Use of inverse parameter in trans_new scales package - r

Question

I've been trying to use the function trans_new with the scales package however I can't get it to display labels correctly
# percent to fold change
fun1 <- function(x) (x/100) + 1
# fold change to percent
inv_fun1 <- function(x) (x - 1) * 100
percent_to_fold_change_trans <- trans_new(name = "transform", transform = fun1, inverse = inv_fun1)
plot_data <- data.frame(x = 1:10,
y = inv_fun1(1:10))
# Plot raw data
p1 <- ggplot(plot_data, aes(x = x, y = y)) +
geom_point()
# This doesn't really change the plot
p2 <- ggplot(plot_data, aes(x = x, y = y)) +
geom_point() +
coord_trans(y = percent_to_fold_change_trans)
p1 and p2 are identical whereas I'm expecting p2 to be a diagonal line since we are reversing the inverting function. If I replace the inverse parameter in trans_new with another function (like fun(x) x) I can see the correct transformation but the labels are completely off. Any ideas of how to define the inverse parameters to get the right label positions?

Answer 1

You wouldn't expect a linear function like fun1 to change the appearance of the y axis. Remember, you are not transforming the data, you are transforming the y axis. This means that you are effectively changing the positions of the horizontal gridlines, but not the values they represent.
Any function that produces a linear transformation will result in fixed spacing between the horizontal grid lines, which is what you have already. The plot therefore won't change.
Let's take a simple example:
plot_data <- data.frame(x = 1:10, y = 1:10)
p <- ggplot(plot_data, aes(x = x, y = y)) +
geom_point() +
scale_y_continuous(breaks = 1:10)
p
Now let's create a straightforward non-linear transformation:
little_trans <- trans_new(name = "transform",
transform = function(x) x^2,
inverse = function(x) sqrt(x))
p + coord_trans(y = little_trans)
Note the values on the y axis are the same, but because we applied a non-linear transformation, the distances between the gridlines now varies.
In fact, if we plot a transformed version of our data, we would get the same shape:
ggplot(plot_data, aes(x = x, y = y^2)) +
geom_point() +
scale_y_continuous(breaks = (1:10)^2)
In a sense, this is all that the transform does, except it applies the inverse transform to the axis labels. We could do that manually here:
ggplot(plot_data, aes(x = x, y = y^2)) +
geom_point() +
scale_y_continuous(breaks = (1:10)^2, labels = sqrt((1:10)^2))
Now, suppose I instead do a more complicated but linear function of x:
little_trans <- trans_new(name = "transform",
transform = function(x) (0.1 * x + 20) / 3,
inverse = function(x) (x * 3 - 20) / 0.1)
ggplot(plot_data, aes(x = x, y = y)) +
geom_point() +
coord_trans(y = little_trans)
It's unchanged from before. We can see why if we again apply our transform directly:
ggplot(plot_data, aes(x = x, y = (0.1 * y + 20) / 3)) +
geom_point() +
scale_y_continuous(breaks = (0.1 * (1:10) + 20) / 3)
Obviously, if we do the inverse transform on the axis labels we will have 1:10, which means we will just have the original plot back.
The same holds true for any linear transform, and therefore the results you are getting are exactly what are to be expected.