ESTIMATION PARAMETERS AND MODELLING ZERO INFLATED NEGATIVE BINOMIAL
ABSTRACT: Regression analysis
is used to determine relationship between one or several response variable (Y)
with one or several predictor variables (X). 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
(variance is higher than mean). Poisson regression model is commonly used to
analyze the count data. On the count data type, it is often to encounteredd
some observations that have zero value with large proportion of zero value on
the response variable (zero Inflation). 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.
KEYWORDS: Overdispersion;
Tetanus Neonatorum; Zero Inflation; Zero Inflated Negative Binomial (ZINB)
Author: Cindy Cahyaning
Astuti, Angga Dwi Mulyanto
Journal Code: jpmatematikagg160043
