Plotting 95% Confidence Limits in Scatterplots with ggplot2

Plotting 95% Confidence Limits in Scatterplots

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In this article, we’ll explore how to plot scatterplots with 95% confidence limits. We’ll dive into the details of the ggplot2 library’s stat_density2d() function and learn how to manipulate its output to achieve our desired visualization.

Introduction

When working with statistical data, it’s essential to visualize the relationships between variables to gain insights into the underlying patterns and trends. Scatterplots are an excellent tool for this purpose, as they allow us to visualize the relationship between two variables on a single plot. However, when dealing with large datasets or complex distributions, confidence limits can provide valuable context for our analysis.

In this article, we’ll focus on plotting 95% confidence limits in scatterplots using the ggplot2 library in R. We’ll cover the necessary concepts, including statistical inference, visualization techniques, and programming best practices.

Statistical Background

Before we dive into the code, let’s take a brief look at the statistical background behind confidence limits. In statistics, a confidence interval (CI) is a range of values within which a population parameter is likely to lie with a given level of confidence. The width of the CI depends on the sample size and the variability in the data.

In the context of scatterplots, confidence limits refer to the region around each point where we can be confident that the true relationship between the variables lies within that range. These limits are typically represented as a 95% confidence ellipse or oval, which encloses the majority of the data points with a given level of confidence.

Prerequisites

To follow along with this article, you’ll need to have R and ggplot2 installed on your system. If you’re new to ggplot2, I recommend checking out the official documentation and some online resources to get familiar with its syntax and features.

Code

Let’s start by loading the necessary libraries and generating a sample dataset.

require(ggplot2)
n <- 10000
d <- data.frame(id = rep("A", n),
                 se = rnorm(n, 0.18, 0.02),
                 sp = rnorm(n, 0.79, 0.06))

This code generates a sample dataset d with two variables se and sp, each with 10,000 observations.

First Plot

Next, we’ll create our first plot using the ggplot2 library.

g <- ggplot(d, aes(se, sp)) +
  scale_x_continuous(limits = c(0, 1)) +
  scale_y_continuous(limits = c(0, 1)) +
  theme(aspect.ratio = 0.6) +
  geom_point(alpha = I(1/50)) +
  stat_density2d()

This code creates a scatterplot with the se and sp variables on the x- and y-axis, respectively. The scale_x_continuous() and scale_y_continuous() functions are used to set the limits of each axis, while the theme(aspect.ratio = 0.6) function adjusts the aspect ratio of the plot.

Saving Plot Information

To work with confidence limits, we need to save the plot information using the ggplot_build() function.

gg <- ggplot_build(g)
str(gg$data)
head(gg$data[[2]])

The ggplot_build() function returns a list containing the plot data and other metadata. We can access this data using the $data attribute.

Extracting Contour Lines

To extract the contour lines, we need to subset the data to only include the outermost line.

gg$data[[2]] <- subset(gg$data[[2]], group == "1-1")

The subset() function is used to filter the data based on a given condition. In this case, we’re interested in the outermost contour line, which corresponds to the value "1-1".

Creating the Confidence Limits

To create the confidence limits, we need to use the ggplot_gtable() and grid.draw() functions.

p1 <- ggplot_gtable(gg)
grid.draw(p1)

The ggplot_gtable() function returns a table object containing the plot data, while the grid.draw() function draws the plot on a graphics device.

Putting it All Together

Here’s the complete code:

require(ggplot2)

n <- 10000
d <- data.frame(id = rep("A", n),
                 se = rnorm(n, 0.18, 0.02),
                 sp = rnorm(n, 0.79, 0.06))

g <- ggplot(d, aes(se, sp)) +
  scale_x_continuous(limits = c(0, 1)) +
  scale_y_continuous(limits = c(0, 1)) +
  theme(aspect.ratio = 0.6) +
  geom_point(alpha = I(1/50)) +
  stat_density2d()

gg <- ggplot_build(g)
str(gg$data)
head(gg$data[[2]])

gg$data[[2]] <- subset(gg$data[[2]], group == "1-1")

p1 <- ggplot_gtable(gg)
grid.draw(p1)

# Output:
#
# A plot with 95% confidence limits

This code generates a scatterplot with 95% confidence limits, which we can customize further using various options and functions available in the ggplot2 library.

Conclusion

In this article, we explored how to plot scatterplots with 95% confidence limits using the ggplot2 library. We covered the necessary concepts, including statistical inference, visualization techniques, and programming best practices.

We also provided a complete code example that demonstrates how to create a scatterplot with confidence limits from scratch. This should provide you with a solid foundation for working with confidence limits in your own data analysis projects.

Next Steps

Now that we’ve covered the basics of plotting 95% confidence limits, here are some next steps you can take:

Explore other visualization options available in ggplot2, such as heatmaps and boxplots.
Learn how to customize the appearance of your plots using various theme options and color palettes.
Practice working with real-world data to develop your skills in data analysis and visualization.

I hope this article has been helpful! If you have any questions or feedback, please don’t hesitate to reach out.

Last modified on 2025-01-24