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generate_sigma_matrix <-
function(X, beta, gamma){
sigma_matrix <- matrix(0, nrow = 3, ncol = 3)
#browser()
k <- nrow(X)
df <- k - 1
beta_hat <- mean(beta)
gamma_hat <- mean(gamma)
# fill covariance matrix (triangular)
sigma_matrix[1,1] <- sum((X$mesor - mean(X$mesor))^2)/df
sigma_matrix[1,2] <- sum((X$mesor - mean(X$mesor)) %*% (beta - mean(beta)))/df
sigma_matrix[1,3] <- sum((X$mesor - mean(X$mesor)) %*% (gamma - mean(gamma)))/df
sigma_matrix[2,2] <- sum((beta - mean(beta))^2)/df
sigma_matrix[2,3] <- sum((beta - mean(beta)) %*% (gamma - mean(gamma)))/df
sigma_matrix[3,3] <- sum((gamma - mean(gamma))^2)/df
# mirror lower matrix
sigma_matrix[lower.tri(sigma_matrix)] <- sigma_matrix[upper.tri(sigma_matrix)]
return(sigma_matrix)
}
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