Two Categorical Variables
Harold Nelson
10/3/2022
Setup
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## ✔ tibble 3.1.8 ✔ dplyr 1.0.10
## ✔ tidyr 1.2.1 ✔ stringr 1.4.1
## ✔ readr 2.1.2 ✔ forcats 0.5.2
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## ✖ dplyr::filter() masks stats::filter()
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library(socviz)
library(gmodels)
library(vcd)
## Loading required package: grid
load("~/Dropbox/Documents/SMU/CSC 463/cdc2.Rdata")
Religion and Region
These are two categorical variables and we want to use them as an
example to study different ways of displaying the relationship between
them. The usual non-visual way to do this is called a “cross-tab.” The
standard table function provides a very rudimentary version.
table(gss_sm$bigregion,gss_sm$religion)
##
## Protestant Catholic Jewish None Other
## Northeast 158 162 27 112 28
## Midwest 325 172 3 157 33
## South 650 160 11 170 50
## West 238 155 10 180 48
Note that these numbers are different from those in the book. The
version of the data is apparently different, probably reflecting a
difference in years.
Fancy Crosstab
There is a more elaborate version, CrossTable, in the gmodels
package. Interpreting the output requires a layout of each cell in the
table provided in the upper left corner.
CrossTable(gss_sm$bigregion,gss_sm$religion)
##
##
## Cell Contents
## |-------------------------|
## | N |
## | Chi-square contribution |
## | N / Row Total |
## | N / Col Total |
## | N / Table Total |
## |-------------------------|
##
##
## Total Observations in Table: 2849
##
##
## | gss_sm$religion
## gss_sm$bigregion | Protestant | Catholic | Jewish | None | Other | Row Total |
## -----------------|------------|------------|------------|------------|------------|------------|
## Northeast | 158 | 162 | 27 | 112 | 28 | 487 |
## | 24.877 | 23.502 | 38.340 | 0.362 | 0.025 | |
## | 0.324 | 0.333 | 0.055 | 0.230 | 0.057 | 0.171 |
## | 0.115 | 0.250 | 0.529 | 0.181 | 0.176 | |
## | 0.055 | 0.057 | 0.009 | 0.039 | 0.010 | |
## -----------------|------------|------------|------------|------------|------------|------------|
## Midwest | 325 | 172 | 3 | 157 | 33 | 690 |
## | 0.149 | 1.397 | 7.080 | 0.335 | 0.788 | |
## | 0.471 | 0.249 | 0.004 | 0.228 | 0.048 | 0.242 |
## | 0.237 | 0.265 | 0.059 | 0.254 | 0.208 | |
## | 0.114 | 0.060 | 0.001 | 0.055 | 0.012 | |
## -----------------|------------|------------|------------|------------|------------|------------|
## South | 650 | 160 | 11 | 170 | 50 | 1041 |
## | 44.346 | 25.093 | 3.128 | 13.953 | 1.129 | |
## | 0.624 | 0.154 | 0.011 | 0.163 | 0.048 | 0.365 |
## | 0.474 | 0.247 | 0.216 | 0.275 | 0.314 | |
## | 0.228 | 0.056 | 0.004 | 0.060 | 0.018 | |
## -----------------|------------|------------|------------|------------|------------|------------|
## West | 238 | 155 | 10 | 180 | 48 | 631 |
## | 14.194 | 0.882 | 0.149 | 13.426 | 4.641 | |
## | 0.377 | 0.246 | 0.016 | 0.285 | 0.076 | 0.221 |
## | 0.174 | 0.239 | 0.196 | 0.291 | 0.302 | |
## | 0.084 | 0.054 | 0.004 | 0.063 | 0.017 | |
## -----------------|------------|------------|------------|------------|------------|------------|
## Column Total | 1371 | 649 | 51 | 619 | 159 | 2849 |
## | 0.481 | 0.228 | 0.018 | 0.217 | 0.056 | |
## -----------------|------------|------------|------------|------------|------------|------------|
##
##
Note that the column and row percents, “marginals” in Healy’s
terminology closely match the results in Healy’s tables, 5.1 and
5.2.
Exercise
Do a crosstable of gender and genhlth in cdc2.
Solution
CrossTable(cdc2$gender,cdc2$genhlth)
##
##
## Cell Contents
## |-------------------------|
## | N |
## | Chi-square contribution |
## | N / Row Total |
## | N / Col Total |
## | N / Table Total |
## |-------------------------|
##
##
## Total Observations in Table: 19997
##
##
## | cdc2$genhlth
## cdc2$gender | excellent | very good | good | fair | poor | Row Total |
## -------------|-----------|-----------|-----------|-----------|-----------|-----------|
## m | 2298 | 3380 | 2721 | 884 | 283 | 9566 |
## | 2.214 | 0.628 | 0.017 | 6.933 | 5.155 | |
## | 0.240 | 0.353 | 0.284 | 0.092 | 0.030 | 0.478 |
## | 0.493 | 0.485 | 0.480 | 0.438 | 0.418 | |
## | 0.115 | 0.169 | 0.136 | 0.044 | 0.014 | |
## -------------|-----------|-----------|-----------|-----------|-----------|-----------|
## f | 2359 | 3590 | 2953 | 1135 | 394 | 10431 |
## | 2.030 | 0.576 | 0.015 | 6.359 | 4.727 | |
## | 0.226 | 0.344 | 0.283 | 0.109 | 0.038 | 0.522 |
## | 0.507 | 0.515 | 0.520 | 0.562 | 0.582 | |
## | 0.118 | 0.180 | 0.148 | 0.057 | 0.020 | |
## -------------|-----------|-----------|-----------|-----------|-----------|-----------|
## Column Total | 4657 | 6970 | 5674 | 2019 | 677 | 19997 |
## | 0.233 | 0.349 | 0.284 | 0.101 | 0.034 | |
## -------------|-----------|-----------|-----------|-----------|-----------|-----------|
##
##
Visualize a Crosstab
Our goal in this course is to master ways of displaying the
information visually.
Before getting into Healy’s methods, I’ll demonstrate two simple
methods based on the idea of a scatterplot of two categorical variables.
The simple scatterplot of two categorical results is not very useful.
Try this and see what you get.
Answer
gss_sm %>% select(religion,bigregion) %>% ggplot(aes(x=bigregion,y=religion)) +
geom_point()
Method 1
The first of the two simple methods uses the raw data and simply
replaces geom_point() with geom_jitter(). Manual adjustment of the alpha
and size parameters may improve on the result.
Try this.
Answer
gss_sm %>% select(religion,bigregion) %>% ggplot(aes(x=bigregion,y=religion)) +
geom_jitter(alpha=.5,size=.5)
Exercise
Adjust size and alpha to get a result you find effective.
Another Method
My second method is to use dplyr to count the observations in the
cells of the table and produce a scatterplot of the categorical
variables. The counts are mapped to the size of the dots in the
scatterplot.
gss_sm %>%
select(religion,bigregion) %>%
group_by(religion, bigregion) %>%
summarize(count = n()) %>%
ungroup() %>%
ggplot(aes(x=bigregion,y=religion,size=count)) +
geom_point()
## `summarise()` has grouped output by 'religion'. You can override using the
## `.groups` argument.
A variant on this idea is to map count to color instead of size. This
requires larger size dots to have any hope of success.
gss_sm %>%
select(religion,bigregion) %>%
group_by(religion, bigregion) %>%
summarize(count = n()) %>%
ungroup() %>%
ggplot(aes(x=bigregion,y=religion,color=count)) + geom_point(size=9)
## `summarise()` has grouped output by 'religion'. You can override using the
## `.groups` argument.
Mosaic Plots
The mosaic plot is another alernative for looking at relationships
among categorical variables. The best version is in the vcd
(Visualization of Categorical Data) package. Here’s a look at our
relationship.
mosaic(~religion + bigregion,data=gss_sm)
Exercise
Use a mosaic plot to explore the relationship between gender and
genhlth in cdc2.
Solution
mosaic(~gender + genhlth,data=cdc2)
And flipped
mosaic(~genhlth + gender,data=cdc2)
Discussion
Do any of these methods work? which do you prefer?
Healy’s rel_by_region
rel_by_region <- gss_sm %>%
group_by(bigregion, religion) %>%
summarize(N = n()) %>%
mutate(freq = N / sum(N),
pct = round((freq*100), 0))
## `summarise()` has grouped output by 'bigregion'. You can override using the
## `.groups` argument.
## # A tibble: 10 × 5
## # Groups: bigregion [2]
## bigregion religion N freq pct
## <fct> <fct> <int> <dbl> <dbl>
## 1 Northeast Protestant 158 0.324 32
## 2 Northeast Catholic 162 0.332 33
## 3 Northeast Jewish 27 0.0553 6
## 4 Northeast None 112 0.230 23
## 5 Northeast Other 28 0.0574 6
## 6 Northeast <NA> 1 0.00205 0
## 7 Midwest Protestant 325 0.468 47
## 8 Midwest Catholic 172 0.247 25
## 9 Midwest Jewish 3 0.00432 0
## 10 Midwest None 157 0.226 23
Note that there is an alternative choice, region with religion. Do
this as an exercise before you look at the next slide..
My region_by_rel
region_by_rel <- gss_sm %>%
group_by(religion,bigregion) %>%
summarize(N = n()) %>%
mutate(freq = N / sum(N),
pct = round((freq*100), 0))
## `summarise()` has grouped output by 'religion'. You can override using the
## `.groups` argument.
## # A tibble: 10 × 5
## # Groups: religion [3]
## religion bigregion N freq pct
## <fct> <fct> <int> <dbl> <dbl>
## 1 Protestant Northeast 158 0.115 12
## 2 Protestant Midwest 325 0.237 24
## 3 Protestant South 650 0.474 47
## 4 Protestant West 238 0.174 17
## 5 Catholic Northeast 162 0.250 25
## 6 Catholic Midwest 172 0.265 27
## 7 Catholic South 160 0.247 25
## 8 Catholic West 155 0.239 24
## 9 Jewish Northeast 27 0.529 53
## 10 Jewish Midwest 3 0.0588 6
Note the difference.
Healy’s First Plot
p <- ggplot(rel_by_region, aes(x = bigregion, y = pct, fill = religion))
p + geom_col(position = "dodge2") +
labs(x = "Region",y = "Percent", fill = "Religion") +
theme(legend.position = "top")
Trivial Exercise
What is the difference if you set position to dodge instead of
dodge2?
Answer
p <- ggplot(rel_by_region, aes(x = bigregion, y = pct, fill = religion))
p + geom_col(position = "dodge") +
labs(x = "Region",y = "Percent", fill = "Religion") +
theme(legend.position = "top")
## Another Trivial Exercise
What does the graph look like if you use geom_point() instead of
geom_col(). Think for a minute before you do this.
Answer
p <- ggplot(rel_by_region, aes(x = bigregion, y = pct))
p + geom_point(aes(color = religion),size=4) +
labs(x = "Region",y = "Percent", fill = "Religion") +
theme(legend.position = "top")
Note that since the default plot character is a solid dot, you must
use color instead of fill to get the color to show. There is some
overplotting. Would jitter help? Would a smaller or larger dot be
preferred? Experiment!
Answer
p <- ggplot(rel_by_region, aes(x = bigregion, y = pct))
p + geom_jitter(aes(color = religion),size=4) +
labs(x = "Region",y = "Percent", fill = "Religion") +
theme(legend.position = "top")
My First Plot (Exercise)
Repeat the graphics above reversing the roles of region and religion.
Produce the dodge2 geom_col() and the corresponding geom_point.
Answer
p <- ggplot(region_by_rel, aes(x = religion, y = pct, fill = bigregion))
p + geom_col(position = "dodge2") +
labs(x = "Religion",y = "Percent", fill = "Region") +
theme(legend.position = "top")
Exercise
Try geom_jitter instead of geom_col.
Answer
p <- ggplot(region_by_rel, aes(x = religion, y = pct))
p + geom_jitter(aes(color = bigregion),size=4) +
labs(x = "Religion",y = "Percent", fill = "Region") +
theme(legend.position = "top")
Healy’s Facet Example
p <- ggplot(rel_by_region, aes(x = religion, y = pct, fill = religion))
p + geom_col(position = "dodge2") +
labs(x = NULL, y = "Percent", fill = "Religion") +
guides(fill = FALSE) +
coord_flip() +
facet_grid(~ bigregion)
## Warning: `guides(<scale> = FALSE)` is deprecated. Please use `guides(<scale> =
## "none")` instead.
Is there any difference if we use facet_wrap() with nrow=1 instead of
facet_grid()?
Answer
p <- ggplot(rel_by_region, aes(x = religion, y = pct, fill = religion))
p + geom_col(position = "dodge2") +
labs(x = NULL, y = "Percent", fill = "Religion") +
guides(fill = FALSE) +
coord_flip() +
facet_wrap(~ bigregion,nrow=1)
## Warning: `guides(<scale> = FALSE)` is deprecated. Please use `guides(<scale> =
## "none")` instead.
Exercise
Repeat this with the roles of religion and region reversed.
Answer
p <- ggplot(region_by_rel, aes(x = bigregion, y = pct, fill = bigregion))
p + geom_col(position = "dodge2") +
labs(x = NULL, y = "Percent", fill = "bigregion") +
guides(fill = FALSE) +
coord_flip() +
facet_grid(~ religion)
## Warning: `guides(<scale> = FALSE)` is deprecated. Please use `guides(<scale> =
## "none")` instead.
We started by examining visualizations which emphasized symmetry
between religion and region. Could thsi be done by with facet_grid(),
putting a simple block to represent the count in each cell of the grid.
In effect, this would use the grid to make the scatterplot. Try it.
Answer
rr = gss_sm %>%
select(religion,bigregion) %>%
group_by(religion, bigregion) %>%
summarize(count = n()) %>%
ungroup() %>%
mutate(relreg = " ")
## `summarise()` has grouped output by 'religion'. You can override using the
## `.groups` argument.
ggplot(data = rr,aes(x=relreg,y=count)) + geom_col() +
facet_grid(religion~bigregion) +
labs(x="")
Exercise
Try that with point instead of col. Also map color to religion.
Answer
rr = gss_sm %>%
select(religion,bigregion) %>%
group_by(religion, bigregion) %>%
summarize(count = n()) %>%
ungroup() %>%
mutate(relreg = " ")
## `summarise()` has grouped output by 'religion'. You can override using the
## `.groups` argument.
ggplot(data = rr,aes(x=relreg,y=count,color = religion)) + geom_point() +
facet_grid(religion~bigregion) +
labs(x="")
For comparison, here is the simple table.
t = table(gss_sm$religion,gss_sm$bigregion, useNA="ifany")
t
##
## Northeast Midwest South West
## Protestant 158 325 650 238
## Catholic 162 172 160 155
## Jewish 27 3 11 10
## None 112 157 170 180
## Other 28 33 50 48
## <NA> 1 5 11 1