# Manly transformation selection Runs forward or backward model selection procedures for finding the optimal model in terms of BIC. ```r Manly.select(X, model, method, tol = 1e-5, max.iter = 1000, silent = FALSE) ``` ## Arguments - `X`: dataset matrix (n x p) - `model`: list containing parameters of the initial model - `method`: model selection method (options 'forward' and 'backward') - `tol`: tolerance level - `max.iter`: maximum number of iterations - `silent`: output control ## Details Runs Manly forward and backward model selection procedures for a provided dataset. Forward and backward selection can be started from any ManlyMix object provided in 'model'. Manly transformation parameters are provided in matrix 'model$la'. If some transformations are not needed for specific components, zeros have to be specified in corresponding poisition. When all transformation parameters are set to zero, Manly mixture model degenerates to a Gaussian mixture model. Notation: n - sample size, p - dimensionality of the dataset X, K - number of mixture components. ## Returns - **la**: matrix of the estimated transformation parameters (K x p) - **tau**: vector of mixing proportions (length K) - **Mu**: matrix of the estimated mean vectors (K x p) - **S**: array of the estimated covariance matrices (p x p x K) - **gamma**: matrix of posterior probabilities (n x K) - **id**: estimated membership vector (length n) - **ll**: log likelihood value - **bic**: Bayesian Information Criterion - **iter**: number of EM iterations run - **flag**: convergence flag (0 - success, 1 - failure) ## See Also Manly.EM ## Examples ```r set.seed(123) K <- 3; p <- 4 X <- as.matrix(iris[,-5]) id.true <- rep(1:K, each = 50) # Obtain initial memberships based on the K-means algorithm id.km <- kmeans(X, K)$cluster # Run the EM algorithm for a Gaussian mixture model based on K-means solution G <- Manly.EM(X, id = id.km) id.G <- G$id # Run FORWARD SELECTION ('silent' is on) F <- Manly.select(X, model = G, method = "forward", silent = TRUE) # Run the EM algorithm for a full Manly mixture model based on Gaussian mixture solution la <- matrix(0.1, K, p) M <- Manly.EM(X, id = id.G, la = la) # Run BACKWARD SELECTION ('silent' is off) B <- Manly.select(X, model = M, method = "backward") BICs <- c(G$bic, M$bic, F$bic, B$bic) names(BICs) <- c("Gaussian", "Manly", "Forward", "Backward") BICs ```

Manly.select function