geom_smooth() with median instead of mean - r

Question

I am building a plot with ggplot. I have data where y is mostly independent of X, but I randomly have a few extreme values of Y at low values of X. Like this:
set.seed(1)
X <- rnorm(500, mean=5)
y <- rnorm(500)
y[X < 3] <- sample(c(0, 1000), size=length(y[X < 3]),prob=c(0.9, 0.1),
replace=TRUE)
I want to make the point that the MEDIAN y-value is still constant over X values. I can see that this is basically true here:
mean(y[X < 3])
median(y[X < 3])
If I make a geom_smooth() plot, it does mean, and is very affected by outliers:
ggplot(data=NULL, aes(x=X, y=y)) + geom_smooth()
I have a few potential fixes. For example, I could first use group_by/summarize to make a dataset of binned medians and then plot that. I would rather NOT do this because in my real data I have a lot of facetting and grouping variables, and it would be a lot to keep track of (non-ideal). A lot plot definitely looks better, but log does not have nice interpretation in my application (median does have nice interpretation)
ggplot(data=NULL, aes(x=X, y=y)) + geom_smooth() +
scale_y_log10()
Finally, I know about geom_quantile but I think I'm using it wrong. Is there a way to add an error bar? Also- this geom_quantile plot looks way too smooth, and I don't understand why it is sloping down. Am I using it wrong?
ggplot(data=NULL, aes(x=X, y=y)) +
geom_quantile(quantiles=c(0.5))
I realize that this problem probably has a LOT of workarounds, but if possible I would love to use geom_smooth and just provide an argument that tells it to use a median. I want geom_smooth for a side-by-side comparison with consistency. I want to put the mean and median geom_smooths side-by-side to show "hey look, super strong pattern between Y and X is driven by a few large outliers, if we look only at median the pattern disappears".
Thanks!!

Answer 1

You can create your own method to use in geom_smooth. As long as you have a function that produces an object on which the predict generic works to take a data frame with a column called x and translate into appropriate values of y.
As an example, let's create a simple model that interpolates along a running median. We wrap it in its own class and give it its own predict method:
rolling_median <- function(formula, data, n_roll = 11, ...) {
x <- data$x[order(data$x)]
y <- data$y[order(data$x)]
y <- zoo::rollmedian(y, n_roll, na.pad = TRUE)
structure(list(x = x, y = y, f = approxfun(x, y)), class = "rollmed")
}
predict.rollmed <- function(mod, newdata, ...) {
setNames(mod$f(newdata$x), newdata$x)
}
Now we can use our method in geom_smooth:
ggplot(data = NULL, aes(x = X, y = y)) +
geom_smooth(formula = y ~ x, method = "rolling_median", se = FALSE)
Now of course, this doesn't look very "flat", but it is way flatter than the line calculated by the loess method of the standard geom_smooth() :
ggplot(data = NULL, aes(x = X, y = y)) +
geom_smooth(formula = y ~ x, color = "red", se = FALSE) +
geom_smooth(formula = y ~ x, method = "rolling_median", se = FALSE)
Now, I understand that this is not the same thing as "regressing on the median", so you may wish to explore different methods, but if you want to get geom_smooth to plot them, this is how you can go about it. Note that if you want standard errors, you will need to have your predict function return a list with members called fit and se.fit

Answer 2

Here's a modification of #Allan's answer that uses a fixed x window rather than a fixed number of points. This is useful for irregular time series and series with multiple observations at the same time (x value). It uses a loop so it's not very efficient and will be slow for larger data sets.
# running median with time window
library(dplyr)
library(ggplot2)
library(zoo)
# some irregular and skewed data
set.seed(1)
x <- seq(2000, 2020, length.out = 400) # normal time series, gives same result for both methods
x <- sort(rep(runif(40, min = 2000, max = 2020), 10)) # irregular and repeated time series
y <- exp(runif(length(x), min = -1, max = 3))
data <- data.frame(x = x, y = y)
# ggplot(data) + geom_point(aes(x = x, y = y))
# 2 year window
xwindow <- 2
nwindow <- xwindow * length(x) / 20 - 1
# rolling median
rolling_median <- function(formula, data, n_roll = 11, ...) {
x <- data$x[order(data$x)]
y <- data$y[order(data$x)]
y <- zoo::rollmedian(y, n_roll, na.pad = TRUE)
structure(list(x = x, y = y, f = approxfun(x, y)), class = "rollmed")
}
predict.rollmed <- function(mod, newdata, ...) {
setNames(mod$f(newdata$x), newdata$x)
}
# rolling time window median
rolling_median2 <- function(formula, data, xwindow = 2, ...) {
x <- data$x[order(data$x)]
y <- data$y[order(data$x)]
ys <- rep(NA, length(x)) # for the smoothed y values
xs <- setdiff(unique(x), NA) # the unique x values
i <- 1 # for testing
for (i in seq_along(xs)){
j <- xs[i] - xwindow/2 < x & x < xs[i] + xwindow/2 # x points in this window
ys[x == xs[i]] <- median(y[j], na.rm = TRUE) # y median over this window
}
y <- ys
structure(list(x = x, y = y, f = approxfun(x, y)), class = "rollmed2")
}
predict.rollmed2 <- function(mod, newdata, ...) {
setNames(mod$f(newdata$x), newdata$x)
}
# plot smooth
ggplot(data) +
geom_point(aes(x = x, y = y)) +
geom_smooth(aes(x = x, y = y, colour = "nwindow"), formula = y ~ x, method = "rolling_median", se = FALSE, method.args = list(n_roll = nwindow)) +
geom_smooth(aes(x = x, y = y, colour = "xwindow"), formula = y ~ x, method = "rolling_median2", se = FALSE, method.args = list(xwindow = xwindow))
Created on 2022-01-05 by the reprex package (v2.0.1)