scholarly journals Quasi-Likelihood Ratio Tests for Homoscedasticity in Linear Regression

2020 ◽  
Vol 18 (1) ◽  
pp. 2-16
Author(s):  
Lili Yu ◽  
Varadan Sevilimedu ◽  
Robert Vogel ◽  
Hani Samawi
Keyword(s):  
Linear Regression ◽  
Likelihood Ratio ◽  
Regression Models ◽  
Likelihood Ratio Tests ◽  
Simulation Studies ◽  
Linear Regression Models

Two quasi-likelihood ratio tests are proposed for the homoscedasticity assumption in the linear regression models. They require few assumptions than the existing tests. The properties of the tests are investigated through simulation studies. An example is provided to illustrate the usefulness of the new proposed tests.

Kernel density‐based likelihood ratio tests for linear regression models

2020 ◽  
Vol 40 (1) ◽  
pp. 119-132
Author(s):  
Feifei Yan ◽  
Qing‐Song Xu ◽  
Man‐Lai Tang ◽  
Ziqi Chen
Keyword(s):  
Linear Regression ◽  
Likelihood Ratio ◽  
Regression Models ◽  
Kernel Density ◽  
Likelihood Ratio Tests ◽  
Linear Regression Models

scholarly journals Robust Bayesian Regression with Synthetic Posterior Distributions

Entropy ◽  
2020 ◽  
Vol 22 (6) ◽  
pp. 661 ◽  
Author(s):  
Shintaro Hashimoto ◽  
Shonosuke Sugasawa
Keyword(s):  
Linear Regression ◽  
Regression Models ◽  
Bayesian Variable Selection ◽  
Bayesian Regression ◽  
Simulation Studies ◽  
Posterior Distributions ◽  
Linear Regression Models ◽  
Computation Algorithm ◽  
Shrinkage Priors ◽  
Variable Selection And Estimation

Although linear regression models are fundamental tools in statistical science, the estimation results can be sensitive to outliers. While several robust methods have been proposed in frequentist frameworks, statistical inference is not necessarily straightforward. We here propose a Bayesian approach to robust inference on linear regression models using synthetic posterior distributions based on γ-divergence, which enables us to naturally assess the uncertainty of the estimation through the posterior distribution. We also consider the use of shrinkage priors for the regression coefficients to carry out robust Bayesian variable selection and estimation simultaneously. We develop an efficient posterior computation algorithm by adopting the Bayesian bootstrap within Gibbs sampling. The performance of the proposed method is illustrated through simulation studies and applications to famous datasets.

scholarly journals Homoscedasticity: an overlooked critical assumption for linear regression

2019 ◽  
Vol 32 (5) ◽  
pp. e100148
Author(s):  
Kun Yang ◽  
Justin Tu ◽  
Tian Chen
Keyword(s):  
Monte Carlo Simulation ◽  
Monte Carlo ◽  
Linear Regression ◽  
Regression Models ◽  
Data Distribution ◽  
The Other ◽  
Simulation Studies ◽  
Linear Regression Models ◽  
Popular Belief

Linear regression is widely used in biomedical and psychosocial research. A critical assumption that is often overlooked is homoscedasticity. Unlike normality, the other assumption on data distribution, homoscedasticity is often taken for granted when fitting linear regression models. However, contrary to popular belief, this assumption actually has a bigger impact on validity of linear regression results than normality. In this report, we use Monte Carlo simulation studies to investigate and compare their effects on validity of inference.

Zero-inflated Conway-Maxwell Poisson Distribution to Analyze Discrete Data

2018 ◽  
Vol 14 (1) ◽  
Author(s):  
Shin Zhu Sim ◽  
Ramesh C. Gupta ◽  
Seng Huat Ong
Keyword(s):  
Regression Model ◽  
Poisson Distribution ◽  
Likelihood Ratio ◽  
Regression Models ◽  
Discrete Data ◽  
Likelihood Ratio Tests ◽  
Simulation Studies ◽  
Generalized Poisson ◽  
Proposed Model ◽  
Better Than

Abstract In this paper, we study the zero-inflated Conway-Maxwell Poisson (ZICMP) distribution and develop a regression model. Score and likelihood ratio tests are also implemented for testing the inflation/deflation parameter. Simulation studies are carried out to examine the performance of these tests. A data example is presented to illustrate the concepts. In this example, the proposed model is compared to the well-known zero-inflated Poisson (ZIP) and the zero- inflated generalized Poisson (ZIGP) regression models. It is shown that the fit by ZICMP is comparable or better than these models.

Testing modified zeros for Poisson regression models

2018 ◽  
Vol 28 (10-11) ◽  
pp. 3123-3141 ◽  
Author(s):  
Yi Tang ◽  
Wan Tang
Keyword(s):  
Likelihood Ratio ◽  
Poisson Regression ◽  
Regression Models ◽  
Score Test ◽  
Poisson Model ◽  
Real Data ◽  
Likelihood Ratio Tests ◽  
Type I ◽  
Simulation Studies ◽  
Zero Inflated Poisson Models

Excessive zeros are common in practice and may cause overdispersion and invalidate inferences when fitting Poisson regression models. Zero-inflated Poisson regression models may be applied if there are inflated zeros; however, it is desirable to test if there are inflated zeros before such zero-inflated Poisson models are applied. Assuming a constant probability of being a structural zero in a zero-inflated Poisson regression model, the existence of the inflated zeros may be tested by testing whether the constant probability is zero. In such situations, the Wald, score, and likelihood ratio tests can be applied. Without specifying a zero-inflated Poisson model, He et al. recently developed a test by comparing the amount of observed zeros with that expected under the Poisson model. In this paper, we develop a closed form for the test and compare it with the Wald, score, and likelihood ratio tests through simulation studies. The simulation studies show that the test of He et al. is the best in controlling type I errors, while the score test generally has the least power among the tests. The tests are illustrated with two real data examples.

scholarly journals empirical likelihood ratio based comparative study on tests for normality of residuals in linear models

2019 ◽  
Vol 16 (1) ◽  
Author(s):  
Chioneso Marange ◽  
Yongsong Qin
Keyword(s):  
Monte Carlo ◽  
Linear Regression ◽  
Likelihood Ratio ◽  
Empirical Likelihood ◽  
Regression Models ◽  
Linear Models ◽  
Type I Error ◽  
Type I ◽  
Simple Linear Regression ◽  
Linear Regression Models

The application of goodness-of-fit (GoF) tests in linear regression modeling is a common practice in applied statistical sciences. For instance, in simple linear regression the assumption of normality of residuals is always necessary to test before making any further inferences. The growing popularity of the use of powerful and efficient empirical likelihood ratio (ELR) based GoF tests in checking for departures from normality in various continuous distributions can be of great use in checking for distributional assumptions of residuals in linear models. Motivated by the attractive properties of the ELR based GoF tests the researchers conducted an extensive Type I error rate assessment as well as a Monte Carlo power comparison of selected ELR GoF tests with well-known existing tests against symmetric and asymmetric alternative OLS and BLUS residuals. Under the simulated scenarios, all the studied tests have good control of Type I error rates. The Monte Carlo experiments revealed the superiority of the ELR GoF tests under certain alternatives of both the OLS and BLUS residuals. Our findings also demonstrated the superiority of OLS over BLUS residuals when one is testing for normality in simple linear regression models. A real data study further revealed the applicability of the ELR based GoF tests in testing normality of residuals in linear regression models.

FAKTOR DETERMINAN PENYALURAN KREDIT BANK PERSERO

2018 ◽  
Vol 23 (1) ◽  
pp. 60-71
Author(s):  
Wigiyanti Masodah
Keyword(s):  
Interest Rate ◽  
Linear Regression ◽  
Interest Rates ◽  
Regression Models ◽  
Linear Regression Models ◽  
Negative Impacts ◽  
Main Activity ◽  
The Impact ◽  
The Given ◽  
Multiple Linear Regression Models

Offering credit is the main activity of a Bank. There are some considerations when a bank offers credit, that includes Interest Rates, Inflation, and NPL. This study aims to find out the impact of Variable Interest Rates, Inflation variables and NPL variables on credit disbursed. The object in this study is state-owned banks. The method of analysis in this study uses multiple linear regression models. The results of the study have shown that Interest Rates and NPL gave some negative impacts on the given credit. Meanwhile, Inflation variable does not have a significant effect on credit given. Keywords: Interest Rate, Inflation, NPL, offered Credit.

Linear Regression Models for Interval-Valued Data using Log-transformation

2020 ◽  
Author(s):  
Nykolas Mayko Maia Barbosa ◽  
João Paulo Pordeus Gomes ◽  
César Lincoln Cavalcante Mattos ◽  
Diêgo Farias Oliveira
Keyword(s):  
Linear Regression ◽  
Regression Models ◽  
Linear Regression Models ◽  
Log Transformation ◽  
Interval Valued
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