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.

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 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.

scholarly journals Bayesian model evidence as a practical alternative to deviance information criterion

2018 ◽  
Vol 5 (3) ◽  
pp. 171519 ◽  
Author(s):  
C. M. Pooley ◽  
G. Marion
Keyword(s):  
Linear Regression ◽  
Bayesian Model ◽  
Regression Models ◽  
Deviance Information Criterion ◽  
Information Criterion ◽  
The Other ◽  
Model Choice ◽  
Linear Regression Models ◽  
True Model ◽  
Model Evidence

While model evidence is considered by Bayesian statisticians as a gold standard for model selection (the ratio in model evidence between two models giving the Bayes factor), its calculation is often viewed as too computationally demanding for many applications. By contrast, the widely used deviance information criterion (DIC), a different measure that balances model accuracy against complexity, is commonly considered a much faster alternative. However, recent advances in computational tools for efficient multi-temperature Markov chain Monte Carlo algorithms, such as steppingstone sampling (SS) and thermodynamic integration schemes, enable efficient calculation of the Bayesian model evidence. This paper compares both the capability (i.e. ability to select the true model) and speed (i.e. CPU time to achieve a given accuracy) of DIC with model evidence calculated using SS. Three important model classes are considered: linear regression models, mixed models and compartmental models widely used in epidemiology. While DIC was found to correctly identify the true model when applied to linear regression models, it led to incorrect model choice in the other two cases. On the other hand, model evidence led to correct model choice in all cases considered. Importantly, and perhaps surprisingly, DIC and model evidence were found to run at similar computational speeds, a result reinforced by analytically derived expressions.

scholarly journals A study on factors related to readership of scientific articles

2017 ◽  
Vol 3 (2) ◽  
pp. 1-15 ◽  
Author(s):  
Tony Xu ◽  
Shayan Khalili ◽  
Cynthia Deng
Keyword(s):  
Linear Regression ◽  
Regression Models ◽  
Scientific Research ◽  
The Other ◽  
Linear Regression Models ◽  
Research Papers ◽  
Scatter Plots ◽  
The Subject ◽  
Moderate Effect ◽  
The Relationship

This paper analyzes the relationship between the number of Twitter and Mendeley readers with the article’s subject, publisher, journal, and title length. It also looks at which country has the greatest number of readers to see if researchers can garner more visibility by publishing an article relevant to issues in those countries. The purpose of this report is to help researchers improve the visibility and impact value of their research. The data was gathered from 550,000 scientific research papers published between January 1st and July 1st of 2016. Python’s built-in JSON library was used to extract the number of Twitter and Mendeley readers, as well as the article count for each factor. The correlation between readers per article and each factor was then visualized using bubble graphs, linear regression models, and scatter plots. This paper concludes that the length of the title is the strongest factor affecting readership. In particular, titles with lengths between 51 and 90 characters have the greatest number of readers. Moreover, articles relevant to issues in countries with a higher GDP have the highest overall readership. On the other hand, the publisher and the journal did not have a significant effect on readership, while the subject of the article had a moderate effect on readership.

scholarly journals Economic Growth and Public Indebtedness in the Last Four Decades: Is Portugal different from the other PIIGS’ economies?

2015 ◽  
Vol 61 (6) ◽  
pp. 3-11 ◽  
Author(s):  
Ricardo Ferraz ◽  
António Portugal Duarte
Keyword(s):  
Economic Growth ◽  
Linear Regression ◽  
Public Debt ◽  
Regression Models ◽  
Time Horizon ◽  
Negative Relationship ◽  
The Other ◽  
Extended Time ◽  
Linear Regression Models ◽  
The Relationship

Abstract Portugal is a member of the group known by investors as ‘PIIGS’, countries characterised by having high public debt and weak economic growth. Using an extended time horizon, 1974–2014, this study seeks to empirically explore the relationship between economic growth and public debt in the PIIGS economies, particularly in the case of Portugal. Based on the estimation of linear regression models, it was concluded that in the last four decades there has been a negative relationship between economic growth and public debt in both cases, which is consistent with the literature. The negative relationship was even more pronounced in the case of the PIIGS than it was in the case of Portugal.

scholarly journals PENGARUH INFLASI, BI RATE, SUKU BUNGA KREDIT UMKM TERHADAP NON PERFORMING LOAN KREDIT UMKM PADA BANK UMUM

2020 ◽  
Vol 8 (2) ◽  
pp. 156
Author(s):  
Suharna Suharna
Keyword(s):  
Interest Rate ◽  
Linear Regression ◽  
Multiple Linear Regression ◽  
Commercial Banks ◽  
Regression Models ◽  
Inflation Rate ◽  
Secondary Data ◽  
The Other ◽  
Linear Regression Models ◽  
Multiple Linear Regression Models

This study aims to obtain empirical evidence on the influence of inflation, rate of Bank Indonesia, and credit interest rate on non - performing SMEs credit loan at Commercial Banks. This study uses secondary data obtained from quarterly OJK reports and Bank Indonesia monthly reports for the period of 2014 - 2018. Multiple linear regression models are used to test the hypotheses of this study. It was found that the inflation rate and the rate of Bank Indonesia individually doesn't have a siignificant influence on non - performing SMEs credit loans. On the other hand, it was found that credit interest rate has a signifinicant influence on non - performing SMEs credit loans.

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