coord transform

[adam.l...@pnc.com]

Hi,

Is it possible to use the coord_trans function to transform the y-axis of the following plot so that it's on the log-odds scale?

data(iris)
iris$virginica <- ifelse(iris$Species=="virginica",1,0)
ggplot(iris,aes( Petal.Width, virginica )) + stat_smooth(method="glm", family="binomial")







Adam Loveland

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[Dennis Murphy]

Hi Adam:

Not the way you have defined it. The problem is that a coordinate
transform works on the _data_ *after* the x- and y-scales have been
trained, not on model predictions derived from the data. In your
example, virginica is a numeric y-variable with values 0 and 1, which,
on the logit scale, map to -Inf and Inf, respectively. An axis scale,
or a coordinate transformation thereof, is meant to be applied to the
y-variable in the ggplot()/qplot() call, and you evidently want to
apply the logit transformation to the model predictions. I believe
you'll have to pass the predicted probabilities as the y-variable,
logit transform them in advance before passing them to ggplot() or
using ggplot_build() to get the data that produced the fit and then
plot/coordinate transform that.

This is probably easier to do in ggvis because it has a
compute_model_prediction() function that can handle the model fit as a
data transformation. If you want to do this in ggplot2, I think it
would be easier to fit the model and the predictions/confidence limits
in advance, save the results to a data frame, and then set the y-axis
on the logit scale. That would be the 'easier' way IMO. You could
also use ggplot_build() to grab the output from ggplot(), which I'll
do at the end.

Here's a fairly simple way to do this, which you probably already
know, but in case this topic comes up again...

# Generate a data frame of appropriate elements from a model object
using predict()
m <- glm(virginica ~ Petal.Width, data = iris2, family = "binomial")
p <- predict(m, se.fit = TRUE) # default predictions are on the logit scale

DF <- data.frame(iris2, phat = p$fit,
lcl = p$fit - 1.96 * p$se.fit, # Wald-based CIs
ucl = p$fit + 1.96 * p$se.fit)

ggplot(DF, aes(x = Petal.Width, y = phat)) +
geom_ribbon(aes(ymin = lcl, ymax = ucl), fill = "gray80") +
geom_line(color = "blue", size = 1) +
ylab("Log odds")


The CIs were produced using the Wald procedure (large-sample
normality). If you have a better CI method, then apply it when
building the data frame.

To get what I think you want based on the ggplot fit, here's one way to do it:

# Define a coordinate transformation function, which requires
# definition of a transformation and its inverse. The new scale
# is defined by scales::trans_new()
logodds_trans <- function()
{
trans <- function(x) log(x/(1 - x))
inv <- function(x) exp(x)/(1 + exp(x))
breaks <- function(x) log_breaks(exp(1))(x)

scales::trans_new("logodds", trans, inv, breaks)
}

# Use ggplot_build() to get the data used in the smooth
q <- ggplot(iris2, aes( Petal.Width, virginica )) +

stat_smooth(method="glm", family="binomial")

qq <- ggplot_build(q)
qqq <- qq$data[[1]]

# This is the default appearance
ggplot(qqq, aes(x = x, y = y)) +
geom_ribbon(aes(ymin = ymin, ymax = ymax), fill = "gray80") +
geom_line(color = "blue", size = 1) +
coord_trans(ytrans = "logodds")

# Two escape routes:

# (i) Manually add scale breaks using scale_y_continuous()

ggplot(qqq, aes(x = x, y = y)) +
geom_ribbon(aes(ymin = ymin, ymax = ymax), fill = "gray80") +
geom_line(color = "blue", size = 1) +
scale_y_continuous(breaks = c(0.0001, 0.001, 0.01, 0.1, 0.5,
0.9, 0.99, 0.999, 0.9999)) +
coord_trans(ytrans = "logodds")

## As you can see when plotting this, it's not an ideal approach.

Another approach is to redefine the function used in the breaks object
of logodds_trans(), but this may or may not be productive. When
spreading out a scale from (0, 1) to (-Inf, Inf), the original breaks
are going to be pretty tightly packed in the transformed scale unless
you define a suitable set of breaks on the probability scale. This is
why I mentioned the idea of plotting on the logit scale up front.

If you have designs on doing this kind of thing routinely, I'd suggest
wrapping it up into a function. There are likely better ways to do
this, so if others have ideas, feel free to chime in.

HTH,
Dennis

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[adam.l...@pnc.com]

Thanks Dennis. This was very helpful.



Adam Loveland