glm.cmp: COM-Poisson and Zero-Inflated COM-Poisson Regression

In lotze/COMPoissonReg: Conway-Maxwell Poisson (COM-Poisson) Regression

COM-Poisson and Zero-Inflated COM-Poisson Regression

Description

Fit COM-Poisson regression using maximum likelihood estimation. Zero-Inflated COM-Poisson can be fit by specifying a regression for the overdispersion parameter.

Usage

glm.cmp(
  formula.lambda,
  formula.nu = ~1,
  formula.p = NULL,
  data = NULL,
  init = NULL,
  fixed = NULL,
  control = NULL,
  ...
)

Arguments

formula.lambda	regression formula linked to log(lambda). The response should be specified here.
formula.nu	regression formula linked to log(nu). The default, is taken to be only an intercept.
formula.p	regression formula linked to logit(p). If NULL (the default), zero-inflation term is excluded from the model.
data	An optional data.frame with variables to be used with regression formulas. Variables not found here are read from the envionment.
init	A data structure that specifies initial values. See the helper function get.init.
fixed	A data structure that specifies which coefficients should remain fixed in the maximum likelihood procedure. See the helper function get.fixed.
control	A control data structure. See the helper function get.control. If NULL, a global default will be used.
...	other arguments, such as subset and na.action.

Details

The COM-Poisson regression model is

y_i \sim \rm{CMP}(\lambda_i, \nu_i), \;\;\; \log \lambda_i = \bm{x}_i^\top \beta, \;\;\; \log \nu_i = \bm{s}_i^\top \gamma.

The Zero-Inflated COM-Poisson regression model assumes that y_i is 0 with probability p_i or y_i^* with probability 1 - p_i, where

y_i^* \sim \rm{CMP}(\lambda_i, \nu_i), \;\;\; \log \lambda_i = \bm{x}_i^\top \beta, \;\;\; \log \nu_i = \bm{s}_i^\top \gamma, \;\;\; \rm{logit} \, p_i = \bm{w}_i^\top \zeta.

Value

glm.cmp produces an object of either class cmpfit or zicmpfit, depending on whether zero-inflation is used in the model. From this object, coefficients and other information can be extracted.

Author(s)

Kimberly Sellers, Thomas Lotze, Andrew Raim

References

Kimberly F. Sellers & Galit Shmueli (2010). A Flexible Regression Model for Count Data. Annals of Applied Statistics, 4(2), 943-961.

Kimberly F. Sellers and Andrew M. Raim (2016). A Flexible Zero-Inflated Model to Address Data Dispersion. Computational Statistics and Data Analysis, 99, 68-80.

lotze/COMPoissonReg documentation built on Feb. 11, 2024, 12:03 p.m.