library(mclust) library(boot) data_df = read.csv("Data_2.csv") # Load your data here # Fit the two-component normal mixture model model = Mclust(data_df, G = 2) cluster_stat <- function(data, indices) { bootstrap_sample <- data[indices, ] model <- Mclust(bootstrap_sample) return(model$G) } set.seed(123) # for reproducibility B=99 results <- boot(data_df, cluster_stat, R = B) mean(results$t == 3) mean(results$t == 2) print(results) above codes whether can solve Use the bootstrap with B = 99 bootstrap replications to test the null hypothesis H0 : g = 2 versus H1 : g = 3.
Question
library(mclust) library(boot) data_df = read.csv("Data_2.csv") # Load your data here
Fit the two-component normal mixture model
model = Mclust(data_df, G = 2)
cluster_stat <- function(data, indices) { bootstrap_sample <- data[indices, ] model <- Mclust(bootstrap_sample) return(modelG) } set.seed(123) # for reproducibility B=99 results <- boot(data_df, cluster_stat, R = B) mean(resultst == 3) mean(results$t == 2) print(results) above codes whether can solve Use the bootstrap with B = 99 bootstrap replications to test the null hypothesis H0 : g = 2 versus H1 : g = 3.
Solution
The code you provided does perform a bootstrap procedure with B = 99 replications, but it doesn't directly test the null hypothesis H0: g = 2 versus H1: g = 3. Instead, it calculates the proportion of bootstrap samples for which the best number of clusters (according to BIC) is 2 or 3.
However, you can modify the code to perform a bootstrap test of the null hypothesis. Here's how you can do it:
library(mclust)
library(boot)
data_df = read.csv("Data_2.csv") # Load your data here
# Fit the two-component and three-component normal mixture models
model2 = Mclust(data_df, G = 2)
model3 = Mclust(data_df, G = 3)
# Define a function that calculates the log-likelihood for a given dataset and a given model
logLikFun <- function(data, indices, model) {
bootstrap_sample = data[indices, ]
modelResample = Mclust(bootstrap_sample, G = model$G)
return(modelResample$loglik)
}
# Perform the bootstrap procedure for both models
set.seed(123) # for reproducibility
B = 99
boot2 = boot(data_df, statistic = logLikFun, R = B, model = model2)
boot3 = boot(data_df, statistic = logLikFun, R = B, model = model3)
# Calculate the difference in mean log-likelihoods and its standard error
diffMean = mean(boot3$t) - mean(boot2$t)
diffSE = sqrt(var(boot3$t) + var(boot2$t))
# Calculate the z-value and the p-value for the test
zValue = diffMean / diffSE
pValue = 2 * (1 - pnorm(abs(zValue)))
# Print the p-value
print(pValue)
This code will perform a bootstrap test of the null hypothesis H0: g = 2 versus H1: g = 3. The p-value is printed at the end. If the p-value is less than your chosen significance level (e.g., 0.05), you reject the null hypothesis and conclude that g = 3 is a better model. If the p-value is greater than your significance level, you do not reject the null hypothesis and conclude that g = 2 is a better model.
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