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 $$ y_i \sim \rm{CMP}(\lambda_i, \nu_i), \;\;\; \log \lambda_i = \bm{x}_i^\top \beta, \;\;\; \log \nu_i = \bm{s}_i^\top \gamma. $$
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 $$ y_i^* \sim \rm{CMP}(\lambda_i, \nu_i), \;\;\; \log \lambda_i = \bm{x}_i^\top \beta, \;\;\; \log \nu_i = \bm{s}_i^\top \gamma, \;\;\; \log p_i = \bm{w}_i^\top \zeta. $$
glm.cmp(formula.lambda, formula.nu = ~ 1, formula.p = NULL,
beta.init = NULL, gamma.init = NULL, zeta.init = NULL, ...) # S3 method for cmp
AIC(object, ..., k = 2)
# S3 method for cmp
BIC(object, ...)
# S3 method for cmp
coef(object, ...)
# S3 method for cmp
deviance(object, ...)
# S3 method for cmp
equitest(object, ...)
# S3 method for cmp
leverage(object, ...)
# S3 method for cmp
logLik(object, ...)
# S3 method for cmp
nu(object, ...)
# S3 method for cmp
parametric_bootstrap(object, reps = 1000, report.period = reps + 1, ...)
# S3 method for cmp
predict(object, newdata = NULL, ...)
# S3 method for cmp
print(x, ...)
# S3 method for cmp
residuals(object, type = c("raw", "quantile"), ...)
# S3 method for cmp
sdev(object, ...)
# S3 method for cmp
summary(object, ...)
# S3 method for cmp
vcov(object, ...)
# S3 method for zicmp
AIC(object, ..., k = 2)
# S3 method for zicmp
BIC(object, ...)
# S3 method for zicmp
coef(object, ...)
# S3 method for zicmp
deviance(object, ...)
# S3 method for zicmp
equitest(object, ...)
# S3 method for zicmp
leverage(object, ...)
# S3 method for zicmp
logLik(object, ...)
# S3 method for zicmp
nu(object, ...)
# S3 method for zicmp
parametric_bootstrap(object, reps = 1000, report.period = reps + 1, ...)
# S3 method for zicmp
predict(object, newdata = NULL, ...)
# S3 method for zicmp
print(x, ...)
# S3 method for zicmp
residuals(object, type = c("raw", "quantile"), ...)
# S3 method for zicmp
sdev(object, ...)
# S3 method for zicmp
summary(object, ...)
# S3 method for zicmp
vcov(object, ...)
regression formula linked to log(lambda)
regression formula linked to log(nu). By default, is taken to be intercept only.
regression formula linked to logit(p). If NULL (the default), zero-inflation term is excluded from the model.
initial values for regression coefficients of lambda.
initial values for regression coefficients of nu.
initial values for regression coefficients of p.
other model parameters, such as data
object of type 'cmp' or 'zicmp'.
object of type 'cmp' or 'zicmp'.
Penalty per parameter to be used in AIC calculation.
New covariates to be used for prediction.
Type of residual to be computed.
Number of bootstrap repetitions.
Report progress every report.period iterations.
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.
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.