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.

himelmallick / AMAZonn