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, Use an available program to fit this mixture model via the EM algorithm such as MClust, FlexMix, and EMMIX, 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. use mclust of R studio
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, Use an available program to fit this mixture model via the EM algorithm such as MClust, FlexMix, and EMMIX, 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. use mclust of R studio
Solution
To apply the EM algorithm to fit a two-component normal mixture density with common variances using MClust in R studio, follow these steps:
- Install and load the necessary packages:
install.packages("mclust")
library(mclust)
- Load your data:
data <- read.csv("Data-A1a.csv")
- Apply the EM algorithm using MClust:
model <- Mclust(data)
The Mclust function automatically estimates the number of clusters (in this case, the number of components in the mixture model) using the Bayesian Information Criterion (BIC). It also initializes the EM algorithm with hierarchical clustering and uses the BIC to select the best model.
- To see the results of the model:
summary(model)
This will give you the number of clusters, the parameters of the mixture model (means, variances, and mixing proportions), and the classification of the observations.
- To see the starting points used in the EM algorithm:
model$parameters$pro
model$parameters$mean
model$parameters$variance
- The stopping criterion adopted in Mclust is based on the relative change in the log-likelihood. The algorithm stops when this change is less than a small positive tolerance value (the default is 1e-8).
Please note that the actual code might vary depending on the structure of your data and the specific requirements of your analysis.
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