glm.cmp: 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,
  ...
)

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.

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.

Author

Kimberly Sellers, Thomas Lotze, Andrew Raim

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

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.