Heuristically chosen starting value of theta

Description

This function uses a k-means algorithm to heuristically select suitable starting values for the general model.

Usage

choose.theta(u, m, ...)

Arguments

Details

The function selects the centers from the k-means algorithm as an initial estimate of the means. The proportional sizes of the clusters are selected as the initial values of the mixture proportions. The within cluster standard deviations are used as the variance of the clusters. The correlations between each dimension are taken to be zero.

Value

A list of parameters for the GMCM model on the form described in rtheta.

Note

The function uses the kmeans function from the stats-package.

Author(s)

Anders Ellern Bilgrau <anders.ellern.bilgrau@gmail.com>

Examples

set.seed(2)

# Simulating data
data1 <- SimulateGMCMData(n = 10000, m = 3, d = 2)
obs.data <- Uhat(data1$u)  # The ranked observed data

# Using choose.theta to get starting estimates
theta <- choose.theta(u = obs.data, m = 3)
print(theta)

# To illustrate theta, we simulate from the model
data2 <- SimulateGMMData(n = 10000, theta = theta)

cols <- apply(get.prob(obs.data,theta),1,which.max)

# Plotting
par(mfrow = c(1,3))
plot(data1$z, main = "True latent GMM")
plot(Uhat(data1$u), col = cols,
     main = "Observed GMCM\nColoured by k-means clustering")
plot(data2$z, main = "initial GMM")

Results

R version 3.3.1 (2016-06-21) -- "Bug in Your Hair"
Copyright (C) 2016 The R Foundation for Statistical Computing
Platform: x86_64-pc-linux-gnu (64-bit)

R is free software and comes with ABSOLUTELY NO WARRANTY.
You are welcome to redistribute it under certain conditions.
Type 'license()' or 'licence()' for distribution details.

R is a collaborative project with many contributors.
Type 'contributors()' for more information and
'citation()' on how to cite R or R packages in publications.

Type 'demo()' for some demos, 'help()' for on-line help, or
'help.start()' for an HTML browser interface to help.
Type 'q()' to quit R.

> library(GMCM)
> png(filename="/home/ddbj/snapshot/RGM3/R_CC/result/GMCM/choose.theta.Rd_%03d_medium.png", width=480, height=480)
> ### Name: choose.theta
> ### Title: Heuristically chosen starting value of theta
> ### Aliases: choose.theta
> 
> ### ** Examples
> 
> set.seed(2)
> 
> # Simulating data
> data1 <- SimulateGMCMData(n = 10000, m = 3, d = 2)
> obs.data <- Uhat(data1$u)  # The ranked observed data
> 
> # Using choose.theta to get starting estimates
> theta <- choose.theta(u = obs.data, m = 3)
> print(theta)
$m
[1] 3

$d
[1] 2

$pie
  pie1   pie2   pie3 
0.4690 0.4002 0.1308 

$mu
$mu$comp1
[1] 0 0

$mu$comp2
[1] -10.527002  -9.741925

$mu$comp3
[1] -13.372135   6.747667


$sigma
$sigma$comp1
     [,1]     [,2]
[1,]    1 0.000000
[2,]    0 1.004652

$sigma$comp2
         [,1]      [,2]
[1,] 1.165814 0.0000000
[2,] 0.000000 0.9295826

$sigma$comp3
         [,1]      [,2]
[1,] 1.892084 0.0000000
[2,] 0.000000 0.5284667


> 
> # To illustrate theta, we simulate from the model
> data2 <- SimulateGMMData(n = 10000, theta = theta)
> 
> cols <- apply(get.prob(obs.data,theta),1,which.max)
> 
> # Plotting
> par(mfrow = c(1,3))
> plot(data1$z, main = "True latent GMM")
> plot(Uhat(data1$u), col = cols,
+      main = "Observed GMCM\nColoured by k-means clustering")
> plot(data2$z, main = "initial GMM")
> 
> 
> 
> 
> 
> dev.off()
null device 
          1 
>