How to Easily Create Kernel Density Plots in R

A kernel density plot is a non-parametric method used to estimate the probability density function of a random variable. It visualizes the distribution of values in a dataset using a single, smooth, continuous curve. Unlike discrete representations, the KDE curve provides an intuitive visual representation of where data points are concentrated and how they thin out.

While conceptually similar to a histogram, the kernel density plot is often preferred for its superior ability to display the true underlying shape of a statistical distribution. Crucially, the KDE curve is not affected by the arbitrary choice of the number or width of bins, which can significantly skew the interpretation of a traditional histogram. This smoothness is achieved through the use of a kernel function applied across the data points.

Understanding Kernel Density Estimation (KDE)

KDE works by placing a small, smooth function—the kernel—over each individual data point. These individual kernels are then summed up to create the final continuous density curve. The resulting plot shows the relative frequency or probability density across the range of values, allowing analysts to quickly identify modes (peaks) and potential skewness or multimodality within the dataset.

The two most critical parameters influencing the shape of the resulting KDE curve are the choice of the kernel function and the bandwidth. The default settings in R often utilize a Gaussian kernel and an automatically calculated bandwidth based on Silverman’s or Scott’s rule of thumb. However, advanced users should understand how to adjust these parameters to refine the estimation.

The Role of Bandwidth and Kernel Selection

The bandwidth parameter is arguably the most influential factor in KDE. It controls the width of the smoothing kernel applied to each data point. A narrow bandwidth results in an undersmoothed plot that closely follows the individual data points (potentially showing spurious peaks), while a wide bandwidth results in an oversmoothed plot that may obscure important structural features of the underlying distribution. Experimentation is often necessary to find the optimal balance for visualization.

While the default Gaussian kernel is robust for most applications, R’s density() function supports others, such as Epanechnikov, rectangular, triangular, and biweight kernels. Although the choice of the kernel usually has less impact than the bandwidth, different kernels can produce slightly different estimates, particularly in the tails of the distribution.

Core Methods for Generating KDE Plots in R

We can use the following methods to create a kernel density plot in R, starting from the simplest visualization to more complex comparative plots:

Method 1: Create One Basic Kernel Density Plot (Line Plot)

This method utilizes the density() function to calculate the KDE estimates for a single dataset, followed by the standard plot() command to render the result as a simple line graph.

#define kernel density object using the density() function
kd <- density(data)

#create kernel density plot using the plot() function
plot(kd)

Method 2: Create an Enhanced Filled-In Kernel Density Plot

To improve visual appeal and clarity, we can fill the area beneath the density curve. This is achieved by using the polygon() function immediately after plotting the density line, allowing for specific color customization.

#define kernel density
kd <- density(data)

#create kernel density plot (initial setup)
plot(kd)

#fill in kernel density plot with specific color and black border
polygon(kd, col='blue', border='black')

Method 3: Create Multiple Kernel Density Plots for Comparison

When comparing multiple datasets, it is necessary to plot the first density using plot() and subsequently add additional densities using the lines() function to overlay them on the same graph, distinguishing them by color and line thickness.

#plot first kernel density plot (uses plot() to initialize graph)
kd1 <- density(data1)
plot(kd1, col='blue')

#plot second kernel density plot (uses lines() to add to existing graph)
kd2 <- density(data2)
lines(kd2, col='red')

#plot third kernel density plot
kd3 <- density(data3)
lines(kd3, col='purple')

...

The following practical examples illustrate how to implement each method using sample data, providing clear visualization of the concepts outlined above.

Detailed Implementation: Single KDE Plot (Method 1)

This first example demonstrates the most straightforward way to generate a kernel density plot for a single, small dataset. We define the raw data vector, calculate the density object, and then use the plot() function to render the result, adding a descriptive title for clarity.

#create sample data vector
data <- c(3, 3, 4, 4, 5, 6, 7, 7, 7, 8, 12, 13, 14, 17, 19, 19)

#define kernel density object
kd <- density(data)

#create kernel density plot with custom title
plot(kd, main='Kernel Density Plot of Sample Data')

In this visualization, the x-axis represents the range of values within the dataset, while the y-axis indicates the estimated probability density. The height of the curve at any point reflects the relative frequency of values occurring near that point. Observing the plot, we can see two distinct peaks, suggesting a potential bimodal distribution where values are highly concentrated around 7 and 19.

Detailed Implementation: Aesthetic Enhancements (Method 2)

While the line plot provides the necessary information, filling the area under the curve significantly improves the visualization’s aesthetic quality and ease of interpretation. Method 2 shows how to integrate the polygon() function to achieve this effect, using the calculated density object kd as the boundary for the shape.

#create sample data
data <- c(3, 3, 4, 4, 5, 6, 7, 7, 7, 8, 12, 13, 14, 17, 19, 19)

#define kernel density object
kd <- density(data)

#create kernel density plot (initializes axes without filling)
plot(kd)

#add color filling using polygon()
polygon(kd, col='steelblue', border='black')

Note that the polygon() function requires the density object (kd) as its primary input. The col argument specifies the fill color (here, ‘steelblue’), and the border argument ensures the outline of the density curve remains visible and distinct. This technique is especially useful when presenting findings, as it emphasizes the continuous nature of the estimated probability function.

Detailed Implementation: Comparative Analysis (Method 3)

One of the most powerful applications of kernel density plots is the direct, visual comparison of the distributions of two or more groups. This requires careful use of the base R plotting functions. We use plot() only for the first dataset (to set up the plotting area and axes) and then use lines() for all subsequent datasets, preventing the graph from being reset each time.

#create two distinct datasets for comparison
data1 <- c(3, 3, 4, 4, 5, 6, 7, 7, 7, 8, 12, 13, 14, 17, 19, 19)
data2 <- c(12, 3, 14, 14, 4, 5, 6, 10, 14, 7, 7, 8, 10, 12, 17, 20)

#Calculate and plot first density (data1)
kd1 <- density(data1)
plot(kd1, col='blue', lwd=2, main="Comparative Kernel Density Plot")

#Calculate and plot second density (data2)
kd2 <- density(data2)
lines(kd2, col='red', lwd=2)

In this comparative visualization, the blue curve (Data 1) clearly shows a multimodal structure, while the red curve (Data 2) appears more centralized around a single peak, albeit with a broader spread. The use of the lwd argument (line width) enhances the visibility of the lines, making differentiation easier. This methodology is scalable; one can use the lines() function repeatedly to add as many kernel density plots as needed for complex, multi-group analyses on a single chart. It is generally recommended to also add a legend when comparing multiple groups to ensure clear identification.

Advanced Customization of KDE Parameters

For more sophisticated analysis, the density() function provides several arguments that allow fine-tuning of the estimation process. The two most important parameters for customization are kernel and bw (for bandwidth).

• Kernel Selection: To change the underlying smoothing function, use the kernel argument. For example, density(data, kernel = "epanechnikov") replaces the default Gaussian kernel with the Epanechnikov kernel, which is often considered optimal in a mean-square error sense.

• Bandwidth Adjustment: To manually control the degree of smoothing, use the bw argument. If the default automatic bandwidth estimate seems too rough (undersmoothed), a larger numerical value for bw will result in a smoother curve: density(data, bw = 2.5). Conversely, a smaller value will reveal more detail.

Understanding these parameters is key to generating plots that accurately reflect the underlying structure of the data without introducing visual artifacts due to over- or under-smoothing.

Conclusion and Further Resources

Kernel density plots are an indispensable tool in the R visualization toolkit, offering a robust and aesthetically pleasing alternative to the traditional histogram for exploring data distributions. By mastering the density() and plot() functions, and utilizing enhancement techniques like coloring and overlaying multiple plots, users can create informative and publication-ready graphics for statistical reporting.

For those looking to deepen their R visualization skills, the following tutorials explain how to create other common plots and analyses:

• Understanding the calculation of the bandwidth parameter in R.
• Creating advanced visualizations using the ggplot2 package, which offers more sophisticated control over KDE aesthetics.
• Comparing continuous distributions using boxplots and violin plots.