Introduction to Gam Smoothing Regression and Pairing with ggally

Gam smoothing regression, also known as generalized additive models (GAMs), is a type of regression analysis that uses non-parametric functions to model the relationship between variables. In this article, we’ll delve into the world of gam’ smoothing regression and explore how to pair different types of smoothness penalties using ggally in R.

Background on Gam Smoothing Regression

Gam smoothing regression was introduced by Hastie and Tibbalds (1990) as an extension of the generalized additive model (GAM). The goal of GAMs is to use non-parametric functions, such as polynomials or splines, to model the relationship between variables. Unlike traditional linear regression models, which assume a specific functional form for the relationship between variables, GAMs do not impose any restrictions on the functional form.

One key feature of GAMs is the choice of smoothing penalty, also known as the basis function. The most common types of smoothing penalties are:

• Basis polynomial (bs=“poly”): This method uses a polynomial basis to model the relationship between variables.
• Thin plate spline (tp) basis (bs=“tp”): This method uses a thin plate spline basis to model the relationship between variables. The thin plate spline is a type of spline that is particularly useful for modeling spatial relationships.

Introduction to ggally

ggally is a data visualization library in R that provides an interface for plotting various types of plots, including regression plots. In this article, we’ll explore how to pair different types of smoothness penalties using ggally.

Pairing Different Smoothing Penalties with ggally

To pair different smoothing penalties with ggally, you need to specify the upper and lower arguments in the ggpairs() function. The upper argument specifies the type of regression plot to use for the upper triangular part of the plot, while the lower argument specifies the type of regression plot to use for the lower triangular part of the plot.

In this article, we’ll demonstrate how to pair different types of smoothness penalties using ggally. We’ll use the following code as an example:

library(ggally)

# Create a sample dataset
set.seed(123)
df <- data.frame(x = rnorm(36), y = rnorm(36))

# Define the upper and lower regression plots
my_fn3 <- function(data, mapping, method = "gam", ...) {
    p3 <- ggplot(data = data, mapping = mapping) + 
        geom_point() + 
        geom_smooth(method = method, colour = "blue", ...)
    return(p3)
}

my_fn4 <- function(data, mapping, method = mgcv::gam(), ...) {
    p4 <- ggplot(data = data, mapping = mapping) + 
        geom_point() + 
        geom_smooth(method = method, formula = y ~ s(x, bs = "tp"), colour = "orangered2", ...)
    return(p4)
}

# Create the plot
sel1 <- select(df, x, y)
plot2 <- ggpairs(sel1, columnLabels = c("x", "y"),
                 upper = list(continuous = my_fn3),
                 lower = list(continuous = my_fn4)) +
    theme_bw() + 
    theme(axis.text.x = (element_text(size = rel(0.7), angle = 0)),
          axis.text.y = (element_text(size = rel(0.7), angle = 0)), panel.grid.major = element_blank(),
          panel.grid.minor = element_blank(), panel.border = element_rect(fill = NA, colour = "grey35"))

Explanation of the Code

In this code snippet, we define two regression functions, my_fn3 and my_fn4, which specify the type of smoothness penalty to use for the upper and lower triangular parts of the plot, respectively.

The my_fn3 function uses a basis polynomial basis (bs=“poly”) to model the relationship between variables. The my_fn4 function uses a thin plate spline basis (tp) to model the relationship between variables.

We then create a sample dataset using rnorm(), which generates 36 random values for both the x and y variables.

Next, we define the upper and lower regression plots using the ggpairs() function. The upper argument specifies the type of regression plot to use for the upper triangular part of the plot, while the lower argument specifies the type of regression plot to use for the lower triangular part of the plot.

We then create the plot using ggpairs(), specifying the sel1 dataset and the upper and lower regression plots defined earlier. The resulting plot shows the relationship between the x and y variables using both a basis polynomial basis and a thin plate spline basis.

Conclusion

In this article, we explored how to pair different types of smoothness penalties using ggally in R. We discussed the background on gam’ smoothing regression and introduced some key concepts, such as the choice of smoothing penalty and the use of non-parametric functions. We also provided an example code snippet that demonstrates how to pair different smoothing penalties using ggally.

By following this article, you should now have a better understanding of how to use ggally to visualize the relationship between variables in R. Additionally, you can explore other types of regression plots and visualization techniques using ggally to gain further insights into your data.

Last modified on 2024-07-29