glm.cmp {COMPoissonReg}R Documentation

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.

The COM-Poisson regression model is

y_i ~ CMP(lambda_i, nu_i), log lambda_i = x_i^T beta, log nu_i = s_i^T 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^* ~ CMP(lambda_i, nu_i), log lambda_i = x_i^T beta, log nu_i = s_i^T gamma, log p_i = w_i^T zeta.

Usage

	glm.cmp(formula.lambda, formula.nu = ~ 1, formula.p = NULL,
        beta.init = NULL, gamma.init = NULL, zeta.init = NULL, ...)

	## S3 method for class 'cmp'
AIC(object, ..., k = 2)
	## S3 method for class 'cmp'
BIC(object, ...)
	## S3 method for class 'cmp'
coef(object, ...)
	## S3 method for class 'cmp'
deviance(object, ...)
	## S3 method for class 'cmp'
equitest(object, ...)
	## S3 method for class 'cmp'
leverage(object, ...)
	## S3 method for class 'cmp'
logLik(object, ...)
	## S3 method for class 'cmp'
nu(object, ...)
	## S3 method for class 'cmp'
parametric_bootstrap(object, reps = 1000, report.period = reps + 1, ...)
	## S3 method for class 'cmp'
predict(object, newdata = NULL, ...)
	## S3 method for class 'cmp'
print(x, ...)
	## S3 method for class 'cmp'
residuals(object, type = c("raw", "quantile"), ...)
	## S3 method for class 'cmp'
sdev(object, ...)
	## S3 method for class 'cmp'
summary(object, ...)
	## S3 method for class 'cmp'
vcov(object, ...)

	## S3 method for class 'zicmp'
AIC(object, ..., k = 2)
	## S3 method for class 'zicmp'
BIC(object, ...)
	## S3 method for class 'zicmp'
coef(object, ...)
	## S3 method for class 'zicmp'
deviance(object, ...)
	## S3 method for class 'zicmp'
equitest(object, ...)
	## S3 method for class 'zicmp'
leverage(object, ...)
	## S3 method for class 'zicmp'
logLik(object, ...)
	## S3 method for class 'zicmp'
nu(object, ...)
	## S3 method for class 'zicmp'
parametric_bootstrap(object, reps = 1000, report.period = reps + 1, ...)
	## S3 method for class 'zicmp'
predict(object, newdata = NULL, ...)
	## S3 method for class 'zicmp'
print(x, ...)
	## S3 method for class 'zicmp'
residuals(object, type = c("raw", "quantile"), ...)
	## S3 method for class 'zicmp'
sdev(object, ...)
	## S3 method for class 'zicmp'
summary(object, ...)
	## S3 method for class 'zicmp'
vcov(object, ...)

Arguments

formula.lambda

regression formula linked to log(lambda)

formula.nu

regression formula linked to log(nu). By default, is taken to be intercept only.

formula.p

regression formula linked to logit(p). If NULL (the default), zero-inflation term is excluded from the model.

beta.init

initial values for regression coefficients of lambda.

gamma.init

initial values for regression coefficients of nu.

zeta.init

initial values for regression coefficients of p.

...

other model parameters, such as data

object

object of type 'cmp' or 'zicmp'.

x

object of type 'cmp' or 'zicmp'.

k

Penalty per parameter to be used in AIC calculation.

newdata

New covariates to be used for prediction.

type

Type of residual to be computed.

reps

Number of bootstrap repetitions.

report.period

Report progress every report.period iterations.

Value

glm.cmp produces an object of either class 'cmp' or 'zicmp', 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.


[Package COMPoissonReg version 0.6.1 Index]