Two-parameter ridge estimator in the binary logistic regression

Asar, Yasin; Genç, Aşır

doi:10.1080/03610918.2016.1224348

Cited by 16 publications

(7 citation statements)

References 14 publications

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“…In this section, we compare the performance of the logistic regression estimators using a simulation study. A significant number of simulation studies have been conducted to compare the performance of estimators for both linear and logistic regression models [24][25][26][27][28][29][30][31][32][33][34][35]. The MSE is a function of β,σ 2 , p and is minimized subject to constraint β β = 1 [36,37].…”

Section: Monte Carlo Simulationmentioning

confidence: 99%

K-L Estimator: Dealing with Multicollinearity in the Logistic Regression Model

et al. 2023

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Multicollinearity negatively affects the efficiency of the maximum likelihood estimator (MLE) in both the linear and generalized linear models. The Kibria and Lukman estimator (KLE) was developed as an alternative to the MLE to handle multicollinearity for the linear regression model. In this study, we proposed the Logistic Kibria-Lukman estimator (LKLE) to handle multicollinearity for the logistic regression model. We theoretically established the superiority condition of this new estimator over the MLE, the logistic ridge estimator (LRE), the logistic Liu estimator (LLE), the logistic Liu-type estimator (LLTE) and the logistic two-parameter estimator (LTPE) using the mean squared error criteria. The theoretical conditions were validated using a real-life dataset, and the results showed that the conditions were satisfied. Finally, a simulation and the real-life results showed that the new estimator outperformed the other considered estimators. However, the performance of the estimators was contingent on the adopted shrinkage parameter estimators.

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Section: Monte Carlo Simulationmentioning

confidence: 99%

K-L Estimator: Dealing with Multicollinearity in the Logistic Regression Model

et al. 2023

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“…Proof. We find the following difference of the asymptotic mse of the estimators given in Equations ( 60) and (62):…”

Section: Let Us Derive the Asymptotic Mse Formulas Of The Initial Ste...mentioning

confidence: 99%

“…Asar 60 and Asar and Genç 61 investigated shrinkage parameters of Liu type logistic estimator. Asar and Genç 62 defined two‐parameter RE in the logistic regression model. Asar 63 offered new methods for selecting shrinkage parameters of Liu type logistic estimator proposed by İnan and Erdoğan 58 .…”

Section: Introductionmentioning

confidence: 99%

Two‐parameter estimation forTobitmodel: An application to national health and nutrition examination survey dataset

Özbay

Şiray

Toker

et al. 2022

Concurrency and Computation

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Fixed censorship is usually encountered in medical fields, as well as biological, econometric, and engineering researches. It is quite possible to come across censored data with multicollinearity in real-life studies. The multicollinearity affects traditional Tobit maximum likelihood estimation, which is often used in presence of censored data.Biased estimators such as Tobit Liu estimator with one biasing parameter can be used for solving the multicollinearity. In this study, Tobit two-parameter estimator with two biasing parameters is proposed as an alternative to the classical Tobit maximum likelihood and Tobit Liu estimators for the censored data. This new estimator provides advantages from two different aspects thanks to having two biasing parameters. With a simulation study consisting of several scenarios where various levels of factors like the number of independent variables, sample size, correlation degree, variance, and censorship are examined, an in-depth experimental analysis is conducted. In these scenarios, two different biasing parameters' selection methods where one of the biasing parameters is fixed to determine the other one are used and their corresponding outputs are obtained. In addition, a real-life application is carried out with the National Health and Nutrition Examination Survey public-use dataset which includes some demographic and health-related laboratory measurements. The simulation study and data analysis results show that the proposed estimator is more advantageous to its competitors.

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“…. Coefficient vector is chosen using the widespread restriction, β T β = 1, that has been used in GLMs by many authors (see, e.g., [1,3,6]). Condition number (κ), is used to check whether collinearity exist among the explanatory variables or not, is given as…”

Section: Simulation Designmentioning

confidence: 99%

“…In the LRM, Toker and Kaçıranlar [21] compare the TPRE with ordinary least squares (OLS) estimator and RE via matrix mean square error (MMSE) criteria. In the GLMs framework, TPRE has been used in the binary logistic regression model by [6].…”

Section: Introductionmentioning

confidence: 99%

Two parameter Ridge estimator in the inverse Gaussian regression model

Bulut

Işilar

2021

Hacettepe Journal of Mathematics and Statistics

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It is well known that multicollinearity, which occurs among the explanatory variables, has adverse effects on the maximum likelihood estimator in the inverse Gaussian regression model. Biased estimators are proposed to cope with the multicollinearity problem in the inverse Gaussian regression model. The main interest of this article is to introduce a new biased estimator. Also, we compare newly proposed estimator with the other estimators given in the literature. We conduct a Monte Carlo simulation and provide a real data example to illustrate the performance of the proposed estimator over the maximum likelihood and Ridge estimators. As a result of the simulation study and real data example, the newly proposed estimator is superior to the other estimators used in this study.

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Two-parameter ridge estimator in the binary logistic regression

Cited by 16 publications

References 14 publications

K-L Estimator: Dealing with Multicollinearity in the Logistic Regression Model

K-L Estimator: Dealing with Multicollinearity in the Logistic Regression Model

Two‐parameter estimation forTobitmodel: An application to national health and nutrition examination survey dataset

Two parameter Ridge estimator in the inverse Gaussian regression model

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