Zero inflated Poisson and negative binomial regression {MXM}

Zero inflated Poisson and negative binomial regression

Description

Zero inflated Poisson and negative binomial regression.

Usage

zip.mod(target, dataset, wei = NULL, xnew = NULL) 
zip.reg(target, dataset, wei = NULL, lgy = NULL) 
zinb.mod(target, dataset, xnew = NULL)
zinb.reg(target, dataset, lgy = NULL)

Arguments

target

The target (dependent) variable. It must be a numerical vector with integers.

dataset

The indendent variable(s). It can be a vector, a matrix or a dataframe with continuous only variables, a data frame with mixed or only categorical variables. If this is NULL, a zero inflated Poisson distribution is fitted, no covariates are present.

wei

A vector of weights to be used for weighted regression. The default value is NULL. An example where weights are used is surveys when stratified sampling has occured. This is applicable only in the zero inflated Poisson distribution.

xnew

If you have new values for the predictor variables (dataset) whose target variable you want to predict insert them here. If you put the "dataset" or leave it NULL it will calculate the regression fitted values.

lgy

If you have already calculated the constant term of the ZIP regression plug it here. This is the sum of the logarithm of the factorial of the values.

Details

The zero inflated Poisson regression as suggested by Lambert (1992) is fitted. Unless you have a sufficient number of zeros, there is no reason to use this model. The "zip.reg" is an internal wrapper function and is used for speed up purposes. It is not to be called directly by the user unless they know what they are doing. The zero inflated negative binomial regression does not accept weights though.

Value

A list including:

be

The estimated coefficients of the model and for the zip.mod and zinb.mod the standard errors, Wald test statistics and p-values are included.

prop

The estimated proportion of zeros.

loglik

The log-likelihood of the regression model.

est

The estimated values if "xnew" is not NULL.

Author(s)

Michail Tsagris

R implementation and documentation: Michail Tsagris [e-mail]

References

Lambert D. (1992). Zero-inflated Poisson regression, with an application to defects in manufacturing. Technometrics, 34(1):1-14.

Rui Fang (2013). Zero-inflated neagative binomial (ZINB) regression model for over-dispersed count data with excess zeros and repeated measures, an application to human microbiota sequence data. MSc thesis, University of Colorado. https://mountainscholar.org/bitstream/handle/10968/244/FANG_ucdenveramc_1639M_10037.pdf?sequence=1&isAllowed=y

See Also

testIndZIP, zip.regs, reg.fit, ridge.reg

Examples

y <- rpois(100, 2)
x <- matrix( rnorm(100 * 2), ncol = 2)
a1 <- glm(y ~ x, poisson)
a2 <- zip.mod(y, x) 
summary(a1)
logLik(a1)
a2  ## a ZIP is not really necessary
y[1:20] <- 0
a1 <- glm(y ~ x, poisson)
a2 <- zip.mod(y, x) 
summary(a1)
logLik(a1)
a2  ## a ZIP is probably more necessary