Influence Diagnostic Methods in the Poisson Regression Model with the 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.

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A multivariate Poisson regression model for count data

Journal of Applied Statistics ◽

10.1080/02664763.2021.1877637 ◽

2021 ◽

pp. 1-17

Author(s):

J. M. Muñoz-Pichardo ◽

R. Pino-Mejías ◽

J. García-Heras ◽

F. Ruiz-Muñoz ◽

M. Luz González-Regalado

Keyword(s):

Regression Model ◽

Count Data ◽

Poisson Regression ◽

Poisson Regression Model

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PARAMETER ESTIMATION ON HURDLE POISSON REGRESSION MODEL WITH CENSORED DATA

Jurnal Teknologi ◽

10.11113/jt.v57.1533 ◽

2012 ◽

Vol 57 (1) ◽

Author(s):

SEYED EHSAN SAFFAR ◽

ROBIAH ADNAN ◽

WILLIAM GREENE

Keyword(s):

Regression Model ◽

Count Data ◽

Poisson Regression ◽

Goodness Of Fit ◽

Poisson Model ◽

Likelihood Method ◽

Poisson Regression Model ◽

Response Variable ◽

The Mean ◽

Over Dispersion

A Poisson model typically is assumed for count data. In many cases, there are many zeros in the dependent variable and because of these many zeros, the mean and the variance values of the dependent variable are not the same as before. In fact, the variance value of the dependent variable will be much more than the mean value of the dependent variable and this is called over–dispersion. Therefore, Poisson model is not suitable anymore for this kind of data because of too many zeros. Thus, it is suggested to use a hurdle Poisson regression model to overcome over–dispersion problem. Furthermore, the response variable in such cases is censored for some values. In this paper, a censored hurdle Poisson regression model is introduced on count data with many zeros. In this model, we consider a response variable and one or more than one explanatory variables. The estimation of regression parameters using the maximum likelihood method is discussed and the goodness–of–fit for the regression model is examined. We study the effects of right censoring on estimated parameters and their standard errors via an example.

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Flexiblity of Using Com-Poisson Regression Model for Count Data

Statistics Optimization & Information Computing ◽

10.19139/soic.v6i2.278 ◽

2018 ◽

Vol 6 (2) ◽

Author(s):

Esin AVCI

Keyword(s):

Regression Model ◽

Count Data ◽

Poisson Regression ◽

Poisson Regression Model

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

F1000Research ◽

10.12688/f1000research.53987.1 ◽

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.

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

F1000Research ◽

10.12688/f1000research.53987.2 ◽

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.

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Estimating Recreational Value of Foy's Lake: An Application of Travel Cost Count Data Model for Truncated Zeros

10.20944/preprints201702.0032.v1 ◽

2017 ◽

Author(s):

Md. Touhidul Alam ◽

Anis-Ul-Ekram Chowdury ◽

Md. Sajib Hossian

Keyword(s):

Regression Model ◽

Count Data ◽

Data Model ◽

Poisson Regression ◽

Consumer Surplus ◽

Travel Cost ◽

Travel Cost Method ◽

Poisson Regression Model ◽

Recreational Value ◽

Recreational Benefits

To estimate the recreational value provided by the Foy’s Lake annually using the most applicable model for on-site data is the main objective of this study. Adhere to the objective of this study; Individual Travel Cost Method (ITCM) has been applied and Zero Truncated Poisson Regression Model has been found plausible among other models to estimate consumer surplus. Based on the findings of the study, an estimate of the consumer surplus or recreational benefits per trip per visitor can be recommended as BDT 5,875 or US $ 73.44 and counting the consumer surplus per trip per visitor, the annual recreational value (total consumer surplus) provided by the lake is found to be BDT 321 million or US $ 40.2 million.

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An Estimation of a Hybrid Log-Poisson Regression Using a Quadratic Optimization Program for Optimal Loss Reserving in Insurance

Advances in Fuzzy Systems ◽

10.1155/2019/1393946 ◽

2019 ◽

Vol 2019 ◽

pp. 1-14 ◽

Cited By ~ 1

Author(s):

Apollinaire Woundjiagué ◽

Martin Le Doux Mbele Bidima ◽

Ronald Waweru Mwangi

Keyword(s):

Regression Model ◽

Mean Square Error ◽

Hybrid Model ◽

Poisson Regression ◽

Estimation Method ◽

Error Prediction ◽

Mean Square ◽

Poisson Regression Model ◽

Loss Reserving ◽

The Mean

In this article, we are interested in developing an alternative estimation method of the parameters of the hybrid log-Poisson regression model. In our previous paper, we have proposed a hybrid log-Poisson regression model where we have derived the analytical expression of the fuzzy parameters. We found that the hybrid model provide better results than the classical log-Poisson regression model according to the mean square error prediction and the goodness of fit index. However, nowhere we have taken into account the optimal value of h(α-cut) which is of greatest importance in fuzzy regressions literature. In this paper, we provide an alternative estimation method of our hybrid model using a quadratic optimization program and the optimized h-value (α-cut). The expected value of fuzzy number is used as a defuzzification procedure to move from fuzzy values to crisp values. We perform the hybrid model with the alternative estimation we are suggesting on two different numerical data to predict incremental payments in loss reserving. From the mean square error prediction, we prove that the alternative estimation of the new hybrid model with an optimized h-value predicts incremental payments better than the classical log-Poisson regression model as well as the same hybrid model with analytical estimation of parameters. Hence we have optimized the outstanding loss reserves.

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