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## first let's make a noisy gamma distribution plot... | |
x <- seq(from=0, to=20, by=0.1) | |
y.gamma <- dgamma(x, shape=2, scale=2) | |
y.gamma.scaled <- y.gamma * 100 | |
y.norm <- vector(length=201) | |
for (i in 1:201) { | |
y.norm[i] <- rnorm(n=1, mean=y.gamma.scaled[i], sd=2) | |
} | |
data <- data.frame(x, y.norm) | |
plot(data, frame.plot=FALSE, xlab="", ylab="", col="#d95f0e", lwd=1.5) | |
## Now that we have the data, let's look at the differences | |
## and similarities between R's lowess() function and the loess() function. | |
## We'll start with the lowess() function... | |
## | |
## By default "lowess()" fits a line in each window using | |
## 2/3's of the data points. | |
## | |
## the first parameter, y.norm ~ x, says that y.norm is being | |
## modeled by x, and the second parameter, f, is the fraction | |
## of points to use in each window. Here, we're using 1/5 of the | |
## data points in each window. | |
lo.fit.gamma <- lowess(y.norm ~ x, f=1/5) | |
plot(data, frame.plot=FALSE, xlab="", ylab="", col="#d95f0e", lwd=1.5) | |
lines(x, lo.fit.gamma$y, col="black", lwd=3) | |
## Now use loess() to fit a curve to the data... | |
## | |
## By default "loess()" fits a parabola in each window using | |
## 75% of the data points. | |
plx<-predict(loess(y.norm ~ x, span=1/5, degree=2, family="symmetric", iterations=4), se=T) | |
plot(data, frame.plot=FALSE, xlab="", ylab="", col="#d95f0e", lwd=1.5) | |
lines(x, plx$fit, col="black", lwd=3) | |
## Now let's add a confidence interval to the loess() fit... | |
plot(data, type="n", frame.plot=FALSE, xlab="", ylab="", col="#d95f0e", lwd=1.5) | |
polygon(c(x, rev(x)), c(plx$fit + qt(0.975,plx$df)*plx$se, rev(plx$fit - qt(0.975,plx$df)*plx$se)), col="#99999977") | |
points(data, col="#d95f0e", lwd=1.5) | |
lines(x, plx$fit, col="black", lwd=3) | |
## Now that we know how those functions work... we can skip all that | |
## nasty stuff and just use ggplot2 with geom_point() and geom_smooth() | |
library(ggplot2) | |
ggplot(data=data, aes(x=x, y=y.norm)) + | |
geom_point() + | |
geom_smooth(span=1/5) |