emMixRHLP {flamingos}

emMixRHLP implements the EM algorithm to fit a mixture of RHLP models.

Description

emMixRHLP implements the maximum-likelihood parameter estimation of a mixture of RHLP models by the Expectation-Maximization (EM) algorithm.

Usage

emMixRHLP(X, Y, K, R, p = 3, q = 1,
  variance_type = c("heteroskedastic", "homoskedastic"),
  init_kmeans = TRUE, n_tries = 1, max_iter = 1000,
  threshold = 1e-05, verbose = FALSE, verbose_IRLS = FALSE)

Arguments

X

Numeric vector of length m representing the covariates/inputs x_{1},\dots,x_{m}.

Y

Matrix of size (n, m) representing the observed responses/outputs. Y consists of n functions of X observed at points 1,\dots,m.

K

The number of clusters (Number of RHLP models).

R

The number of regimes (RHLP components) for each cluster.

p

Optional. The order of the polynomial regression. By default, p is set at 3.

q

Optional. The dimension of the logistic regression. For the purpose of segmentation, it must be set to 1 (which is the default value).

variance_type

Optional character indicating if the model is "homoskedastic" or "heteroskedastic". By default the model is "heteroskedastic".

init_kmeans

Optional. A logical indicating whether or not the curve partition should be initialized by the K-means algorithm. Otherwise the curve partition is initialized randomly.

n_tries

Optional. Number of runs of the EM algorithm. The solution providing the highest log-likelihood will be returned.

If n_tries > 1, then for the first run, parameters are initialized by uniformly segmenting the data into R segments, and for the next runs, parameters are initialized by randomly segmenting the data into R contiguous segments.

max_iter

Optional. The maximum number of iterations for the EM algorithm.

threshold

Optional. A numeric value specifying the threshold for the relative difference of log-likelihood between two steps of the EM as stopping criteria.

verbose

Optional. A logical value indicating whether or not values of the log-likelihood should be printed during EM iterations.

verbose_IRLS

Optional. A logical value indicating whether or not values of the criterion optimized by IRLS should be printed at each step of the EM algorithm.

Details

emMixRHLP function implements the EM algorithm. This function starts with an initialization of the parameters done by the method initParam of the class ParamMixRHLP, then it alternates between the E-Step (method of the class StatMixRHLP) and the M-Step (method of the class ParamMixRHLP) until convergence (until the relative variation of log-likelihood between two steps of the EM algorithm is less than the threshold parameter).

Value

EM returns an object of class ModelMixRHLP.

See Also

ModelMixRHLP, ParamMixRHLP, StatMixRHLP

Examples

data(toydataset)

# Let's fit a mixRHLP model on a dataset containing 2 clusters:
data <- toydataset[1:190,1:21]
x <- data$x
Y <- t(data[,2:ncol(data)])

mixrhlp <- emMixRHLP(X = x, Y = Y, K = 2, R = 2, p = 1, verbose = TRUE)

mixrhlp$summary()

mixrhlp$plot()