poisregmixEM: EM Algorithm for Mixtures of Poisson Regressions

Description

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

Usage

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

Arguments

An n-vector of response values.

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 is generated by binning the data into k bins and using glm

Number of components. Ignored unless lambda and beta are both NULL.

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

poisregmixEM returns a list of class mixEM with items:
xThe predictor values.
yThe response values.
lambdaThe final mixing proportions.
betaThe final Poisson regression coefficients.
loglikThe final log-likelihood.
posteriorAn nxk matrix of posterior probabilities for observations.
all.loglikA vector of each iteration's log-likelihood.
restartsThe number of times the algorithm restarted due to unacceptable choice of initial values.
ftA character vector giving the name of the function.

References

McLachlan, G. J. and Peel, D. (2000) Finite Mixture Models, John Wiley & Sons, Inc. Wang, P., Puterman, M. L., Cockburn, I. and Le, N. (1996) Mixed Poisson Regression Models with Covariate Dependent Rates, Biometrics, 52(2), 381--400.

Examples

Run this code

## EM output for data generated from a 2-component model.

set.seed(100)
beta <- matrix(c(1, .5, .7, -.8), 2, 2)
x <- runif(50, 0, 10)
xbeta <- cbind(1, x)%*%beta
w <- rbinom(50, 1, .5)
y <- w*rpois(50, exp(xbeta[, 1]))+(1-w)*rpois(50, exp(xbeta[, 2]))
out <- poisregmixEM(y, x, verb = TRUE,  epsilon = 1e-03)
out