Axis transforms in ggplot2 to focus on value

Question

Here is a plot that I have made using ggplot2 (data dput at end of question).

Here I have calculated some means using some different methods which I have shown in different facets. The code to recreate this plot is here

data %>%
  ggplot() +
  aes(
    x = grad,
    y = mean
  ) +
  geom_errorbar(
    aes(
      ymin = lb,
      ymax = ub
    ),
    width = 0.2,
    alpha = 0.4
  ) +
  geom_point(
    size = 2
  ) +
  geom_line(
    linewidth = 0.8
  ) +
  geom_hline(
    yintercept = 50,
    linetype = "dashed",
    colour = "#FF0000"
  ) +
  facet_wrap(
    ~ method,
    ncol = 2,
    scales = "free"
  ) +
  theme_bw()

It's important to me to see both the error bars but also to compare the value of the points between the different methods. Is there a way of doing some sort of axis transform on the y-axis (like scale_y_log10()) which will essentially "zoom in" the y-axis around 50? (Such that the gap between 50 and 51 is bigger than the gap between 51 and 52 etc... and that this is symmetric around 50 such that the gap between 49 and 50 is the same as 50 and 51 and the gap between 48 and 49 is the same as 51 and 52 and so on).

DPUT:

structure(list(method = structure(c(1L, 2L, 3L, 4L, 6L, 5L, 1L, 
2L, 3L, 4L, 6L, 5L, 1L, 2L, 3L, 4L, 6L, 5L, 1L, 2L, 3L, 4L, 6L, 
5L, 1L, 2L, 3L, 4L, 6L, 5L), .Label = c("raw", "norm", "bank", 
"rand", "floor", "ceil"), class = "factor"), grad = c(2, 2, 2, 
2, 2, 2, 4, 4, 4, 4, 4, 4, 6, 6, 6, 6, 6, 6, 8, 8, 8, 8, 8, 8, 
10, 10, 10, 10, 10, 10), mean = c(49.99667915, 50.2454844, 49.9967503, 
49.996759, 50.2454844, 49.7478739, 49.994064725, 50.1187028, 
49.9940469, 49.9940169, 50.3682549, 49.6200129, 50.00164035, 
50.0847906, 50.0015683, 50.0016874, 50.4176783, 49.5857625, 50.00176225, 
50.0643196, 50.0019263, 50.0018275, 50.4386578, 49.5647442, 50.00713535, 
50.0572266, 50.0072163, 50.007149, 50.456595, 49.5574979), sd = c(0.91473404644074, 
0.91478017995276, 0.9151151931487, 0.914942290015281, 0.91478017995276, 
0.914757425175375, 0.912161337763246, 0.912320011976382, 0.912328572194664, 
0.912293149537724, 0.912251012998649, 0.912065855377804, 0.909061418603362, 
0.909071357608941, 0.909021915808113, 0.909025127237655, 0.909130605608961, 
0.909030928525895, 0.910690862745318, 0.910911812026153, 0.91094121042864, 
0.910847754625854, 0.910551266903806, 0.910647546563305, 0.906676002734588, 
0.906779575074459, 0.906664057457677, 0.906712448654729, 0.906661779570118, 
0.906787505291932), ub = c(51.7895578810238, 52.0384535527074, 
51.7903760785715, 51.7900458884299, 52.0384535527074, 51.5407984533437, 
51.781900947016, 51.9068500234737, 51.7822109015015, 51.7821114730939, 
52.1562668854774, 51.4076619765405, 51.7834007304626, 51.8665704609135, 
51.7832512549839, 51.7833766493858, 52.1995742869936, 51.3674631199108, 
51.7867163409808, 51.8497067515713, 51.7873710724401, 51.7870890990667, 
52.2233382831315, 51.3496133912641, 51.7842203153598, 51.8345145671459, 
51.7842778526171, 51.7843053993633, 52.2336520879574, 51.3348014103722
), lb = c(48.2038004189762, 48.4525152472926, 48.2031245214285, 
48.2034721115701, 48.4525152472926, 47.9549493466563, 48.206228502984, 
48.3305555765263, 48.2058828984985, 48.2059223269061, 48.5802429145226, 
47.8323638234595, 48.2198799695374, 48.3030107390865, 48.2198853450161, 
48.2199981506142, 48.6357823130064, 47.8040618800892, 48.2168081590192, 
48.2789324484287, 48.2164815275599, 48.2165659009333, 48.6539773168685, 
47.7798750087359, 48.2300503846402, 48.2799386328541, 48.230154747383, 
48.2299926006367, 48.6795379120426, 47.7801943896278)), row.names = c(NA, 
-30L), class = c("tbl_df", "tbl", "data.frame"))

You can do a custom transformation. I'd suggest something like a shifted signed square root, say `f(y) = abs(y - 50) ^ 0.5 * sign(y)` with inverse transformation `g(y) = y^2 * sign(y) + 50`. You can adjust the exponent to adjust the distortion. [This answer](https://stackoverflow.com/a/11054781/903061) has a nice example of defining a custom transformation. — Gregor Thomas, Mar 28 '23 at 03:47

score 1 · Accepted Answer · answered Mar 28 '23 at 21:59

I have an answer to this thanks to @Gregor Thomas' comment, thank you!

I defined my own scale transformation using the scales package

library(scales)

zoom_trans <- function(center = 0) {
  trans <- \(x) {sqrt(abs(x - center)) * sign(x - center)}
  inv <- \(x) {x^2 * sign(x) + 50}
  trans_new(
    paste0("sqrt_zoom_on_", center),
    trans,
    inv,
    breaks_extended(n = 5)
  )
}

We can then take the previous plotting code and add a new layer

<PLOTTING_CODE_FROM_QUESTION> +
  scale_y_continuous(
    trans = zoom_trans(center = 50)
  )

and this will create a plot that looks like something like this

The answer from Gregor was spot on except note that in the transformation I had to use sign(x - 50) not sign(x).

Thanks for posting the answer! Glad it worked out :) – Gregor Thomas Mar 29 '23 at 02:37 — Gregor Thomas, Mar 29 '23 at 02:37

Axis transforms in ggplot2 to focus on value

1 Answers1