Consider an observed random sample of size n, w1, . . . , wn, from a normal distribution N(µ, σ2 ). To the 75 observations in the dataset Data-A1a.csv apply the EM algorithm to fit via maximum likelihood the two-component normal mixture density with common variances, To this end, Use an available program to fit this mixture model via the EM algorithm such as Mclust, which may be found on CRAN. Explicitly give the starting or starting points tried in your fitting of the EM algorithm and the stopping criterion adopted. how can use R studio set starting points tried in fitting of the EM algorithm and the stopping criterion
Question
Consider an observed random sample of size n, w1, . . . , wn, from a normal distribution N(µ, σ2 ). To the 75 observations in the dataset Data-A1a.csv apply the EM algorithm to fit via maximum likelihood the two-component normal mixture density with common variances, To this end, Use an available program to fit this mixture model via the EM algorithm such as Mclust, which may be found on CRAN. Explicitly give the starting or starting points tried in your fitting of the EM algorithm and the stopping criterion adopted. how can use R studio set starting points tried in fitting of the EM algorithm and the stopping criterion
Solution
In R, the Mclust package automatically determines the starting points and the stopping criterion for the EM algorithm. However, if you want to manually set the starting points and the stopping criterion, you can use the normalmixEM function from the mixtools package. Here's how you can do it:
- Install and load the necessary packages:
install.packages("mixtools")
library(mixtools)
- Load your data:
data <- read.csv("Data-A1a.csv")
- Set your starting points. For a two-component normal mixture model, you need to provide initial values for the means (mu), standard deviations (sigma), and mixing proportions (lambda) of the two components:
mu <- c(0, 1) # replace with your chosen starting points
sigma <- c(1, 1) # replace with your chosen starting points
lambda <- c(0.5, 0.5) # replace with your chosen starting points
- Apply the EM algorithm using normalmixEM:
model <- normalmixEM(data, mu=mu, sigma=sigma, lambda=lambda)
- The stopping criterion in normalmixEM is based on the relative change in the log-likelihood. The algorithm stops when this change is less than a small positive tolerance value. You can set this value using the 'epsilon' argument:
model <- normalmixEM(data, mu=mu, sigma=sigma, lambda=lambda, epsilon=1e-8)
- To see the results of the model:
summary(model)
This will give you the parameters of the mixture model (means, variances, and mixing proportions), the log-likelihood, and the number of iterations.
Please note that the actual code might vary depending on the structure of your data and the specific requirements of your analysis.
Similar Questions
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