hmeEM {mixtools}

EM Algorithm for Mixtures-of-Experts

Description

Returns EM algorithm output for a mixture-of-experts model. Currently, this code only handles a 2-component mixture-of-experts, but will be extended to the general k-component hierarchical mixture-of-experts.

Usage

hmeEM(y, x, lambda = NULL, beta = NULL, sigma = NULL, w = NULL,
      k = 2, addintercept = TRUE, epsilon = 1e-08, 
      maxit = 10000, verb = FALSE)

Arguments

y

An n-vector of response values.

x

An nxp matrix of predictors. See addintercept below.

lambda

Initial value of mixing proportions, which are modeled as an inverse logit function of the predictors. Entries should sum to 1. If NULL, then lambda is taken as 1/k for each x.

beta

Initial value of beta parameters. Should be a pxk matrix, where p is the number of columns of x and k is number of components. If NULL, then beta has standard normal entries according to a binning method done on the data.

sigma

A vector of standard deviations. If NULL, then 1/\code{sigma}^2 has random standard exponential entries according to a binning method done on the data.

w

A p-vector of coefficients for the way the mixing proportions are modeled. See lambda.

k

Number of components. Currently, only k=2 is accepted.

addintercept

If TRUE, a column of ones is appended to the x matrix before the value of p is calculated.

epsilon

The convergence criterion.

maxit

The maximum number of iterations.

verb

If TRUE, then various updates are printed during each iteration of the algorithm.

Value

hmeEM returns a list of class mixEM with items:

x

The set of predictors (which includes a column of 1's if addintercept = TRUE).

y

The response values.

w

The final coefficients for the functional form of the mixing proportions.

lambda

An nxk matrix of the final mixing proportions.

beta

The final regression coefficients.

sigma

The final standard deviations. If arbmean = FALSE, then only the smallest standard deviation is returned. See scale below.

loglik

The final log-likelihood.

posterior

An nxk matrix of posterior probabilities for observations.

all.loglik

A vector of each iteration's log-likelihood.

restarts

The number of times the algorithm restarted due to unacceptable choice of initial values.

ft

A character vector giving the name of the function.

References

Jacobs, R. A., Jordan, M. I., Nowlan, S. J. and Hinton, G. E. (1991) Adaptive Mixtures of Local Experts, Neural Computation 3(1), 79–87.

McLachlan, G. J. and Peel, D. (2000) Finite Mixture Models, John Wiley and Sons, Inc.

See Also

regmixEM

Examples

## EM output for NOdata.
 
data(NOdata)
attach(NOdata)
set.seed(100)
em.out <- regmixEM(Equivalence, NO)
hme.out <- hmeEM(Equivalence, NO, beta = em.out$beta)
hme.out[3:7]