通过 x 和 y 绘制第三个变量的平滑平均值

Question

I am trying to make a 2D plot where the x and y axes are predictor variables. I would like to summarize a third variable smoothly as the counts at a particular coordinate are very low.

For example, I might want to plot the probability of default against assets and debt. This is similar to a density plot, but rather than plot the smoothed density of the observations, I want to plot an arbitrary smoothed value such as default rate.

I have tried using stat_density_2d in ggplot2 but have not figured out how to make it summarize a third variable as the "density" instead of observation counts.

Sample data:

data(iris)
plt <- data.frame(iris[c(1,2)], y=as.numeric(iris$Species == "setosa"))

I want the output to look something like this:

library(ggplot2)

ggplot(plt, aes(x=Sepal.Length, y=Sepal.Width)) + 
  stat_density_2d(aes(fill= ..density..), geom="tile", contour=FALSE)

But instead of the color representing the density of observations. I want it to represent a summarized variable. In this case, the probability that species == "setosa"

Answer 1

UPDATE2: Based on the discussion in chat , it looks like you're referring to a two-dimensional kernel smoothing function. The smoothie package might have what you need.

Regardless of how you estimate the loan default probability (the variable that gets mapped to the fill color, which I've called p.default below) at a given (x,y) point (eg, binned averages, logistic regression, kernel smoothing, etc.), you can create the plot with something like this:

ggplot(df, aes(assets, debt, fill=p.default)) + geom_tile() 

UPDATE: Regarding your comment, for the iris example, you'd need to average the y values over regions of Sepal.Length and Sepal.Width to get the average probability. These data are pretty sparse, so you'll need relatively large cells to get more than one observation per cell. Also, Sepal.Length and Sepal.Width fall in almost completely different regions for each species, so you'll still get all 1's or all 0's in almost all cells. In the example below, I just assign random values of 1 and 0 in order to get a mix of 1s and 0s in several cells.

library(ggplot2)
library(dplyr)

# Fake data
set.seed(5)
plt <- data.frame(iris[c(1,2)], y=sample(0:1, nrow(iris), replace=TRUE))

In the code below, we use the cut function to cut Sepal.Length and Sepal.Width into 10 ranges each. Then we average the 1s and 0s in each cell to get the average of y for each cell. This average y value is then represented by the fill color gradient.

plt %>% group_by(Sepal.Length = cut(Sepal.Length, 10),
                 Sepal.Width = cut(Sepal.Width, 10)) %>%
  summarise(y=mean(y)) %>%
  ggplot(aes(Sepal.Width, Sepal.Length, fill=y)) +
  geom_tile() + 
  theme_classic()

Or, we could fit a logistic regression model, which would give us predictions of y for any combination of Sepal.Length and Sepal.Width :

# Logistic regression model
m1 = glm(y ~ poly(Sepal.Length,2)*poly(Sepal.Width,2), family="binomial", data=plt)

# Get predictions on a grid of values
df = expand.grid(Sepal.Length=seq(4,8,length=100), Sepal.Width=seq(2,5,length=100))
df$y.pred = predict(m1, newdata=df, type="response")

ggplot(df, aes(Sepal.Width, Sepal.Length, fill=y.pred)) +
  geom_tile() + 
  theme_classic() +
  scale_fill_gradient2(low="blue",mid="yellow",high="red", midpoint=0.5,limits=c(0,1))

The general idea is that you need a single value (let's call it z ) to associate with each (x,y) point on your graph. You can calculate those z values by averaging over regions in the (x,y) plane, with a model, etc. Once you have the z values that go with each (x,y) point, you can generate a tile plot where z is the fill aesthetic.

Original Answer

It sounds like maybe you want a heat map. The fill color would represent the value of the third variable, in this case probability of default. Perhaps something like this:

library(ggplot2)

# Fake data
df = expand.grid(income=seq(1,1e5,length=100), debt=seq(1,5e5,length=100))
df$p.default = df$income - 0.3*df$debt
df$p.default = df$p.default - max(df$p.default)
df$p.default = abs(df$p.default)/max(abs(df$p.default))

ggplot(df, aes(income, debt, fill=p.default)) + 
  geom_tile() +
  scale_fill_gradient2(limits=c(0,1), low="blue", mid="yellow", high="red", midpoint=0.5)