Mean-squared error experiment design for linear regression models*

2012 ◽  
Vol 45 (16) ◽  
pp. 1629-1634 ◽  
Author(s):  
Diego Eckhard ◽  
Håkan Hjalmarsson ◽  
Cristian R. Rojas ◽  
Michel Gevers
Keyword(s):  
Linear Regression ◽  
Regression Models ◽  
Mean Squared Error ◽  
Experiment Design ◽  
Linear Regression Models ◽  
Squared Error

scholarly journals Analysis of SF-6D Health State Utility Scores: Is Beta Regression Appropriate?

Healthcare ◽  
2020 ◽  
Vol 8 (4) ◽  
pp. 525
Author(s):  
Samer A Kharroubi
Keyword(s):  
Linear Regression ◽  
Regression Model ◽  
Random Effects ◽  
Regression Models ◽  
Mean Squared Error ◽  
Health State Utility ◽  
Beta Regression ◽  
Health State ◽  
Linear Regression Models ◽  
Utility Scores

Background: Typically, modeling of health-related quality of life data is often troublesome since its distribution is positively or negatively skewed, spikes at zero or one, bounded and heteroscedasticity. Objectives: In the present paper, we aim to investigate whether Bayesian beta regression is appropriate for analyzing the SF-6D health state utility scores and respondent characteristics. Methods: A sample of 126 Lebanese members from the American University of Beirut valued 49 health states defined by the SF-6D using the standard gamble technique. Three different models were fitted for SF-6D via Bayesian Markov chain Monte Carlo (MCMC) simulation methods. These comprised a beta regression, random effects and random effects with covariates. Results from applying the three Bayesian beta regression models were reported and compared based on their predictive ability to previously used linear regression models, using mean prediction error (MPE), root mean squared error (RMSE) and deviance information criterion (DIC). Results: For the three different approaches, the beta regression model was found to perform better than the normal regression model under all criteria used. The beta regression with random effects model performs best, with MPE (0.084), RMSE (0.058) and DIC (−1621). Compared to the traditionally linear regression model, the beta regression provided better predictions of observed values in the entire learning sample and in an out-of-sample validation. Conclusions: Beta regression provides a flexible approach to modeling health state values. It also accounted for the boundedness and heteroscedasticity of the SF-6D index scores. Further research is encouraged.

scholarly journals A Comparative Analysis on Some Estimators of Parameters of Linear Regression Models in Presence of Multicollinearity

2018 ◽  
pp. 1-8
Author(s):  
Warha, Abdulhamid Audu ◽  
Yusuf Abbakar Muhammad ◽  
Akeyede, Imam
Keyword(s):  
Linear Regression ◽  
Least Squares ◽  
Regression Models ◽  
Mean Squared Error ◽  
Least Squares Method ◽  
Ordinary Least Squares ◽  
Least Square ◽  
Linear Regression Models ◽  
Independent Variables ◽  
Different Levels

Linear regression is the measure of relationship between two or more variables known as dependent and independent variables. Classical least squares method for estimating regression models consist of minimising the sum of the squared residuals. Among the assumptions of Ordinary least squares method (OLS) is that there is no correlations (multicollinearity) between the independent variables. Violation of this assumptions arises most often in regression analysis and can lead to inefficiency of the least square method. This study, therefore, determined the efficient estimator between Least Absolute Deviation (LAD) and Weighted Least Square (WLS) in multiple linear regression models at different levels of multicollinearity in the explanatory variables. Simulation techniques were conducted using R Statistical software, to investigate the performance of the two estimators under violation of assumptions of lack of multicollinearity. Their performances were compared at different sample sizes. Finite properties of estimators’ criteria namely, mean absolute error, absolute bias and mean squared error were used for comparing the methods. The best estimator was selected based on minimum value of these criteria at a specified level of multicollinearity and sample size. The results showed that, LAD was the best at different levels of multicollinearity and was recommended as alternative to OLS under this condition. The performances of the two estimators decreased when the levels of multicollinearity was increased.

scholarly journals Modified Liu estimators in the linear regression model: An application to Tobacco data

PLoS ONE ◽  
2021 ◽  
Vol 16 (11) ◽  
pp. e0259991
Author(s):  
Iqra Babar ◽  
Hamdi Ayed ◽  
Sohail Chand ◽  
Muhammad Suhail ◽  
Yousaf Ali Khan ◽  
...  
Keyword(s):  
Linear Regression ◽  
Mean Squared Error ◽  
Prediction Interval ◽  
Evaluation Criteria ◽  
Absolute Error ◽  
Vital Role ◽  
Predictor Variables ◽  
Linear Regression Models ◽  
Squared Error ◽  
Optimal Value

Background The problem of multicollinearity in multiple linear regression models arises when the predictor variables are correlated among each other. The variance of the ordinary least squared estimator become unstable in such situation. In order to mitigate the problem of multicollinearity, Liu regression is widely used as a biased method of estimation with shrinkage parameter ‘d’. The optimal value of shrinkage parameter plays a vital role in bias-variance trade-off. Limitation Several estimators are available in literature for the estimation of shrinkage parameter. But the existing estimators do not perform well in terms of smaller mean squared error when the problem of multicollinearity is high or severe. Methodology In this paper, some new estimators for the shrinkage parameter are proposed. The proposed estimators are the class of estimators that are based on quantile of the regression coefficients. The performance of the new estimators is compared with the existing estimators through Monte Carlo simulation. Mean squared error and mean absolute error is considered as evaluation criteria of the estimators. Tobacco dataset is used as an application to illustrate the benefits of the new estimators and support the simulation results. Findings The new estimators outperform the existing estimators in most of the considered scenarios including high and severe cases of multicollinearity. 95% mean prediction interval of all the estimators is also computed for the Tobacco data. The new estimators give the best mean prediction interval among all other estimators. The implications of the findings We recommend the use of new estimators to practitioners when the problem of high to severe multicollinearity exists among the predictor variables.

scholarly journals THEORETICAL AND INSILCO PHARMACOKINETIC INVESTIGATIONS ON SOME PHENYL PIPERIDINE DERIVATIVES AS NOVEL ANTIDEPRESSANT AGENTS

2020 ◽  
Vol 6 (2) ◽  
pp. 0107-0128
Author(s):  
Olasupo Sabitu Babatunde Babatunde ◽  
Adamu Uzairu ◽  
Gideon Adamu Shallangwa ◽  
Sani Uba
Keyword(s):  
Regression Models ◽  
Density Functional ◽  
Mean Squared Error ◽  
Linear Regression Models ◽  
Statistical Parameters ◽  
Functional Theory ◽  
Squared Error ◽  
Antipsychotic Activity ◽  
Chi Squared ◽  
Multi Linear Regression

A theoretical bioinformatic investigation was carried out on some Inhibitors of serotonin transporter (SERT) of Phenyl piperidine derivatives using Density Functional Theory (DFT/B3LYP/6-31G*) at ground state with Spartan 14 V1.1.4 software in modeling the antipsychotic activity of the compounds. The molecular descriptors were computed using the PaDEL-Descriptor software 2.20 version. Penta-parametric Multi-linear regression models were developed using the MLR-GFA for selecting the most important descriptors. The statistical parameters for the best model are; R2Train= 0.8572, R 2adj = 0.8274, R2Test = 0.678, Q2cv (LOO) = 0.7664, Ꭓ2= 0.0036, r2m (LOO)= 0.694 and Delta r2m (LOO)= 0.0051). Also, the estimated Chi-squared (Ꭓ2= 0.0036), Root-mean squared error (RMSE= 0.168) and and

scholarly journals Nonlinear Tactile Estimation Model based on Perceptibility of Mechanoreceptors improves Quantitative Tactile Sensing

2022 ◽  
Author(s):  
Momoko Sagara ◽  
Lisako Nobuyama ◽  
Kenjiro Takemura
Keyword(s):  
Linear Regression ◽  
Sensory Evaluation ◽  
Regression Models ◽  
Mean Squared Error ◽  
Consumer Products ◽  
Average Error ◽  
Tactile Sensing ◽  
Linear Regression Models ◽  
Estimation Model ◽  
Physical Measurements

Abstract Tactile sensing has attracted significant attention as a tactile quantitative evaluation method because the tactile sensation is an important factor while evaluating consumer products. While the human tactile perception mechanism has nonlinearity, previous studies have often developed linear regression models. In contrast, this study proposes a nonlinear tactile estimation model that can estimate sensory evaluation scores from physical measurements. We extracted features from the vibration data obtained by a tactile sensor based on the perceptibility of mechanoreceptors. In parallel, a sensory evaluation test was conducted using 10 evaluation words. Then, the relationship between the extracted features and the tactile evaluation results was modeled using linear/nonlinear regressions. The best model was concluded by comparing the mean squared error between the model predictions and the actual values. The result implies that there are multiple evaluation words suitable for adopting nonlinear regression models, and the average error was 43.8% smaller than that of building only 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

THE PREDICTIVE CONTENT OF DISAGGREGATED NORMAL INCOME: An Empirical Study in the JSX

2003 ◽  
Vol 5 (3) ◽  
pp. 363 ◽  
Author(s):  
Slamet Sugiri
Keyword(s):  
Linear Regression ◽  
Regression Models ◽  
Stock Exchange ◽  
Manufacturing Firms ◽  
Single Step ◽  
Model Parameters ◽  
Linear Regression Models ◽  
Operating Income ◽  
Predictive Content ◽  
Multiple Step

The main objective of this study is to examine a hypothesis that the predictive content of normal income disaggregated into operating income and nonoperating income outperforms that of aggregated normal income in predicting future cash flow. To test the hypothesis, linear regression models are developed. The model parameters are estimated based on fifty-five manufacturing firms listed in the Jakarta Stock Exchange (JSX) up to the end of 1997.This study finds that empirical evidence supports the hypothesis. This evidence supports arguments that, in reporting income from continuing operations, multiple-step approach is preferred to single-step one.

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