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copied!<p>In ggplot2, the rule is that scale transformation precedes statistical transformation which in turn precedes coordinate transformation. In this context, the function (via stat_function()) is the statistical transformation. </p> <p>If you use a scale_x/y_*() function in a ggplot2 call, it will apply the scale transformation(s) first before computing the function.</p> <p>Case 0: Plot in the original scales of x and y.</p> <pre><code>ggplot(data.frame(x = 1:1e4, y = 1:1e4), aes(x, y)) + stat_function(fun = function(x) x) </code></pre> <p>Case 1a: Both x and y are log transformed before the function is computed because of the presence of scale_x/y_log10(). You can see this from the values on their respective scales (compare to Case 0).</p> <pre><code>ggplot(data.frame(x = 1:1e4, y = 1:1e4), aes(x, y)) + stat_function(fun = function(x) x) + scale_x_log10() + scale_y_log10() </code></pre> <p>Case 1b: x is log transformed in the original data frame. Consequently, the function actually operates on the log10(x) values, so will still be a straight line, but on the log10 scale in both x and y.</p> <pre><code>ggplot(data.frame(x = log10(seq(1e4)), y = seq(1e4)), aes(x, y)) + stat_function(fun = function(x) x) </code></pre> <p>Case 1c: The same as 1b, with one exception: the x-scale is in the original units but the y-scale is in log10(x) units, because the scale transformation on x occurs before the statistical transformation f(y) = y is computed, where y = log10(x).</p> <pre><code>ggplot(data.frame(x = seq(1e4), y = seq(1e4)), aes(x, y)) + stat_function(fun = function(x) x) + scale_x_log10() </code></pre> <p>Case 2: By contrast, coordinate transformations take place <em>after</em> statistical transformation; i.e., the function is computed in the original units first and then the coordinate transformation on x takes place, which warps the function:</p> <pre><code>ggplot(data.frame(x = seq(1e4), y = seq(1e4)), aes(x, y)) + stat_function(fun = function(x) x) + coord_trans(xtrans = "log10") </code></pre> <p>...unless, of course, you apply the same transformation to both x and y:</p> <pre><code>ggplot(data.frame(x = seq(1e4), y = seq(1e4)), aes(x, y)) + stat_function(fun = function(x) x) + coord_trans(xtrans = "log10", ytrans = "log10") </code></pre>

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