emTMoE {meteorits}

emTMoE implements the ECM algorithm to fit a t Mixture of Experts (TMoE).

Description

emTMoE implements the maximum-likelihood parameter estimation of a Student Mixture of Experts (TMoE) model by the Conditional Expectation Maximization (ECM) algorithm.

Usage

emTMoE(X, Y, K, p = 3, q = 1, n_tries = 1, max_iter = 1500,
  threshold = 1e-06, verbose = FALSE, verbose_IRLS = FALSE)

Arguments

X

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

Y

Numeric vector of length n representing the observed response/output y_{1},\dots,y_{n}.

K

The number of experts.

p

Optional. The order of the polynomial regression for the experts.

q

Optional. The order of the logistic regression for the gating network.

n_tries

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

max_iter

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

threshold

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

verbose

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

Details

emTMoE function implements the ECM algorithm for the TMoE model. This function starts with an initialization of the parameters done by the method initParam of the class ParamTMoE, then it alternates between the E-Step (method of the class StatTMoE) and the M-Step (method of the class ParamTMoE) until convergence (until the relative variation of log-likelihood between two steps of the ECM algorithm is less than the threshold parameter).

Value

ECM returns an object of class ModelTMoE.

See Also

ModelTMoE, ParamTMoE, StatTMoE

Examples

data(tempanomalies)
x <- tempanomalies$Year
y <- tempanomalies$AnnualAnomaly

tmoe <- emTMoE(X = x, Y = y, K = 2, p = 1, verbose = TRUE)

tmoe$summary()

tmoe$plot()