scholarly journals An application of two sided power distribution in Bayesian analysis of paired comparison of relative importance of predictors in linear regression models

2015 ◽  
Vol 3 (2) ◽  
pp. 169 ◽  
Author(s):  
Xiaoyin Wang
Keyword(s):  
Power Distribution ◽  
Regression Models ◽  
Paired Comparison ◽  
Multiple Regression Model ◽  
Link Function ◽  
Relative Importance ◽  
Simulation Studies ◽  
Research Practice ◽  
Linear Regression Models ◽  
The Individual

<p>The purpose of determining the relative importance of predictors is to expose the extent of the individual contribution of a predictor in the presence of other predictors within a selected model. The goal of this article is to expand the current research practice by developing a statistical paired comparison model with Two Sided Power (TSP) link function in the Bayesian framework to evaluate the relative importance of each predictor in a multiple regression model. Results from simulation studies and empirical example reveal that the proposed Two Sided Power link function provides similar conclusions as the commonly used logit link function, but has more advantages from both practical and computational perspectives.</p>

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.

Effects of recovered wood on the formaldehyde release of particleboards

Holzforschung ◽  
2014 ◽  
Vol 68 (6) ◽  
pp. 669-678 ◽  
Author(s):  
Sarah Himmel ◽  
Mark Irle ◽  
Guillaume Legrand ◽  
Rosa Perez ◽  
Carsten Mai
Keyword(s):  
Linear Regression ◽  
Regression Models ◽  
Gas Analysis ◽  
Raw Material ◽  
Analysis Method ◽  
Linear Regression Models ◽  
Formaldehyde Release ◽  
The Core ◽  
The Individual

Abstract Three-layer polymeric diphenyl-methane-diisocyanate (pMDI)-bonded particleboards (PBs) were produced with different proportions of simulated recovered wood (rW) in the core layers (cLs) to assess the effect of rW on the formaldehyde (FA) release of PB. A pre-test was conducted on furniture and particle mixtures of rW to determine the range of expectable FA emission of rW. The FA content of the raw particle mixtures could be predicted from the contents of the individual raw material and did not change compared to the PB. FA content correlated strongly with PB-FA emission. It was possible to predict the maximum PB-FA contents, which should not be exceeded according to F**** and CARB 2 by linear regression models. At moderate and high total FA emission levels, the FA emission of the particle mixtures was approximately 60% higher than the emission of PB blocks. At low total FA level, the flask method and the gas analysis method exhibited different results with regard to the emissions from particles and their respective PBs.

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 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 Individual and Combined Associations of Glucose Metabolic Components With Cognitive Function Modified by Obesity

2021 ◽  
Vol 12 ◽  
Author(s):  
Ruixin He ◽  
Ruizhi Zheng ◽  
Jie Li ◽  
Qiuyu Cao ◽  
Tianzhichao Hou ◽  
...  
Keyword(s):  
Insulin Resistance ◽  
Cognitive Function ◽  
Regression Models ◽  
Positive Association ◽  
Digit Symbol Substitution Test ◽  
Metabolic Risk ◽  
Model Assessment ◽  
Linear Regression Models ◽  
Logistic Regression Models ◽  
The Individual

AimWe aimed to detect the individual and combined effect of glucose metabolic components on cognitive function in particular domains among older adults.MethodsData of 2,925 adults aged over 60 years from the 2011 to 2014 National Health and Nutrition Examination Survey were analyzed. Individuals’ cognitive function was evaluated using the Digit Symbol Substitution Test (DSST), the Animal Fluency Test (AF), the Consortium to Establish a Registry for Alzheimer’s Disease Immediate Recall (CERAD-IR), and CERAD Delayed Recall (CERAD-DR). Participants’ glucose metabolic health status was determined based on fasting plasma glucose, insulin, homeostasis model assessment of insulin resistance (HOMA-IR), glycated hemoglobin (HbA1c), and 2-h postload glucose. Linear regression models were used to delineate the associations of cognitive function with individual glucose metabolic component and with metformin use. Logistic regression models were performed to evaluate the associations of cognition with the number of glucose metabolic risk components.ResultsCERAD-IR was significantly associated with HOMA-IR and insulin. HbA1c was related to all the cognitive tests except AF. Among participants without obesity, HOMA-IR and insulin were both negatively associated with CERAD-IR and CERAD-DR. Odds of scoring low in DSST increased with the number of glucose metabolic risk components (odds ratio 1.94, 95% confidence interval [CI] 1.26 to 2.98). Metformin use was associated with better performance in DSST among diabetes patients (β = 4.184, 95% CI 1.655 to 6.713).ConclusionsOur findings support the associations of insulin resistance and glycemic level with cognitive function in key domains, especially among adults without obesity. There is a positive association between metformin use and cognition.

scholarly journals Partially Linear Generalized Single Index Models for Functional Data (PLGSIMF)

Stats ◽  
2021 ◽  
Vol 4 (4) ◽  
pp. 793-813
Author(s):  
Mohamed Alahiane ◽  
Idir Ouassou ◽  
Mustapha Rachdi ◽  
Philippe Vieu
Keyword(s):  
Functional Data ◽  
Regression Models ◽  
Asymptotic Distributions ◽  
Link Function ◽  
Linear Regression Models ◽  
Single Index ◽  
Partially Linear ◽  
Generalize Linear Regression ◽  
Single Index Models ◽  
Non Parametric

Single-index models are potentially important tools for multivariate non-parametric regression analysis. They generalize linear regression models by replacing the linear combination α0⊤X with a non-parametric component η0α0⊤X, where η0(·) is an unknown univariate link function. In this article, we generalize these models to have a functional component, replacing the generalized partially linear single index models η0α0⊤X+β0⊤Z , where α is a vector in IRd, η0(·) and β0(·) are unknown functions that are to be estimated. We propose estimates of the unknown parameter α0, the unknown functions β0(·) and η0(·) and establish their asymptotic distributions, and furthermore, a simulation study is carried out to evaluate the models and the effectiveness of the proposed estimation methodology.

Repeated responses in misclassification binary regression: A Bayesian approach

2018 ◽  
Vol 19 (4) ◽  
pp. 412-443 ◽  
Author(s):  
Magda Carvalho Pires ◽  
Roberto da Costa Quinino
Keyword(s):  
Repeated Measures ◽  
Regression Models ◽  
Data Augmentation ◽  
Simple Majority ◽  
Simulation Studies ◽  
Binary Regression ◽  
Response Variable ◽  
The Individual ◽  
Conditional Means ◽  
Adaptive Rejection Metropolis Sampling

Binary regression models generally assume that the response variable is measured perfectly. However, in some situations, the outcome is subject to misclassification: a success may be erroneously classified as a failure or vice versa. Many methods, described in existing literature, have been developed to deal with misclassification, but we demonstrate that these methods may lead to serious inferential problems when only a single evaluation of the individual is taken. Thus, this study proposes to incorporate repeated and independent responses in misclassification binary regression models, considering the total number of successes obtained or even the simple majority classification. We use subjective prior distributions, as our conditional means prior, to evaluate and compare models. A data augmentation approach, Gibbs sampling, and Adaptive Rejection Metropolis Sampling are used for posterior inferences. Simulation studies suggested that repeated measures significantly improve the posterior estimates, in that these estimates are closer to those obtained in a case with no misclassifications with a lower standard deviation. Finally, we illustrate the usefulness of the new methodology with the analysis about defects in eyeglass lenses.

scholarly journals Individual and joint association of bioavailable testosterone and aging with neutrophil-to-lymphocyte ratio in Chinese middle-aged and elderly men

2019 ◽  
Vol 32 (8) ◽  
pp. 1515-1523 ◽  
Author(s):  
Jian Zhou ◽  
Yaping Wei ◽  
Yuan Lan ◽  
Jingjing Zuo ◽  
Xiangqing Hou ◽  
...  
Keyword(s):  
Regression Models ◽  
Cross Sectional Study ◽  
Neutrophil To Lymphocyte Ratio ◽  
Linear Regression Models ◽  
Elderly Men ◽  
Cross Sectional ◽  
Lymphocyte Ratio ◽  
Bioavailable Testosterone ◽  
Linear Relationships ◽  
The Individual

Abstract Background and objectives Accumulating evidences suggest that chronic systemic inflammation (CSI) is independently associated with large number of major non-communicable chronic diseases (NCDs) ranging from metabolic disorders to cancers, and neutrophil-to-lymphocyte ratio (NLR) has been accepted as a novel, convenient marker for CSI response. Testosterone deficiency in men is linked to high risk of NCDs. This cross-sectional study aimed to investigate the individual and joint association of bioavailable testosterone (BIOT) and aging with NLR. Methods A total of 132 male adults were enrolled during Jan. 2011 and Oct. 2017 in the first affiliated hospital of University of Science and Technology of China. Local weighted regression (LOESS) and multivariable generalized linear regression models were utilized to comprehensively examine the individual and joint association between BIOT and age with NLR. Results Obvious linear relationships between NLR and BIOT or age were observed with the LOESS models. NLR was negatively correlated to BIOT after adjusting for some potential confounding factors (P = 0.034). As compared to the lowest quartile of BIOT, the adjusted decrease of NLR for the 2nd, 3rd and 4th quartiles were 0.40, 0.64 and 0.72, respectively. Meanwhile, NLR was observed to be independently correlated to elevated age (P = 0.043). Furthermore, as compared to the counterparts, men over 70 years combined with plasma BIOT less than 4.7 nmol/L had the highest NLR level, which suggested that low BIOT and aging jointly correlated to the level of NLR (P = 0.005). Conclusion BIOT deficiency and aging were individually and jointly correlated to CSI. Men over 70 years combined with BIOT < 4.7 nmol/L were more like to have higher grade of CSI than others.

scholarly journals PENGARUH PENGGUNAAN E-FILING DAN PEMAHAMAN PERPAJAKAN TERHADAP KEPATUHAN PENYAMPAIAN SPT TAHUNAN WPOP (Studi Pada WPOP Pekerja Bebas Di Kota Salatiga )

2021 ◽  
Vol 12 (1) ◽  
pp. 34-51
Author(s):  
Fadillah Achmad Resandi ◽  
Ika Kristianti
Keyword(s):  
Linear Regression ◽  
Data Collection ◽  
Regression Models ◽  
Sampling Method ◽  
Hypothesis Test ◽  
Questionnaire Data ◽  
Linear Regression Models ◽  
The Individual ◽  
Positive Effect ◽  
Multiple Linear Regression Models

The purpose of this study to determine the effect of using e-filing and understanding of taxation on compliance of annual taxpayer reporting of the individual taxpayer in the Salatiga. The population of this research is non-employee individual taxpayers who are registered in KPP Pratama Salatiga. The sample used is 100 respondents and data collection techniques using an incidental sampling method. The questionnaires were distributed using google form and given directly to respondents. The collected questionnaire data was tested with validity, reliability, and classical assumption tests. Hypothesis test using the T-test with multiple linear regression models. The results of this study indicate that (1) the use of e-filing has a positive effect on compliance with the annual taxpayer reporting of non-employee individual taxpayers in Salatiga. (2) Understanding taxation has a positive effect on compliance with the annual taxpayer reporting of non-employee individual taxpayers in Salatiga.

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