Estimation Parameters And Modelling Zero Inflated Negative Binomial

Abstract

Regression model between predictor variables and the Poisson distributed response variable is called Poisson Regression Model. Since, Poisson Regression requires an equality between mean and variance, it is not appropriate to apply this model on overdispersion. Poisson regression can be used to analyze count data but it has not been able to solve problem of excess zero value on the response variable. An alternative model which is more suitable for overdispersion data and can solve the problem of excess zero value on the response variable is Zero Inflated Negative Binomial (ZINB). In this research, ZINB is applied on the case of Tetanus Neonatorum in East Java. The aim of this research is to examine the likelihood function and to form an algorithm to estimate the parameter of ZINB and also applying ZINB model in the case of Tetanus Neonatorum in East Java. Maximum Likelihood Estimation (MLE) method is used to estimate the parameter on ZINB and the likelihood function is maximized using Expectation Maximization (EM) algorithm. Test results of ZINB regression model showed that the predictor variable have a partial significant effect at negative binomial model is the percentage of pregnant women visits and the percentage of maternal health personnel assisted, while the predictor variables that have a partial significant effect at zero inflation model is the percentage of neonatus visits.

Zero-Inflated Negative Binomial Modeling in Infant Death Case Due to Pneumonia in East Java Province

“…The Zero Inflated Negative Binomial (ZINB) regression model can be used as another alternative in modeling cases by lot valuable observation zero and happened overdispersion because this model does not require variety must be the same as the average, besides that the Zero Inflated Negative Binomial (ZINB) regression model also has a dispersion parameter that is useful for describing variation from the data, which is usually denoted by κ (kappa). ZIP regression modeling and ZINB regression have mostly been done by [6] using the ZIP regression model by applying the model to the data collected from a studies Quality Control.…”

Bayesian and frequentist approaches on estimation and testing for a zero-inflated binomial distribution

“…In the perspective of parameter estimation for zero-inflated models, it is well known that the EM-algorithm works out nicely [3,13,22]. Instead of using numerical methods for the direct maximization of the likelihood function, it is typical to treat the estimation of parameters in the ZIB distribution as a missing data problem and solve it by using the EM algorithm.…”

Improved shrinkage estimators in zero-inflated negative binomial regression model

“…Also, z i is generated from uniform distribution U (0, 1). We consider the number of predictors k = p + q = 9, 12, 15 with (p, q) = (6, 3), (6,6), (8,7). We select the level of significance α = 0.05, 0.50, 0.10 for the pretest and shrinkage pretest methods and the level of confidence in the prior information for the LS and SP estimators is set to λ = 0.25, 0.50, 0.75.…”

“…The ZINB model has been studied by several authors. Interested readers are referred to [8,23,24,[27][28][29].…”