Fitting gaussian to data geom_point in ggplot2 - r

Question

I have the following data set
structure(list(Collimator = structure(c(1L, 1L, 1L, 1L, 1L, 1L,
1L, 1L, 1L, 1L, 1L, 1L, 1L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L,
2L, 2L, 2L, 2L), .Label = c("n", "y"), class = "factor"), angle = c(0L,
15L, 30L, 45L, 60L, 75L, 90L, 105L, 120L, 135L, 150L, 165L, 180L,
0L, 15L, 30L, 45L, 60L, 75L, 90L, 105L, 120L, 135L, 150L, 165L,
180L), X1 = c(2099L, 11070L, 17273L, 21374L, 23555L, 23952L,
23811L, 21908L, 19747L, 17561L, 12668L, 6008L, 362L, 53L, 21L,
36L, 1418L, 6506L, 10922L, 12239L, 8727L, 4424L, 314L, 38L, 21L,
50L), X2 = c(2126L, 10934L, 17361L, 21301L, 23101L, 23968L, 23923L,
21940L, 19777L, 17458L, 12881L, 6051L, 323L, 40L, 34L, 46L, 1352L,
6569L, 10880L, 12534L, 8956L, 4418L, 344L, 58L, 24L, 68L), X3 = c(2074L,
11109L, 17377L, 21399L, 23159L, 23861L, 23739L, 21910L, 20088L,
17445L, 12733L, 6046L, 317L, 45L, 26L, 46L, 1432L, 6495L, 10862L,
12300L, 8720L, 4343L, 343L, 38L, 34L, 60L), average = c(2099.6666666667,
11037.6666666667, 17337, 21358, 23271.6666666667, 23927, 23824.3333333333,
21919.3333333333, 19870.6666666667, 17488, 12760.6666666667,
6035, 334, 46, 27, 42.6666666667, 1400.6666666667, 6523.3333333333,
10888, 12357.6666666667, 8801, 4395, 333.6666666667, 44.6666666667,
26.3333333333, 59.3333333333)), .Names = c("Collimator", "angle",
"X1", "X2", "X3", "average"), row.names = c(NA, -26L), class = "data.frame")
I first scale average counts for both collimator y and n to a make the highest counts 1
df <- ddply(df, .(Collimator), transform,
norm.average = average / max(average))
and plot the curves:
ggplot(df, aes(x=angle,y=norm.average,col=Collimator)) +
geom_point() + geom_line()
Using geom_line is quite unpleasing on the eye and I would rather fit to the data using stat_smooth. Each data set should be symmetric about the mean so I think a Gaussian fit should be ideal. How can I fit a Gaussian to the dataset collimator="y" and collimator="n" in ggplot2 or using base R. Also I would like to output the mean and standard deviation. Can this be done?

Answer 1

By definition your data is not Gaussian but a kind of Gaussian-like shape, and here is the example of the visualization of fitting:
fit <- dlply(df, .(Collimator), function(x) {
co <- coef(nls(norm.average ~ exp(-(angle - m)^2/(2 * s^2)), data = x, start = list(s = 50, m = 80)))
stat_function(fun = function(x) exp(-(x - co["m"])^2/(2 * co["s"]^2)), data = x)
})
ggplot(df, aes(x = angle, y = norm.average, col = Collimator)) + geom_point() + fit
Updated
To obtain the parameters:
fit <- dlply(df, .(Collimator), function(x) {
co <- coef(nls(norm.average ~ exp(-(angle - m)^2/(2 * s^2)), data = x, start = list(s = 50, m = 80)))
r <- stat_function(fun = function(x) exp(-(x - co["m"])^2/(2 * co["s"]^2)), data = x)
attr(r, ".coef") <- co
r
})
then,
> ldply(fit, attr, ".co")
Collimator s m
1 n 52.99117 82.60820
2 y 21.99518 86.61268