Worked Example: Food for Thought

1 Budget Share of Food for Spanish Households

In this worked example, we will make use of our newfound tools to handle a big data set. We will examine a data set consisting of house expenditures on food from Spanish households in 1980. Our study’s objective is to explore how food expenditure relates to the various other variables in the data set.

The data set is available in the Ecdat package. Start by installing it (if you haven’t already).

# install the Ecdat package
install.packages("Ecdat")

Then load the data set directly into your workspace by calling the data() function as we show next.

data("BudgetFood", package = "Ecdat")

There are 23,972 observations and six variables in this dataset:

• wfood: Percentage of total expenditure which the household has spend on food

• totexp: Total expenditure of the household

• age: Age of reference person in the household

• size: Size of the household

• town: size of the town where the household is placed categorized into 5 groups: 1 for small towns, 5 for big ones.

• sex: sex of reference person (man, woman)

2 Wrangling

Before we start visualizing this data set, we need to format it properly. The names of the variables are fine, but the town variable should be formatted as an ordered factor and age and size should be formatted as integers.

library(tidyverse)

budget_food <- 
  BudgetFood %>%
  mutate(
    age = as.integer(age),
    size = as.integer(size),
    town = factor(town, ordered = TRUE),
  )

3 Food and Total Expenditure

Let’s start naively, trying out a simple scatter plot of food expenditure versus total expenditure.

ggplot(budget_food, aes(totexp, wfood)) +
  geom_point() +
  labs(x = "Total Expenditure (Pesetas)", y = "Food Expenditure")

Figure 1: A scatter plot of total expenditure versus expenditure on food as a fraction of total expenditure

Despite the large amount of overlap, we can still glean a few insights. First off, food expenditure as a proportion of total expenditure decreases with total expenditure. This speaks to our intuition. Second, there is a number of observations that report no food expenditure whatsoever. These observations are likely outliers, perhaps people living in elderly care centers or something similar. Let’s remove these observations from the data set.

budget_food_cleaned <- 
  budget_food %>%
  filter(wfood > 0)

At this point we could try to combat the overlap by reducing opacity, but another trick that is sometimes overlooked is to instead try a scale transformation. Instead of a linear scale for total expenditure, we could use a logarithmic scale.

ggplot(budget_food_cleaned, aes(totexp, wfood)) +
  scale_x_log10() +
  geom_point() + 
  labs(x = "Total Expenditure (Pesetas)", y = "Food Expenditure")

Figure 2: A scatter plot of total expenditure versus expenditure on food with total expenditure on a logarithmic scale

Since we have learned a few new tools, let’s make use of them now. For this purpose, we are going to try a hexbin plot.

ggplot(budget_food_cleaned, aes(totexp, wfood)) +
  geom_hex() + 
  labs(x = "Total Expenditure (Pesetas)", y = "Food Expenditure")

Figure 3: A hexbin plot of total expenditure versus expenditure on food as a fraction of total expenditure

This plot definitely works better, showing the relationship in a clear fashion.

4 Household Size

Now that we have managed to create a plot of food and total expenditure, let’s see if we can also find a relationship with the size of the household. Before we look at the complete picture, it is a good idea to first check what the overall relationship between household size and food expenditure is. To do so, we first construct a boxplot.

ggplot(budget_food_cleaned, aes(as.factor(size), wfood)) +
  geom_boxplot() + 
  labs(x = "Household Size", y = "Food Expenditure")

Figure 4: A boxplot of food expenditure as a fraction of total expenditure versus household size

In general, food expenditure tends to be higher with larger households, which is probably what one might expect. However, this trend does not hold for households with only one or two members. Take a minute to figure out if that makes sense to you.

Let’s return to our hexbin plot design, but now introduce household size as facets.

ggplot(budget_food_cleaned, aes(totexp, wfood)) +
  geom_hex() +
  facet_wrap("size", labeller = labeller(size = label_both)) + 
  labs(x = "Total Expenditure (Pesetas)", y = "Food Expenditure")

Figure 5: A hexbin plot of total expenditure versus expenditure on food across household sizes

This plot looks promising but is crippled by the fact that some of the groups are small, which creates problems for the hexbin plot. In fact, hexbin plots can be problematic when the number of observations differs across facets. This is because all facets share the same binning scale..

To get around this problem, we are going to lump all of the households of size 6 or larger into one level, using fct_other(), a function from the forcats package. We specify the levels we want to keep using the keep argument, and all of the others are lumped together.

budget_food_binned <- 
  budget_food_cleaned %>%
  mutate(
    size = as.factor(size),
    size = fct_other(size, keep = paste(c(1:5)), other_level = "+6")
  )

ggplot(budget_food_binned, aes(totexp, wfood)) +
  geom_hex() +
  facet_wrap("size", labeller = labeller(size = label_both)) +
  labs(x = "Total Expenditure (Pesetas)", y = "Food Expenditure")

Figure 6: A hexbin plot of total expenditure versus expenditure on food across household sizes. The 6+ category represents household sizes of 6 or more people.

This is now starting to look quite interesting.

5 Smoothers

As an alternative to the hexbin plots, we could instead use a smoother to look at the relationship between total expenditure and food expenditure.

Smoothers work particularly well when you expect there to be some kind of causal relationship between two variables. They also help when you have a smaller (but still sufficiently large) number of observations in the upper and lower ranges of the variable on the x axis.

Let’s try a smoother using a LOESS model, which makes few assumptions about the data and is relatively robust to outliers.

ggplot(budget_food_binned, aes(totexp, wfood)) +
  geom_point(alpha = 0.05) +
  geom_smooth(method = "loess") +
  facet_wrap("size", labeller = labeller(size = label_both)) +
  labs(x = "Total Expenditure (Pesetas)", y = "Food Expenditure")

Figure 7: A scatter plot of total expenditure, expenditure on food as a fraction of total expenditure, and household size. A LOESS smoother, including approximate 95% confidence intervals, is used.

The problem with this plot is that the smoothers are clearly inappropriate for the extreme values of total expenditure. To work around this problem, we can create a separate data set for use exclusively in the geom_smooth() function.

To do so, we create a new data set, first grouping by the variable we are faceting on, size, and then filtering the data set to include only observations of totexp (total expenditure) that are large than the 0.05 quantile and smaller than the 0.95 quantile.

We then use this data in the data argument to geom_smooth() function.

budget_food_smoother_data <-
  budget_food_binned %>%
  group_by(size) %>%
  filter(totexp > quantile(totexp, 0.05) & totexp < quantile(totexp, 0.95))

ggplot(budget_food_binned, aes(totexp, wfood)) +
  geom_point(alpha = 0.1) +
  geom_smooth(method = "loess", data = budget_food_smoother_data) +
  facet_wrap("size", labeller = labeller(size = label_both)) +
  labs(x = "Total Expenditure (Pesetas)", y = "Food Expenditure")

Figure 8: A hexbin plot of total expenditure versus expenditure on food

Go ahead and see if you can figure out ways to further improve this plot. Consider using the scale transformation we touch on earlier, and explore how it works together with the smoothers and hex binning.

6 Source Code

The source code for this document is available at https://github.com/stat-lu/dataviz/blob/main/worked-examples/food-for-thought.Rmd .