scholarly journals Comparing of Car-Bym, Generalized Poisson dan Negative Binomial on Tuberculosis Data in Banyumas Districs

2021 ◽  
Vol 5 (1) ◽  
pp. 130-140
Author(s):  
Jajang Jajang ◽  
Budi Pratikno ◽  
Mashuri Mashuri
Keyword(s):  
Parameter Estimation ◽  
Maximum Likelihood ◽  
Count Data ◽  
Degrees Of Freedom ◽  
Negative Binomial ◽  
Likelihood Estimation ◽  
Poisson Model ◽  
Generalized Poisson ◽  
Central Java ◽  
Area Data

In 2019 the number of people with TB (Tuberculosis) in Banyumas, Central Java, is high (1,910 people have been detected with TB). The number of people infected Tuberculosis (TB) in Banyumas is the count data and it is also the area data. In modeling, the parameter estimation and characteristic of the data need to be considered. Here, we studied comparing Generalized Poisson (GP), negative binomial (NB), and Poisson and CAR.BYM model for TB cases in Banyumas. Here, we use two methods for parameter estimation, maximum likelihood estimation (MLE) and Bayes. The MLE is used for GP and NB models, whereas Bayes is used for Poisson and CAR-BYM. The results showed that Poisson model detected overdispersion where deviance value is 67.38 for 22 degrees of freedom. Therefore, ratio of deviance to degrees of freedom is 3.06 (>1). This indicates that there was overdispersion. The folowing GP, NB, Poisson-Bayes and CAR-BYM are used to modeling TB data in Banyumas and we compare their RMSE. With refer to RMES criteria, we found that CAR-BYM is the best model for modeling TB in Banyumas because its RMSE is smallest.

Zero-Inflated Poisson Model with Group Data

2012 ◽  
Vol 569 ◽  
pp. 627-631
Author(s):  
Jun Yang ◽  
Xin Zhang
Keyword(s):  
Parameter Estimation ◽  
Maximum Likelihood ◽  
Model Selection ◽  
Count Data ◽  
Maximum Likelihood Estimate ◽  
Poisson Model ◽  
Cigarette Consumption ◽  
Chi Square ◽  
Group Data ◽  
Chi Square Test

The Zero-inflated Poisson model has been widely used in many fields for count data with excessive zeroes. In fact, group data are often collected for many count data, such as cigarette consumption. In order to solve the problem, Zero-inflated Poisson model with group data is investigated in this paper. Parameter estimation is given by the maximum likelihood estimate, model selection is discussed by the Chi-square test, and one real example is given for application in the end.

Semiparametric models for multilevel overdispersed count data with extra zeros

2016 ◽  
Vol 27 (4) ◽  
pp. 1187-1201 ◽  
Author(s):  
Marzieh Mahmoodi ◽  
Abbas Moghimbeigi ◽  
Kazem Mohammad ◽  
Javad Faradmal
Keyword(s):  
Count Data ◽  
Negative Binomial ◽  
Simulated Data ◽  
Likelihood Estimation ◽  
Semiparametric Models ◽  
Multilevel Regression ◽  
Monte Carlo Simulation Study ◽  
Excess Zeros ◽  
Generalized Poisson ◽  
Comprehensive Comparison

This study proposes semiparametric models for analysis of hierarchical count data containing excess zeros and overdispersion simultaneously. The methods discussed in this paper handle nonlinear covariate effects through flexible semiparametric multilevel regression techniques. This is performed by providing a comprehensive comparison of semiparametric multilevel zero-inflated negative binomial and semiparametric multilevel zero-inflated generalized Poisson models under the real and simulated data. An EM algorithm based on Newton–Raphson equations for maximum penalized likelihood estimation approach is developed. The performance of the proposed models is assessed by using a Monte Carlo simulation study. We also illustrated the methods by the analysis of decayed, missing, and filled teeth of children aged 5–14 years old.

scholarly journals On Poisson-Weighted Lindley Distribution and Its Applications

2019 ◽  
Vol 11 (1) ◽  
pp. 1-13
Author(s):  
R. Shanker ◽  
K. K. Shukla
Keyword(s):  
Maximum Likelihood ◽  
Maximum Likelihood Estimation ◽  
Negative Binomial Distribution ◽  
Goodness Of Fit ◽  
Negative Binomial ◽  
Likelihood Estimation ◽  
Poisson Mixture ◽  
Lindley Distribution ◽  
Generalized Poisson ◽  
And Behavior

In this paper the nature and behavior of its coefficient of variation, skewness, kurtosis and index of dispersion of Poisson- weighted Lindley distribution (P-WLD), a Poisson mixture of weighted Lindley distribution, have been proposed and the nature and behavior have been explained graphically. Maximum likelihood estimation has been discussed to estimate its parameters. Applications of the proposed distribution have been discussed and its goodness of fit has been compared with Poisson distribution (PD), Poisson-Lindley distribution (PLD), negative binomial distribution (NBD) and generalized Poisson-Lindley distribution (GPLD).

scholarly journals Modeling zero-inflated count data with glmmTMB

2017 ◽  
Author(s):  
Mollie E. Brooks ◽  
Kasper Kristensen ◽  
Koen J. van Benthem ◽  
Arni Magnusson ◽  
Casper W. Berg ◽  
...  
Keyword(s):  
Maximum Likelihood ◽  
Maximum Likelihood Estimation ◽  
Random Effects ◽  
Count Data ◽  
Negative Binomial ◽  
Automatic Differentiation ◽  
Likelihood Estimation ◽  
R Package ◽  
Monte Carlo Sampling ◽  
Ecological Processes

AbstractEcological phenomena are often measured in the form of count data. These data can be analyzed using generalized linear mixed models (GLMMs) when observations are correlated in ways that require random effects. However, count data are often zero-inflated, containing more zeros than would be expected from the standard error distributions used in GLMMs, e.g., parasite counts may be exactly zero for hosts with effective immune defenses but vary according to a negative binomial distribution for non-resistant hosts.We present a new R package, glmmTMB, that increases the range of models that can easily be fitted to count data using maximum likelihood estimation. The interface was developed to be familiar to users of the lme4 R package, a common tool for fitting GLMMs. To maximize speed and flexibility, estimation is done using Template Model Builder (TMB), utilizing automatic differentiation to estimate model gradients and the Laplace approximation for handling random effects. We demonstrate glmmTMB and compare it to other available methods using two ecological case studies.In general, glmmTMB is more flexible than other packages available for estimating zero-inflated models via maximum likelihood estimation and is faster than packages that use Markov chain Monte Carlo sampling for estimation; it is also more flexible for zero-inflated modelling than INLA, but speed comparisons vary with model and data structure. Our package can be used to fit GLMs and GLMMs with or without zero-inflation as well as hurdle models. By allowing ecologists to quickly estimate a wide variety of models using a single package, glmmTMB makes it easier to find appropriate models and test hypotheses to describe ecological processes.

scholarly journals The Negative Binomial – Weighted Garima Distribution: Model, Properties and Applications

2020 ◽  
pp. 1-10
Author(s):  
Winai Bodhisuwan ◽  
Pornpop Saengthong
Keyword(s):  
Parameter Estimation ◽  
Count Data ◽  
Negative Binomial ◽  
Likelihood Estimation ◽  
Real Data ◽  
Distribution Model ◽  
Data Sets ◽  
Factorial Moments ◽  
Special Cases ◽  
First Four Moments

In this paper, a new mixed negative binomial (NB) distribution named as negative binomial-weighted Garima (NB-WG) distribution has been introduced for modeling count data. Two special cases of the formulation distribution including negative binomial- Garima (NB-G) and negative binomial-size biased Garima (NB-SBG) are obtained by setting the specified parameter. Some statistical properties such as the factorial moments, the first four moments, variance and skewness have also been derived. Parameter estimation is implemented using maximum likelihood estimation (MLE) and real data sets are discussed to demonstrate the usefulness and applicability of the proposed distribution.

scholarly journals Identifying Stabilising Effects on Survey Based Life Satisfaction Using Quasi-maximum Likelihood Estimation

2021 ◽  
Author(s):  
Johannes Klement
Keyword(s):  
Life Satisfaction ◽  
Maximum Likelihood ◽  
Maximum Likelihood Estimation ◽  
Negative Binomial ◽  
Measurement Instrument ◽  
Likelihood Estimation ◽  
Satisfaction Scale ◽  
Quasi Maximum Likelihood ◽  
The Stability

AbstractTo which extent do happiness correlates contribute to the stability of life satisfaction? Which method is appropriate to provide a conclusive answer to this question? Based on life satisfaction data of the German SOEP, we show that by Negative Binomial quasi-maximum likelihood estimation statements can be made as to how far correlates of happiness contribute to the stabilisation of life satisfaction. The results show that happiness correlates which are generally associated with a positive change in life satisfaction, also stabilise life satisfaction and destabilise dissatisfaction with life. In such as they lower the probability of leaving positive states of life satisfaction and increase the probability of leaving dissatisfied states. This in particular applies to regular exercise, volunteering and living in a marriage. We further conclude that both patterns in response behaviour and the quality of the measurement instrument, the life satisfaction scale, have a significant effect on the variation and stability of reported life satisfaction.

scholarly journals Model Generalized Poisson Regression (GPR) dan Penerapannya pada Angka Pengangguran bagi Penduduk Usia Kerja di Provinsi Sulawesi Selatan

2021 ◽  
Vol 3 (2) ◽  
pp. 109
Author(s):  
Hisyam Ihsan ◽  
Wahidah Sanusi ◽  
Risna Ulfadwiyanti
Keyword(s):  
Maximum Likelihood ◽  
Maximum Likelihood Estimation ◽  
Unemployment Rate ◽  
Poisson Regression ◽  
Likelihood Estimation ◽  
Generalized Poisson ◽  
South Sulawesi ◽  
Working Age ◽  
Working Age Population ◽  
Generalized Poisson Regression

Abstrak. Penelitian ini membahas tentang pembentukan model Generalized Poisson Regression (GPR) dan penerapannya pada angka pengangguran bagi penduduk usia kerja di Provinsi Sulawesi Selatan. Jenis penelitian ini adalah penelitian terapan yang menggunakan model regresi nonlinear, yaitu model regresi Poisson dan model GPR. Variabel respon yang digunakan adalah jumlah angka pengangguran pada usia kerja yang termasuk angkatan kerja di Provinsi Sulawesi Selatan pada tahun 2017. Adapun variabel-variabel prediktor yang digunakan yaitu persentase angkatan kerja terhadap penduduk usia kerja, Indeks Pembangunan Manusia, persentase bekerja terhadap angkatan kerja, kepadatan penduduk, dan pertumbuhan ekonomi. Penelitian menggunakan metode Maximum Likelihood Estimation (MLE) untuk mengestimasikan parameter dan menghasilkan sebuah model GPR. Variabel prediktor yang memberikan pengaruh secara signifikan adalah Indeks Pembangunan Manusia dan  persentase bekerja terhadap angkatan kerja.Kata kunci: Angka Pengangguran, Regresi Poisson, Overdispersi, Generalized Poisson Regression, Maximum Likelihood Estimation  Abstract. This study discusses the formation of the Generalized Poisson Regression (GPR) model and its application to the unemployment rate for the working age population in South Sulawesi Province. This type of research is applied research that uses the Poisson regression model, namely Poisson regression and GPR models. The response variabel used is the total unemployment rate at working age which includes the workforce in South Sulawesi Province in 2017. The predictor variables used are the percentage of the workforce on the working age population, the Human Development Index, the percentage of work on the labor force, population density, and economic growth. This research uses the Maximum Likelihood Estimation (MLE) method to estimate parameters and produce a GPR model. The predictor variables which have a significant influence are the Human Development Index and the percentage of work on the labor force.Keywords: Unemployment Rate, Poisson Regression, Overdispersion, Generalized Poisson Regression, Maximum Likelihood Estimation

scholarly journals PERBANDINGAN MODEL REGRESI BINOMIAL NEGATIF BIVARIAT DENGAN MODEL GEOGRAPHICALLY WEIGHTED NEGATIVE BINOMIAL BIVARIAT REGRESSION (GWNBBR) PADA KASUS ANGKA KEMATIAN BAYI DAN KEMATIAN IBU DI JAWA TENGAH

2022 ◽  
Vol 10 (4) ◽  
pp. 488-498
Author(s):  
Yashmine Noor Islami ◽  
Dwi Ispriyanti ◽  
Puspita Kartikasari
Keyword(s):  
Infant Mortality ◽  
Maternal Mortality ◽  
Count Data ◽  
Poisson Regression ◽  
Negative Binomial ◽  
Poor People ◽  
Significant Variable ◽  
Central Java ◽  
Observation Area ◽  
Bivariate Regression

Infant mortality (0-11 months) and maternal mortality (during pregnancy, childbirth, and postpartum) are significant indicators in determining the level of public health. Central Java Province which has 35 regencies/cities is included in the top five regions with the highest number of infant and maternal mortality in Indonesia. The data characteristics of the number of infants and maternal mortality are count data. Therefore, the Poisson Regression method can be used to analyze the factors that influence the number of infants and maternal mortality. In Poisson regression analysis, there must be a fulfilled assumption, called equidispersion. Frequently, the variance of count data is greater than the mean, which is known as the overdispersion. The research, binomial negative bivariate regression is used as a solutions to overcome the problem of overdispersion in poisson regression. This method produce a global model. In reality, the geographical, socio-cultural, and economic conditions of each region will be different. This illustrates the effect of spatial heterogeneity, so it needs to be developed into Geographically Weighted Negative Binomial Bivariate Regression (GWNBBR). The model of GWNBBR provides weighting based on the position or distance from one observation area to another. Significant variables for modeling infant mortality cases included the percentage of obstetric complications treated (X1), the percentage of infants who were exclusively breastfed (X3), and the percentage of poor people (X5). Significant variable for modeling maternal mortality cases is the percentage of poor people (X5). Based on the AIC value, GWNBBR model is better than binomial negatif bivariat regression model because it has a smaller AIC value. 

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