AMAZonn (A Multicollinearity-adjusted Adaptive LASSO for Zero-inflated Count Regression)

Introduction

Algorithms for fitting standard error adjusted adaptive LASSO for both zero-inflated Poisson (ZIP) and zero-inflated negative binomial (ZINB) regression models. AMAZonn relies on an efficient coordinate descent algorithm embedded within an EM algorithm by imposing standard error adjusted adaptive $L_1$ penalties in both count and zero submodels of the corresponding zero-inflated mixture model.

Installation

AMAZonn can be installed using the following command (execute from within a fresh R session):

install.packages("devtools")
devtools::install_github("himelmallick/AMAZonn")
library(AMAZonn)

Basic Usage

AMAZonn(formula, data, family, ...)

• formula symbolic description of the model, similar to that in zeroinfl function in the R package pscl with | to separate the count and zero submodels
• data: an optional data frame (or object coercible by as.data.frame to a data frame) containing the variables in the model
• family: character specification of the count model family with options poisson, negbin, and geometric (a log link is always used)
• ... other arguments that can be passed from the zipath function in the R package mpath (Wang et al., 2015)

The function AMAZonn returns a list of following components:

• coefficients: a list with elements count and zero containing the coefficients from the respective submodels
• ... other components similar tozipath function in the R package mpath (Wang et al., 2015)

Examples

library(zic)
data(docvisits)

dt <- docvisits[, -(2:3)]
tmp <- model.matrix(~age30 * health + age35 * health +
                         age40 * health + age45 * health + age50 * health +
                         age55 * health + age60 * health, data = dt)[, -(1:9)]
dat <- cbind(dt, tmp)
AMAZonn Estimates
fit.zonn <- AMAZonn(docvisits ~ . | ., data = dat, family = "negbin")

rm(list="param") 

minBic <- which.min(BIC(fit.zonn))
coef(fit.zonn, minBic)
cat("theta estimate", fit.zonn$theta[minBic])
Compute standard errors of coefficients and theta (the last one for theta).
se(fit.zonn, minBic, log = FALSE)
Compute AIC, BIC, log-likelihood values of the selected model.
AIC(fit.zonn)[minBic]
BIC(fit.zonn)[minBic]
logLik(fit.zonn)[minBic]

References

Wang, Z., Ma, S., and Wang, C.Y. (2015). Variable Selection for Zero-inflated and Overdispersed Data with Application to Health Care Demand in Germany. Biometrical Journal 57(5):867-884.

Citation

Banerjee, P., Garai, B., Mallick, H., Chowdhury, S., Chatterjee, S. (2018). A Note on the Adaptive LASSO for Zero-inflated Poisson Regression. Journal of Probability and Statistics, 2834183.