               6   325
##   South Dakota                                 0               2    72
##   Tennessee                                    0               9   474
##   Texas                                        2              71  1792
##   Utah                                         0               8   255
##   Vermont                                      0               4    59
##   Virginia                                     4              24   548
##   Washington                                   2              33   524
##   West Virginia                                0               3   168
##   Wisconsin                                    1               8   497
##   Wyoming                                      0               2    47

Another function to make a cross-tab is the xtabs command, which uses formula notation.

xtabs(~ state + race, cen10)

What if we care about proportions within states, rather than counts? Say we'd like to compare the racial composition of a small state (like Delaware) and a large state (like California). In fact, most tasks of inference is about the unobserved population, not the observed data --- and proportions are estimates of a quantity in the population.

One way to transform a table of counts to a table of proportions is the function prop.table. Be careful what you want to take proportions of -- this is set by the margin argument. In R, the first margin (margin = 1) is rows and the second (margin = 2) is columns.

ptab_race_state <- prop.table(xtab_race_state, margin = 2)

Check out each of these table objects in your console and familiarize yourself with the difference.

## 10.7 Composition Plots

How would you make the same figure with ggplot()? First, we want a count for each state $$\times$$ race combination. So group by those two factors and count how many observations are in each two-way categorization. group_by() can take any number of variables, separated by commas.

grp_race_state <- cen10 %>%
count(race, state)

Can you tell from the code what grp_race_state will look like?

# run on your own
grp_race_state

Now, we want to tell ggplot2 something like the following: I want bars by state, where heights indicate racial groups. Each bar should be colored by the race. With some googling, you will get something like this:

ggplot(data = grp_race_state, aes(x =  state, y = n,  fill = race)) +
geom_col(position = "fill") + # the position is determined by the fill ae
scale_fill_brewer(name = "Census Race", palette = "OrRd", direction = -1) + # choose palette
coord_flip() + # flip axes
scale_y_continuous(labels = percent) + # label numbers as percentage
labs(y = "Proportion of Racial Group within State",
x = "",
source = "Source: 2010 Census  sample") +
theme_minimal()

## 10.8 Line graphs

Line graphs are useful for plotting time trends.

The Census does not track individuals over time. So let's take up another example: The U.S. Supreme Court. Take the dataset justices_court-median.csv.

This data is adapted from the estimates of Martin and Quinn on their website http://mqscores.lsa.umich.edu/.21

justice <- read_csv("data/input/justices_court-median.csv")

What does the data look like? How do you think it is organized? What does each row represent?

justice
## # A tibble: 746 x 7
##     term justice_id justice    idealpt idealpt_sd median_idealpt median_justice
##    <dbl>      <dbl> <chr>        <dbl>      <dbl>          <dbl> <chr>
##  1  1937         67 McReynolds   3.44       0.54          -0.568 Brandeis
##  2  1937         68 Brandeis    -0.612      0.271         -0.568 Brandeis
##  3  1937         71 Sutherland   1.59       0.549         -0.568 Brandeis
##  4  1937         72 Butler       2.06       0.426         -0.568 Brandeis
##  5  1937         74 Stone       -0.774      0.259         -0.568 Brandeis
##  6  1937         75 Hughes2     -0.368      0.232         -0.568 Brandeis
##  7  1937         76 O. Roberts   0.008      0.228         -0.568 Brandeis
##  8  1937         77 Cardozo     -1.59       0.634         -0.568 Brandeis
##  9  1937         78 Black       -2.90       0.334         -0.568 Brandeis
## 10  1937         79 Reed        -1.06       0.342         -0.568 Brandeis
## # … with 736 more rows

As you might have guessed, these data can be shown in a time trend from the range of the term variable. As there are only nine justices at any given time and justices have life tenure, there times on the court are staggered. With a common measure of "preference", we can plot time trends of these justices ideal points on the same y-axis scale.

ggplot(justice, aes(x = term, y = idealpt)) +
geom_line()

Why does the above graph not look like the the put in the beginning? Fix it by adding just one aesthetic to the graph.

# enter a correction that draws separate lines by group.

If you got the right aesthetic, this seems to "work" off the shelf. But take a moment to see why the code was written as it is and how that maps on to the graphics. What is the group aesthetic doing for you?

Now, this graphic already indicates a lot, but let's improve the graphics so people can actually read it. This is left for a Exercise.

As social scientists, we should also not forget to ask ourselves whether these numerical measures are fit for what we care about, or actually succeeds in measuring what we'd like to measure. The estimation of these "ideal points" is a subfield of political methodology beyond this prefresher. For more reading, skim through the original paper by Martin and Quinn (2002).22 Also for a methodological discussion on the difficulty of measuring time series of preferences, check out Bailey (2013).23

## Exercises

In the time remaining, try the following exercises. Order doesn't matter.

### 1: Rural states

Make a well-labelled figure that plots the proportion of the state's population (as per the census) that is 65 years or older. Each state should be visualized as a point, rather than a bar, and there should be 51 points, ordered by their value. All labels should be readable.

# Enter yourself

### 2: The swing justice

Using the justices_court-median.csv dataset and building off of the plot that was given, make an improved plot by implementing as many of the following changes (which hopefully improves the graph):

• Label axes
• Use a black-white background.
• Change the breaks of the x-axis to print numbers for every decade, not just every two decades.
• Plots each line in translucent gray, so the overlapping lines can be visualized clearly. (Hint: in ggplot the alpha argument controls the degree of transparency)
• Limit the scale of the y-axis to [-5, 5] so that the outlier justice in the 60s is trimmed and the rest of the data can be seen more easily (also, who is that justice?)
• Plot the ideal point of the justice who holds the "median" ideal point in a given term. To distinguish this with the others, plot this line separately in a very light red below the individual justice's lines.
• Highlight the trend-line of only the nine justices who are currently sitting on SCOTUS. Make sure this is clearer than the other past justices.
• Add the current nine justice's names to the right of the endpoint of the 2016 figure, alongside their ideal point.
• Make sure the text labels do not overlap with each other for readability using the ggrepel package.
• Extend the x-axis label to about 2020 so the text labels of justices are to the right of the trend-lines.
• Add a caption to your text describing the data briefly, as well as any features relevant for the reader (such as the median line and the trimming of the y-axis)
# Enter yourself

### 3: Don't sort by the alphabet

The Figure we made that shows racial composition by state has one notable shortcoming: it orders the states alphabetically, which is not particularly useful if you want see an overall pattern, without having particular states in mind.

Find a way to modify the figures so that the states are ordered by the proportion of White residents in the sample.

# Enter yourself

### 4 What to show and how to show it

As a student of politics our goal is not necessarily to make pretty pictures, but rather make pictures that tell us something about politics, government, or society. If you could augment either the census dataset or the justices dataset in some way, what would be an substantively significant thing to show as a graphic?

1. Module originally written by Shiro Kuriwaki

2. Persily, Nathaniel. 2011. "The Law of the Census: How to Count, What to Count, Whom to Count, and Where to Count Them.”. Cardozo Law Review 32(3): 755–91.

3. Hochschild, Jennifer L., and Brenna Marea Powell. 2008. "Racial Reorganization and the United States Census 1850–1930: Mulattoes, Half-Breeds, Mixed Parentage, Hindoos, and the Mexican Race.". Studies in American Political Development 22(1): 59–96.

4. Kastellec, Jonathan P., and Eduardo L. Leoni. 2007. "Using Graphs Instead of Tables in Political Science.". Perspectives on Politics 5 (4): 755–71.

5. Healy, Kieran. forthcoming. Data Visualization: A Practical Introduction. Princeton University Press

6. This exercise inspired from Princeton's R Camp Assignment.