R: EM Algorithm for Mixtures of Poisson Regressions

poisregmixEM {mixtools} | R Documentation

## 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

`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` is generated by binning the data into k bins and using `glm` on the values in each of the bins. If both `lambda` and `beta` are NULL, then number of components is determined by `k`.
`k` | 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:

`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.

### 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.

### See Also

`logisregmixEM`

### Examples

    ## 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

[Package mixtools version 1.2.0 Index]