Faceted QQplots with ggplot2

Introduction

Quantile-Quantile (QQ) plots are a widely used tool for visualizing the distribution of data. They provide a simple way to compare the empirical distribution function of a dataset with the theoretical distribution, such as the normal distribution. In this article, we will explore how to create faceted QQplots using ggplot2, a popular R package for data visualization.

Background

In order to create a QQplot, we need two samples: one with the empirical quantiles and another with the theoretical quantiles from a known distribution (e.g., normal). The QQplot is then used to compare these two sets of quantiles. By visualizing the relationship between the empirical and theoretical quantiles, we can determine if the data follows a particular distribution.

In this article, we will create a faceted QQplot with ggplot2 that displays two separate QQplots side-by-side: one for each sample.

Combining DataFrames

To begin creating our faceted QQplot, we need to combine both data frames into one. We can do this by using the cbind function in R.

dat &lt;- cbind(datapoints1, vals2 = datapoints2[ , 2])

In this code snippet, we are creating a new dataframe called dat that contains all columns from both dataframes. The vals2 column now holds the values of the second dataset.

Sorting Data

Next, we need to sort our combined data by category (categ). This is necessary because ggplot2 will create separate plots for each unique value of this variable.

dat_sort &lt;- do.call("rbind", lapply(unique(dat$categ), FUN = function(x) {data.frame(categ = x, vals1 = sort(dat$vals1[dat$categ == x]), vals2 = sort(dat$vals2[dat$categ == x]))}))

In this code snippet, we are iterating over each unique value of categ in our data and creating a new dataframe that contains the sorted values for both samples. We then bind these new dataframes together using the rbind function.

Creating the QQplot

With our data sorted, we can now create the faceted QQplot.

ggplot() + 
  geom_point(data = dat_sort, aes(x = vals1, y = vals2)) +
  facet_wrap( ~ categ, scales = "free")

In this code snippet, we are creating a new ggplot object and adding two layers: geom_point to display the points on our plot, and facet_wrap to create separate facets for each unique value of categ. The scales = "free" argument allows us to scale each facet independently.

Example

Here’s an example with 1000 data points.

n &lt; - 1000

# Create sample data
datapoints1 &lt;- data.frame(categ=c(rep(1, n), rep(2, n)), vals1=c(rt(n, 1, 2), rnorm(n, 3, 4)))
datapoints2 &lt;- data.frame(categ=c(rep(1, n), rep(2, n)), vals2=c(rt(n, 5, 6), rnorm(n, 7, 8)))

# Combine dataframes and sort
dat &lt;- cbind(datapoints1, vals2 = datapoints2[ , 2])
dat_sort &lt;- do.call("rbind", lapply(unique(dat$categ), FUN = function(x) {data.frame(categ = x, vals1 = sort(dat$vals1[dat$categ == x]), vals2 = sort(dat$vals2[dat$categ == x]))}))

# Create QQplot
ggplot() + 
  geom_point(data = dat_sort, aes(x = vals1, y = vals2)) +
  facet_wrap( ~ categ, scales = "free")

This code creates a faceted QQplot with two separate plots side-by-side: one for the first dataset and one for the second dataset.

Conclusion

Faceted QQplots are a useful tool for visualizing data distribution. In this article, we explored how to create a faceted QQplot using ggplot2. We combined our dataframes, sorted them by category, and created separate plots for each unique value of this variable. By following these steps, you can easily create your own faceted QQplots with ggplot2.

Advice

Make sure to sort your data before creating the QQplot.
Adjust the scales = "free" argument in the facet_wrap function as needed for your specific plot.
Experiment with different distributions and sample sizes to see how they affect the QQplot.

Last modified on 2024-11-08