scholarly journals Modified Kibria-Lukman (MKL) estimator for the Poisson Regression Model: application and simulation

F1000Research ◽  
2021 ◽  
Vol 10 ◽  
pp. 548
Author(s):  
Benedicta B. Aladeitan ◽  
Olukayode Adebimpe ◽  
Adewale F. Lukman ◽  
Olajumoke Oludoun ◽  
Oluwakemi E. Abiodun
Keyword(s):  
Regression Model ◽  
Poisson Regression ◽  
Generalized Linear Model ◽  
Real Life ◽  
Poisson Regression Model ◽  
Likelihood Estimator ◽  
Ridge Estimator ◽  
Liu Estimator ◽  
Life Study ◽  
Ridge Regression Estimator

Background: Multicollinearity greatly affects the Maximum Likelihood Estimator (MLE) efficiency in both the linear regression model and the generalized linear model. Alternative estimators to the MLE include the ridge estimator, the Liu estimator and the Kibria-Lukman (KL) estimator, though literature shows that the KL estimator is preferred. Therefore, this study sought to modify the KL estimator to mitigate the Poisson Regression Model with multicollinearity. Methods: A simulation study and a real-life study was carried out and the performance of the new estimator was compared with some of the existing estimators. Results: The simulation result showed the new estimator performed more efficiently than the MLE, Poisson Ridge Regression Estimator (PRE), Poisson Liu Estimator (PLE) and the Poisson KL (PKL) estimators. The real-life application also agreed with the simulation result. Conclusions: In general, the new estimator performed more efficiently than the MLE, PRE, PLE and the PKL when multicollinearity was present.

scholarly journals Modified Kibria-Lukman (MKL) estimator for the Poisson Regression Model: application and simulation

F1000Research ◽  
2021 ◽  
Vol 10 ◽  
pp. 548
Author(s):  
Benedicta B. Aladeitan ◽  
Olukayode Adebimpe ◽  
Adewale F. Lukman ◽  
Olajumoke Oludoun ◽  
Oluwakemi E. Abiodun
Keyword(s):  
Regression Model ◽  
Poisson Regression ◽  
Generalized Linear Model ◽  
Real Life ◽  
Poisson Regression Model ◽  
Likelihood Estimator ◽  
Ridge Estimator ◽  
Liu Estimator ◽  
Life Study ◽  
Ridge Regression Estimator

Background: Multicollinearity greatly affects the Maximum Likelihood Estimator (MLE) efficiency in both the linear regression model and the generalized linear model. Alternative estimators to the MLE include the ridge estimator, the Liu estimator and the Kibria-Lukman (KL) estimator, though literature shows that the KL estimator is preferred. Therefore, this study sought to modify the KL estimator to mitigate the Poisson Regression Model with multicollinearity. Methods: A simulation study and a real-life study were carried out and the performance of the new estimator was compared with some of the existing estimators. Results: The simulation result showed the new estimator performed more efficiently than the MLE, Poisson Ridge Regression Estimator (PRE), Poisson Liu Estimator (PLE) and the Poisson KL (PKL) estimators. The real-life application also agreed with the simulation result. Conclusions: In general, the new estimator performed more efficiently than the MLE, PRE, PLE and the PKL when multicollinearity was present.

scholarly journals Prediction of major international soccer tournaments based on team-specific regularized Poisson regression: An application to the FIFA World Cup 2014

2015 ◽  
Vol 11 (2) ◽  
Author(s):  
Andreas Groll ◽  
Gunther Schauberger ◽  
Gerhard Tutz
Keyword(s):  
Variable Selection ◽  
Regression Model ◽  
Linear Model ◽  
Poisson Regression ◽  
Generalized Linear Model ◽  
Poisson Regression Model ◽  
World Cup ◽  
Fifa World Cup ◽  
Specific Effects ◽  
World Champion

AbstractIn this article an approach for the analysis and prediction of international soccer match results is proposed. It is based on a regularized Poisson regression model that includes various potentially influential covariates describing the national teams’ success in previous FIFA World Cups. Additionally, within the generalized linear model (GLM) framework, also differences of team-specific effects are incorporated. In order to achieve variable selection and shrinkage, we use tailored Lasso approaches. Based on preceding FIFA World Cups, two models for the prediction of the FIFA World Cup 2014 are fitted and investigated. Based on the model estimates, the FIFA World Cup 2014 is simulated repeatedly and winning probabilities are obtained for all teams. Both models favor the actual FIFA World Champion Germany.

scholarly journals A new estimator for the multicollinear Poisson regression model: simulation and application

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
Adewale F. Lukman ◽  
Emmanuel Adewuyi ◽  
Kristofer Månsson ◽  
B. M. Golam Kibria
Keyword(s):  
Regression Model ◽  
Poisson Regression ◽  
Mean Squared Error ◽  
Model Simulation ◽  
Real Life ◽  
Poisson Regression Model ◽  
Squared Error ◽  
Damage Data ◽  
The Mean ◽  
Better Than

AbstractThe maximum likelihood estimator (MLE) suffers from the instability problem in the presence of multicollinearity for a Poisson regression model (PRM). In this study, we propose a new estimator with some biasing parameters to estimate the regression coefficients for the PRM when there is multicollinearity problem. Some simulation experiments are conducted to compare the estimators' performance by using the mean squared error (MSE) criterion. For illustration purposes, aircraft damage data has been analyzed. The simulation results and the real-life application evidenced that the proposed estimator performs better than the rest of the estimators.

scholarly journals The Estimation of Generalized Method Moment Poisson Regression Model on the Prevalence of Acute Respiratory Tract Infection (RTI) in South Kalimantan

CAUCHY ◽  
2018 ◽  
Vol 5 (3) ◽  
pp. 161
Author(s):  
Mahpolah Mahpolah ◽  
Suharto Suharto ◽  
Arief Wibowo ◽  
Bambang Widjanarko Otok
Keyword(s):  
Regression Model ◽  
Poisson Regression ◽  
Social Economy ◽  
Acute Respiratory Tract Infection ◽  
Nutrition Status ◽  
Health Clinic ◽  
Poisson Regression Model ◽  
Likelihood Estimator ◽  
Regression Approach ◽  
Important Health

<em>ACUTE (RTI)</em> is still an important health problem because the cause of the death of infants and children under five high enough, 1 from 4 death that happens. The purpose of this research examines the factors that affect the genesis <em>ACUTE (RTI)</em> using poisson regression approach with estimates of the maximum likelihood estimator (MLE) and generalized method moment (GMM). This research done in the area of Health Clinic in South Kalimantan. The results of the study showed that the estimates of the GMM method on Poisson regression model gives better performance in terms of the significance of the parameters than the MLE method. The factors that affect an increasing number of the prevalence of <em>ACUTE (RTI)</em> a region namely persentase Breast Feeding non-exclusive (0.0279), the percentage of low birth weight (0.0569), the percentage of shelter density (0.028), the percentage of the existence of smoker family members in the house (0.0308), the percentage of immunization is not complete (0.0193). While the factors that affect a downturn in the number of the prevalence of <em>ACUTE (RTI)</em> in a region which is the percentage of the number of infants less than 2 (0.0364), the percentage of normal nutrition status (0.0224), the percentage of Mothers Education on high school (0.0339), and the percentage of social economy (<em>UMP</em> enough to top) (0.0194).

scholarly journals Influence Diagnostic Methods in the Poisson Regression Model with the Liu Estimator

2021 ◽  
Vol 2021 ◽  
pp. 1-12
Author(s):  
Aamna Khan ◽  
Muhammad Amanullah ◽  
Muhammad Amin ◽  
Randa Alharbi ◽  
Abdisalam Hassan Muse ◽  
...  
Keyword(s):  
Regression Model ◽  
Count Data ◽  
Poisson Regression ◽  
Model Fitting ◽  
Estimation Method ◽  
Real Data ◽  
Diagnostic Methods ◽  
Influential Observations ◽  
Poisson Regression Model ◽  
Liu Estimator

There is a long history of interest in modeling Poisson regression in different fields of study. The focus of this work is on handling the issues that occur after modeling the count data. For the prediction and analysis of count data, it is valuable to study the factors that influence the performance of the model and the decision based on the analysis of that model. In regression analysis, multicollinearity and influential observations separately and jointly affect the model estimation and inferences. In this article, we focused on multicollinearity and influential observations simultaneously. To evaluate the reliability and quality of regression estimates and to overcome the problems in model fitting, we proposed new diagnostic methods based on Sherman–Morrison Woodbury (SMW) theorem to detect the influential observations using approximate deletion formulas for the Poisson regression model with the Liu estimator. A Monte Carlo method is done for the assessment of the proposed diagnostic methods. Real data are also considered for the evaluation of the proposed methods. Results show the superiority of the proposed diagnostic methods in detecting unusual observations in the presence of multicollinearity compared to the traditional maximum likelihood estimation method.

scholarly journals Biased Adjusted Poisson Ridge Estimators-Method and Application

2020 ◽  
Vol 44 (6) ◽  
pp. 1775-1789
Author(s):  
Muhammad Qasim ◽  
Kristofer Månsson ◽  
Muhammad Amin ◽  
B. M. Golam Kibria ◽  
Pär Sjölander
Keyword(s):  
Poisson Regression ◽  
Regression Estimator ◽  
Mean Square ◽  
Poisson Regression Model ◽  
Negative Effects ◽  
Likelihood Estimator ◽  
Ridge Regression Estimator ◽  
The Mean ◽  
Almost Unbiased ◽  
Better Than

AbstractMånsson and Shukur (Econ Model 28:1475–1481, 2011) proposed a Poisson ridge regression estimator (PRRE) to reduce the negative effects of multicollinearity. However, a weakness of the PRRE is its relatively large bias. Therefore, as a remedy, Türkan and Özel (J Appl Stat 43:1892–1905, 2016) examined the performance of almost unbiased ridge estimators for the Poisson regression model. These estimators will not only reduce the consequences of multicollinearity but also decrease the bias of PRRE and thus perform more efficiently. The aim of this paper is twofold. Firstly, to derive the mean square error properties of the Modified Almost Unbiased PRRE (MAUPRRE) and Almost Unbiased PRRE (AUPRRE) and then propose new ridge estimators for MAUPRRE and AUPRRE. Secondly, to compare the performance of the MAUPRRE with the AUPRRE, PRRE and maximum likelihood estimator. Using both simulation study and real-world dataset from the Swedish football league, it is evidenced that one of the proposed, MAUPRRE ($$ \hat{k}_{q4} $$ k ^ q 4 ) performed better than the rest in the presence of high to strong (0.80–0.99) multicollinearity situation.

scholarly journals Metode Pemilihan Variabel pada Model Regresi Poisson Menggunakan Metode Nordberg

2021 ◽  
Vol 1 (1) ◽  
pp. 35-42
Author(s):  
Muhammad Bangkit Riksa Utama ◽  
Nusar Hajarisman
Keyword(s):  
Regression Model ◽  
Linear Model ◽  
Poisson Regression ◽  
Generalized Linear Model ◽  
Information Criteria ◽  
Infant Mortality Rate ◽  
Poisson Regression Model ◽  
Independent Variables ◽  
Selection Of Variables ◽  
Selection Of

Abstract. In various experiments, data interactions take the form of discrete numbers or counts. The model that can be used for these data is the Poisson regression model. Poisson regression is included in the Generalized Linear Model (GLM). Poisson regression in general is very important in various fields and agreed to receive special attention. Often this model needs many independent variables. Then there needs to be a selection of poisson regression model variables. Due to the number of independent variables that exist, the selection of variables is carried out. Variable selection techniques that are commonly known are the forward, backward method, akaike information criteria and several other methods. In this paper, we will discuss one method of selecting variables in the Poisson regression model that has been made in the algorithm created by Famoye and Rothe. The algorithm created will be compared with the algorithm made by Nordberg. In this study data were used on Infant Mortality Rate (IMR) in West Java Province. Abstrak. Dalam berbagai eksperimen, seringkali data berupa bilangan diskrit atau cacah. Model yang dapat digunakan untuk data tersebut diantaranya adalah model regresi poisson. Regresi poisson termasuk kedalam Generalized Linear Model (GLM).  Regresi poisson secara umum sangat penting dalam berbagai bidang dan karenanya patut mendapat perhatian khusus. Seringkali model ini melibatkan banyak variabel independen. Maka perlu adanya cara untuk mempertimbangkan pemilihan variabel model regresi poisson. Dikarenakan banyaknya variabel independen yang ada maka  dilakukan penyeleksian variabel. Teknik pemilihan variabel yang sudah biasa dikenal yaitu metode forward, backward, akaike information criterion dan beberapa metode lainnya. Pada makalah ini akan dibahas mengenai salah satu metode pemilihan variabel dalam model regresi poisson yang telah dibentuk dalam algoritma yang dibuat oleh Famoye dan Rothe. Algortitma yang dibuat ini akan dibandingkan dengan algoritma yang telah dibuat oleh Nordberg. Pada penelitian ini  digunakan data mengenai Angka Kematian Bayi (AKB) di Provinsi Jawa Barat.

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