regmixEM {mixtools}

EM Algorithm for Mixtures of Regressions

Description

Returns EM algorithm output for mixtures of multiple regressions with arbitrarily many components.

Usage

regmixEM(y, x, lambda = NULL, beta = NULL, sigma = NULL, k = 2,
         addintercept = TRUE, arbmean = TRUE, arbvar = 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. Entries should sum to 1. This determines number of components. If NULL, then lambda is random from uniform Dirichlet and number of components is determined by beta.

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. If both lambda and beta are NULL, then number of components is determined by sigma.

sigma

A vector of standard deviations. If NULL, then 1/sigma^2 has random standard exponential entries according to a binning method done on the data. If lambda, beta, and sigma are NULL, then number of components is determined by k.

k

Number of components. Ignored unless all of lambda, beta, and sigma are NULL.

addintercept

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

arbmean

If TRUE, each mixture component is assumed to have a different set of regression coefficients (i.e., the betas).

arbvar

If TRUE, each mixture component is assumed to have a different sigma.

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

regmixEM 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.

lambda

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.

scale

If arbmean = FALSE, then the scale factor for the component standard deviations is returned. Otherwise, this is omitted from the output.

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

de Veaux, R. D. (1989), Mixtures of Linear Regressions, Computational Statistics and Data Analysis 8, 227-245.

Hurn, M., Justel, A. and Robert, C. P. (2003) Estimating Mixtures of Regressions, Journal of Computational and Graphical Statistics 12(1), 55–79.

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

See Also

regcr, regmixMH

Examples

## EM output for NOdata.
 
data(NOdata)
attach(NOdata)
set.seed(100)
em.out <- regmixEM(Equivalence, NO, verb = TRUE, epsilon = 1e-04)
em.out[3:6]