EM Algorithm for Mixtures of Poisson Regressions
Returns EM algorithm output for mixtures of Poisson regressions with arbitrarily many components.
poisregmixEM(y, x, lambda = NULL, beta = NULL, k = 2,
addintercept = TRUE, epsilon = 1e-08,
maxit = 10000, verb = FALSE)y |
An n-vector of response values. |
x |
An nxp matrix of predictors. See |
lambda |
Initial value of mixing proportions. Entries should sum to
1. This determines number of components. If NULL, then |
beta |
Initial value of |
k |
Number of components. Ignored unless |
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. |
poisregmixEM returns a list of class mixEM with items:
x |
The predictor values. |
y |
The response values. |
lambda |
The final mixing proportions. |
beta |
The final Poisson regression coefficients. |
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. |
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.
## 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
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