geom_smooth on influence plots can be wonky/unstable

[bbolker]

For small data sets the smooth line created by geom_smooth can be very unstable.

Here's an example (reprex below) of an influence plot where the raw y-axis values range from -2 to 1 but the loess line from geom_smooth goes up to about 3.5e10. I don't know what the best approach for solving this is ... Post hoc, you can check the data layer via ggplot_build to see if the smooth component has unrealistically large amplitude, but that seems awkward. (TBH I'm not quite sure why we even need a smooth line here, the trend in this plot doesn't seem to be important?)

Left panel: see influence plot; middle, ggplot with just the points; right, ggplot with points and geom_smooth().

library(performance)
library(ggplot2)
library(patchwork)

sdata <- data.frame(
  TrtLin = factor(rep(
    c("C1", "C2", "C3", "C4", "S1", "S2", "S3", "S4"),
    rep(c(35L, 63L, 62L, 57L), 2)
  )),
  this_male_mated = rep(c(rep(0:1, 98), 0), 
                        c(
      2L, 2L, 6L, 4L, 2L, 1L, 3L, 2L, 1L, 3L, 3L, 1L, 5L, 1L, 1L, 1L, 1L, 1L, 2L,
      1L, 4L, 2L, 3L, 2L, 1L, 11L, 2L, 2L, 1L, 4L, 3L, 6L, 1L, 1L, 4L, 3L, 2L, 1L,
      7L, 2L, 3L, 2L, 2L, 5L, 2L, 1L, 3L, 1L, 1L, 1L, 2L, 1L, 1L, 1L, 3L, 1L, 2L,
      1L, 1L, 2L, 1L, 1L, 1L, 1L, 2L, 1L, 4L, 2L, 2L, 2L, 1L, 1L, 4L, 1L, 1L, 1L,
      1L, 1L, 3L, 1L, 9L, 6L, 1L, 5L, 1L, 1L, 2L, 2L, 2L, 2L, 1L, 1L, 1L, 1L, 1L,
      2L, 2L, 2L, 1L, 2L, 1L, 7L, 1L, 1L, 2L, 8L, 1L, 2L, 1L, 6L, 1L, 4L, 1L, 1L,
      3L, 3L, 2L, 2L, 1L, 1L, 3L, 1L, 2L, 1L, 1L, 1L, 2L, 8L, 3L, 2L, 3L, 3L, 1L,
      4L, 1L, 2L, 3L, 3L, 2L, 1L, 2L, 2L, 2L, 2L, 1L, 2L, 1L, 1L, 1L, 1L, 3L, 5L,
      1L, 2L, 2L, 2L, 3L, 1L, 3L, 4L, 3L, 2L, 1L, 5L, 4L, 1L, 1L, 3L, 1L, 3L, 1L,
      1L, 1L, 1L, 1L, 3L, 2L, 1L, 3L, 3L, 5L, 1L, 1L, 3L, 1L, 2L, 1L, 2L, 2L, 3L,
      3L, 2L, 2L, 1L, 2L, 6L, 1L
    )
  )
)

themodel <- glm(this_male_mated ~ TrtLin,
                data = sdata,
                family = binomial)


dd <- check_model(themodel, check = "outliers")
p1 <- plot(dd)
p0 <- ggplot(dd$INFLUENTIAL, aes(Hat, Std_Residuals)) + geom_point()
p2 <- print(p0)
p3 <- p0 + geom_smooth(se=FALSE)

p1 + p2 + p3 + plot_layout(nrow = 1, ncol = 3)
ggsave("plot123.png")

[bwiernik]

There was a similar example recently. I think a good solution is to either switch to an lm model or omit the smooth entirely if the number of unique x values is less than 10

[bbolker]

still interesting that the loess fit is that unstable on a trivial example ...