tune.rrmix: Reduced-rank mixture models with optimal tuning parameter(s)

Description

Reduced-rank mixture models with optimal tuning parameter(s)

Usage

tune.rrmix(K = NULL, K.max = NULL, X, Y, est = c("FR", "RP", "ANNP"),
           lambda = NULL, n.lambda = 20, gamma = 2,
           ind0 = NULL, para0 = NULL, seed = NULL, kmscale = FALSE, km.nstart = 20,
           n.init = 100, commonvar = FALSE, maxiter = 1000, maxiter.int = 100,
           thres = 1e-05, thres.int = 1e-05, 
           para.true = NULL, ind.true = NULL)

Arguments

number of mixture components. Required when K.max is `NULL'.

K.max

maximum of mixture components. Default is `NULL'. When provided, the argument K is ignored.

n by p design matrix where n is the number of observations and p is the number of predictors.

n by q response matrix where n is the number of observations and q is the number of responses.

est

character, specifying the estimation method. `FR', `RP', and `ANNP' refers to as the full-ranked, rank-penalized, and adaptive nuclear norm penalized method, respectively.

lambda

vector consisting of lambda candidates. Only used in the estimation method of `RP' and `ANNP'. If 0, all estimation methods (`FR', `RP', and `ANNP') provide the same estimation results. Default is 'NULL'. If 'NULL', data-adaptive range of lambda will be provided internally.

n.lambda

number of lambda candidates to explore. Only used when 'lambda' is 'NULL'. Default is 20.

gamma

numerical value, specifying additional tuning parameter, only used in the estimation method of `ANNP'. It must be nonnegative.

ind0

vector of length n, specifying the initial assignment of the mixture membership of n observations when there is prior information on the membership. If `NULL', K-means clustering technique is used to assign the membership for n observations. Default is `NULL'.

para0

array of length K. It consists of K lists, each of which contains initial values of membership probability, coefficient matrix, and variance- covariance matrix.

seed

seed number for the reproducibility of results. Default of `NULL'.

kmscale

logical value, indicating whether Y is scaled prior to K-means clustering for initialization. Default is `FALSE'.

km.nstart

number of random sets considered to perform K-means clustering for initialization. Default is 20.

n.init

number of initializations to try. Two methods for initial clustering are used: K-means and random clustering.

commonvar

logical value, indicating the homogeneity assumption of variance-covariance matrices across K mixture components. Default is `FALSE'.

maxiter

maximum number of iterations for external iterative algorithm, used in all estimation methods.

maxiter.int

maximum number of iterations for internal iterative algorithm, only used in the estimation method of `ANNP'.

thres

threshold value for external EM algorithm, used in all estimation methods. It controls the termination of the EM algorithm.

thres.int

threshold value for internal iterative algorithm, only used in the estimation method of `ANNP'. It controls the termination of the internal algorithm.

para.true

array of length K. It consists of K lists, each of which contains a coefficient matrix and its true rank. Only used when true models are known, e.g., in a simulation study.

ind.true

vector of length n, specifying the true mixture membership for n observations. Only used when true models are known, e.g., in a simulation study.

Value

lambda.cand

lambda values used as input.

penloglik

penalized log-likelihood values corresponding to the set of lambda values.

bic

BIC values corresponding to the set of lambda values.

est.rank

estimated ranks corresponding to the set of lambda values.

References

Kang, S., Chen, K., and Yao, W. (2022+). "Reduced rank estimation in mixtures of multivariate linear regression".

Examples

Run this code

# NOT RUN {
#-----------------------------------------------------------#
# Real Data Example: Tuna Data
#-----------------------------------------------------------#
require(bayesm)
data(tuna)
tunaY <- log(tuna[, c("MOVE1", "MOVE2", "MOVE3", "MOVE4",
                  "MOVE5", "MOVE6", "MOVE7")])
tunaX <- tuna[, c("NSALE1", "NSALE2", "NSALE3", "NSALE4",
              "NSALE5", "NSALE6", "NSALE7",
              "LPRICE1", "LPRICE2", "LPRICE3", "LPRICE4",
              "LPRICE5", "LPRICE6", "LPRICE7")]
tunaX <- cbind(intercept = 1, tunaX)

# }
# NOT RUN {
tuna.tune <- tune.rrmix(K.max = 3, X = tunaX, Y = tunaY, est = "RP",
             lambda = exp(seq(0, log(100), length = 20)),
             seed = 100, n.init = 100)
summary(tuna.tune)
plot(tuna.tune, transform.y = log, ylab = "log(lambda)")
# }