Fit and plot the fitted components of a multi-modal distribution assuming normal distributions as the components.

fit_and_plot_normal_mixtures.R

library(ggplot2)
library(plyr)
library(mixtools)

###
# GLOBAL THEME AND GLOBAL AESTHETICS
###
old <- theme_set(theme_bw() +
                   theme(text = element_text(size=12),
                         axis.title = element_text(size = 14, face="bold"),
                         title = element_text(face = "bold")
                   )
)
update_geom_defaults("point", list(size = 2.5))

###
# FUNCTIONS ###
###
# Motivated by http://tinyheero.github.io/2016/01/03/gmm-em.html
#' Plot a Mixture Component
#' 
#' @param x Input data.
#' @param mu Mean of component.
#' @param sigma Standard of component.
#' @param lam Mixture weight of component.
plot_mix_comps <- function(x, mu, sigma, lam) {
  lam * dnorm(x, mu, sigma)
}

###
# DATA #####
###
# data(faithful)
# attach(faithful)

df <- waiting

# Fit the normal mixture(s)
mixmdl <- normalmixEM(df)

# Base graphics
# plot(mixmdl,which=2, breaks=200)
# lines(density(df), lty=2, lwd=2)

# Using ggplot
# Motivated by http://tinyheero.github.io/2016/01/03/gmm-em.html
p <- data.frame(x = df) %>%
        ggplot(aes(x=x)) +
        geom_histogram(aes(x, ..density..), binwidth = 1, colour = "black", 
                       fill = "white") +
        stat_function(fun = plot_mix_comps, aes(colour="1"),
                      args = list(mixmdl$mu[1], mixmdl$sigma[1], 
                                  lam = mixmdl$lambda[1]), lwd = 1.5) +
        stat_function(fun = plot_mix_comps, aes(colour="2"),
                      args = list(mixmdl$mu[2], mixmdl$sigma[2], 
                                  lam = mixmdl$lambda[2]), lwd = 1.5) +
        geom_density(aes(x, ..density.., colour="joint"),  size=1.5) +
        scale_colour_manual("Component", values = c("1"="red", "2"="blue", "joint" = "black")) +
        ylab("Density") +
        xlab("Values")

print(p)

DESRCIPTION

mixtools provide plotting functionality for the fits, e.g., via plot.mixEM using base graphics (AFAIK).
This code is meant to demonstrate the use of ggplot to create a plot of the data histogram, the "joint" (prior) distribution, and the (posterior) distributions of the individual components, here two components.

Should your data have more than two modes, you should add stat_function() entries according to the number of fitted components.