How can I show different degree polynomial fits in ggplot2 with facet_grid?

Question

I want to use facets (because I like the way they look for this) to show polynomial fits of increasing degree. It's easy enough to plot them separately as follows:

df <- data.frame(x=rep(1:10,each=10),y=rnorm(100))

ggplot(df,aes(x=x,y=y)) + stat_smooth(method="lm",formula=y~poly(x,2))
ggplot(df,aes(x=x,y=y)) + stat_smooth(method="lm",formula=y~poly(x,3))
ggplot(df,aes(x=x,y=y)) + stat_smooth(method="lm",formula=y~poly(x,4))

I know I can always combine them in some fashion using grobs, but I would like to combine them using facet_grid if possible. Maybe something similar to:

poly2 <- df
poly2$degree <- 2
poly3 <- df
poly3$degree <- 3
poly4 <- df
poly4$degree <- 4
polyn <- rbind(poly2,poly3,poly4)

ggplot(polyn,aes(x=x,y=y)) + stat_smooth(method="lm",formula=y~poly(x,degree)) +
  facet_grid(degree~.)

This doesn't work, of course, because the faceting does not work on y~poly(x,degree) so that degree gets pulled from the data. Is there some way to make this work?

Answer 1

You can always predict the points manually and then facet quite easily,

## Data
set.seed(0)
df <- data.frame(x=rep(1:10,each=10),y=rnorm(100))

## Get poly fits
dat <- do.call(rbind, lapply(1:4, function(d)
    data.frame(x=(x=runif(1000,0,10)),
               y=predict(lm(y ~ poly(x, d), data=df), newdata=data.frame(x=x)),
               degree=d)))

ggplot(dat, aes(x, y)) +
  geom_point(data=df, aes(x, y), alpha=0.3) +
  geom_line(color="steelblue", lwd=1.1) +
  facet_grid(~ degree)

To add confidence bands, you can use the option interval='confidence' with predict . You might also be interested in the function ggplot2::fortify to get more fit statistics.

dat <- do.call(rbind, lapply(1:4, function(d) {
    x <- seq(0, 10, len=100)
    preds <- predict(lm(y ~ poly(x, d), data=df), newdata=data.frame(x=x), interval="confidence")
    data.frame(cbind(preds, x=x, degree=d))
}))

ggplot(dat, aes(x, fit)) +
  geom_point(data=df, aes(x, y), alpha=0.3) +
  geom_line(color="steelblue", lwd=1.1) +
  geom_ribbon(aes(x=x, ymin=lwr, ymax=upr), alpha=0.3) +
  facet_grid(~ degree)

Answer 2

I have a very ugly solution, in which de plot is faceted and the fits are plotted for the appropriate subsets of the data:

p1 <- ggplot(polyn,aes(x=x,y=y)) + facet_grid(.~degree)
p1  +
  stat_smooth(data=polyn[polyn$degree==2,],formula=y~poly(x,2),method="lm") +
  stat_smooth(data=polyn[polyn$degree==3,],formula=y~poly(x,3),method="lm") +
  stat_smooth(data=polyn[polyn$degree==4,],formula=y~poly(x,4),method="lm")

yields