ZERO-INFLATED POISSON REGRESSION MODELS: APPLICATIONS IN THE SCIENCES AND SOCIAL SCIENCES

This paper makes a theoretical contribution by presenting a detailed derivation of a zero-inflated Poisson (ZIP) model, and then deriving the parameters of the ZIP model using a fishing data set. This model has several practical applications, and is largely performed to model count data that have an excess number of zero counts. In the scope of the paper, we introduce the complete formulae, the likelihood and log-likelihood functions and the estimating equation of the ZIP model. We then investigate the theory of large sample properties of this model under some regularity conditions. A simulation study and a fishing data set are studied for the ZIP model. The results in the actual application in this work are meaningful, useful and crucial in reality. The results also provide reliable evidence for obtaining the largest number of fish while fishing. This is the contribution of this research in terms of applications. Finally, the important applications of this model in practice, some conclusions, and future work is also presented for consideration.

Model Regresi Hurdle Negative Binomial (HNB) untuk Pemodelan Konsumsi Rokok di Provinsi Sulawesi Tengah

The average expenditure on cigarettes per capita in Sulawesi Tengah Province has increased in 2020. There are several factors that can affect a person's cigarette consumption including gender, age, education and health. To model cigarette consumption with several influencing factors can be use the poison regression model or the Zero Inflated Poisson (ZIP) model. However, the two regression models cannot solve the excess zero and overdispersion problems so use the Hurdle Negative Binomial (HNB) regression model. The results of the analysis of cigarette consumption data in Central Sulawesi Province using the HNB model provide the best modeling results compared to the poisson regression model and the ZIP model because it has the smallest Akaike's Information Criterion (AIC) value. The results of testing the factors that significantly influence cigarette consumption in Central Sulawesi Province in the HNB regression model, namely the count model are gender, age and health. Whereas in the zerohurdle model, it is gender, age and education.

PEMODELAN FAKTOR-FAKTOR YANG MEMPENGARUHI KEMATIAN IBU MELAHIRKAN DI JAWA TENGAH DENGAN ZERO INFLATED POISSON REGRESSION

One of the targets of the Sustainable Development Goals (SDGs) is to reduce the maternal mortality rate by 2030. In reducing the maternal mortality rate, it is necessary to first study the factors that influence it. The number of maternal mortality rate in Central Java Province in 2018 was a discrete random variable that had a Poisson distribution and had many zero values. Generally, a model was used to counting data is Poisson regression model. However, the maternal mortality that has many zero values caused overdispersion. Therefore, Poisson model was not relevant in that case. In this paper, we used Zero Inflated Poisson (ZIP) model to overcome overdispersion caused by many zero values. The results of the research show that ZIP model can explained influence the number of maternal mortality. Based on this research, the factors such as provision of tablets, pregnant women who experience obstetric complications, and households with a clean and healthy lifestyle can explain the number of maternal mortality.

Comparison of the Performance of the Gradient and Newton-Raphson Method to Estimate Parameters in Some Zero-Inflated Regression Models

This paper compares the performance of the gradient and Newton-Raphson (N-R) method to estimate parameters in some zero-inflated (ZI) regression models such as the zero-inflated Poisson (ZIP) model, zero-inflated Bell (ZIBell) model, zero-inflated binomial (ZIB) model and zero-inflated negative binomial (ZINB) model. In the present work, firstly, we briefly present the approach of the gradient and N-R method. We then introduce the origin, formulas and applications of the ZI models. Finally, we compare the performance of two investigated approaches for these models through the simulation studies with numerous sample sizes and several missing rates. A real data set is investigated in this study. Specifically, we compare the results and the execution time of the R code for two methods. Moreover, we provide some important notes on these two approaches and some scalable research directions for future work.This is an Open Access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium provided the original work is properly cited.

Analysis of Acoustic Emission Data for Bearings subject to Unbalance

Acoustic Emission (AE) is an effective nondestructive method for investigating the behavior of materials under stress. In recent decades, AE applications in structural health monitoring have been extended to other areas such as rotating machineries and cutting tools. This research investigates the application of acoustic emission data for unbalance analysis and detection in rotary systems. The AE parameter of interest in this study is a discrete variable that covers the significance of count, duration and amplitude of AE signals. A statistical model based on Zero-Inflated Poisson (ZIP) regression is proposed to handle over-dispersion and excess zeros of the counting data. The ZIP model indicates that faulty bearings can generate more transient wave in the AE waveform. Control charts can easily detect the faulty bearing using the parameters of the ZIP model. Categorical data analysis based on generalized linear models (GLM) is also presented. The results demonstrate the significance of the couple unbalance.

Optimum reactive power compensation for distribution system using dolphin algorithm considering different load models

The distribution system represents the connection between consumers and the entire power network. The radial structure is preferred for distribution system due to its simple design and low cost. The electrical distribution system suffers from problems of rising power losses higher than the transmission system and voltage drop. One of the important solutions to improve the voltage profile and to reduce the electrical distribution system losses is the reactive power compensation which is based on the optimum choice of position and capacitor size in the network. In this paper, different models of electrical loads such as constant power(P), constant current(I), constant impedance(Z), and composite (ZIP) model are implemented with comparisons between them in order to identify the most effective load type that produces the optimal settlement for alleged loss reduction ,enhancement of the voltage profile, and cost savings. To minimize search space, Dolphin Optimization Algorithm (DOA) is applied for selecting the size and location of capacitors. Two case studies (IEEE 16- bus and 33- bus) are employed to evaluate the different load models with optimal reactive power compensation. The results of comparison between the different load models show that ZIP model is the best to produce the optimum solution for capacitor position and size. In addition, comparison of results with literature works are done and showed that DOA is the most robust among other algorithms to achieve the optimum solution for voltage profile enhancement significant reduction of losses, and saving cost.

Analysis of count data in the setting of cervical cancer detection

Women with an abnormal Pap smear are often referred to colposcopy, a procedure during which endocervical curettage (ECC) may be performed. ECC is a scraping of the endocervical canal lining. Our goal was to compare the performance of a naïve Poisson (NP) regression model with that of a zero-inflated Poisson (ZIP) model when identifying predictors of the number of distress/pain vocalizations made by women undergoing ECC. Data on women seen in the colposcopy clinic at a medical school in El Paso, Texas, were analyzed. The outcome was the number of pain vocalizations made by the patient during ECC. Six dichotomous predictors were evaluated. Initially, NP regression was used to model the data. A high proportion of patients did not make any vocalizations, and hence a ZIP model was also fit and relative rates (RRs) and 95% CIs were calculated. AIC was used to identify the best model (NP or ZIP). Of the 210 women, 154 (73.3%) had a value of 0 for the number of ECC vocalizations. NP identified three statistically significant predictors (language preference of the subject, sexual abuse history and length of the colposcopy), while ZIP identified one: history of sexual abuse (yes vs no; adjusted RR=2.70, 95% CI 1.47 to 4.97). ZIP was preferred over NP. ZIP performed better than NP regression. Clinicians and epidemiologists should consider using the ZIP model (or the zero-inflated negative binomial model) for zero-inflated count data.

Implication of Production and Monitoring Techniques in Bayesian Single Sampling Plan using Gamma-Zero Inflated Poisson Distribution

This article explores the problem of investigate Single Sampling Plan (SSP) by attributes under Bayesian theory and illuminate its importance methodology in manufacturing industries. The modern technological advancements and well monitoring of the production process are facilitate to enhance the standard of product. In such situation products are not meeting the specified quality standards is a rare phenomenon. However, random fluctuations in producing processes might lead some merchandise to an imperfect quality. It has been assumed that the number of defects per unit of product follows a Zero Inflated Poisson distribution (ZIP) and the Gamma distribution is the conjugate prior to the average number of non-conformities per item. This article proposed a new sampling procedure as Bayesian Single Sampling plan (BSSP) using Gamma-Zero Inflated Poisson (G-ZIP) distribution. Necessary tables for the selection of optimal plan parameters and numerical illustrations were made for this sampling plan. Furthermore, the applicability and usefulness of the proposed Bayesian sampling plan under the G-ZIP model have been demonstrated by a few examples and comparisons were made with other sampling plans.

Modeling the Rainfall Count data Using Some Zero Type models with application

Count data, including zero counts arise in a wide variety of application, hence models for counts have become widely popular in many fields. In the statistics field, one may define the count data as that type of observation which takes only the non-negative integers value. Sometimes researchers may Counts more zeros than the expected. Excess zero can be defined as Zero-Inflation. Data with abundant zeros are especially popular in health, marketing, finance, econometric, ecology, statistics quality control, geographical, and environmental fields when counting the occurrence of certain behavioral and natural events, such as frequency of alcohol use, take drugs, number of cigarettes smoked, the occurrence of earthquakes, rainfall, and etc. Some models have been used to analyzing count data such as the zero-inflated Poisson (ZIP) model and the negative binomial model. In this paper, the models, Poisson, Negative Binomial, ZIP, and ZINB were been used to analyze rainfall data.