scholarly journals Inverted Weibull Regression Models and Their Applications

Stats ◽  
2021 ◽  
Vol 4 (2) ◽  
pp. 269-290
Author(s):  
Sarah R. Al-Dawsari ◽  
Khalaf S. Sultan
Keyword(s):  
Regression Model ◽  
Bayesian Approach ◽  
Regression Models ◽  
Mean Squared Error ◽  
Information Criterion ◽  
Bayesian Regression ◽  
Loss Functions ◽  
Performance Criteria ◽  
Weibull Regression ◽  
The Bayesian Approach

In this paper, we propose the classical and Bayesian regression models for use in conjunction with the inverted Weibull (IW) distribution; there are the inverted Weibull Regression model (IW-Reg) and inverted Weibull Bayesian regression model (IW-BReg). In the proposed models, we suggest the logarithm and identity link functions, while in the Bayesian approach, we use a gamma prior and two loss functions, namely zero-one and modified general entropy (MGE) loss functions. To deal with the outliers in the proposed models, we apply Huber and Tukey’s bisquare (biweight) functions. In addition, we use the iteratively reweighted least squares (IRLS) algorithm to estimate Bayesian regression coefficients. Further, we compare IW-Reg and IW-BReg using some performance criteria, such as Akaike’s information criterion (AIC), deviance (D), and mean squared error (MSE). Finally, we apply the some real datasets collected from Saudi Arabia with the corresponding explanatory variables to the theoretical findings. The Bayesian approach shows better performance compare to the classical approach in terms of the considered performance criteria.

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.

Parametric Survival Modelling of Risk Factor of Tuberculosis Patients under DOTS Program at Hawassa Town, Ethiopia

2015 ◽  
Vol 4 (1) ◽  
pp. 1-17 ◽  
Author(s):  
Fikadu Zawdie Chere ◽  
Yohannes Yebabe Tesfay ◽  
Fikre Enquoselassie
Keyword(s):  
Regression Model ◽  
Survival Data ◽  
Information Criterion ◽  
Major Health Problem ◽  
Weibull Regression ◽  
Tuberculosis Patients ◽  
Parametric Regression ◽  
Time To Death ◽  
Baseline Weight ◽  
Weibull Regression Model

Tuberculosis (TB) is a chronic infectious disease that has a major health problem over the centuries. This study assessed the risk factors associated with time to death among TB patients treated under directly observed short course treatment program in Health facilities in Hawassa city, Ethiopia. The authors analysed data from a cohort of 1604 TB patients recruited between September 2008 to September 2011. They apply the parametric regression model of survival data analysis. The best fitted parametric regression model is selected by using the Akaike information criterion (AIC). The AIC confirms that the Weibull regression model is found to be the best fit of the survival of tuberculosis patients under the DOTS program at Hawassa town, Ethiopia. The fit of the Weibull regression model result revealed that sex, age, baseline weight, HIV status, category of patients and year of enrolment are the significant factor for the survival of TB patients.

Evaluation of the financial condition of companies after the announcement of arrangement bankruptcy: application of the classical and Bayesian logistic regression

2020 ◽  
Vol 67 (1) ◽  
pp. 5-32
Author(s):  
Barbara Pawełek ◽  
Jadwiga Kostrzewska ◽  
Maciej Kostrzewski ◽  
Krzysztof Gałuszka
Keyword(s):  
Logistic Regression ◽  
Regression Model ◽  
Construction Industry ◽  
Bayesian Approach ◽  
Logistic Regression Model ◽  
Likelihood Method ◽  
Logistic Regression Models ◽  
Financial Condition ◽  
Bayesian Logistic Regression ◽  
The Bayesian Approach

The aim of this paper is to present the results of an assessment of the financial condition of companies from the construction industry after the announcement of arrangement bankruptcy, in comparison to the condition of healthy companies. The logistic regression model estimated by means of the maximum likelihood method and the Bayesian approach were used. The first achievement of our study is the assessment of the financial condition of companies from the construction industry after the announcement of bankruptcy. The second achievement is the application of an approach combining the classical and Bayesian logistic regression models to assess the financial condition of companies in the years following the declaration of bankruptcy, and the presentation of the benefits of such a combination. The analysis described in the paper, carried out in most part by means of the ML logistic regression model, was supplemented with information yielded by the application of the Bayesian approach. In particular, the analysis of the shape of the posterior distribution of the repeat bankruptcy probability makes it possible, in some cases, to observe that the financial condition of a company is not clear, despite clear assessments made on the basis of the point estimations.

scholarly journals A Study of Count Regression Models for Mortality Rate

CAUCHY ◽  
2021 ◽  
Vol 7 (1) ◽  
pp. 142-151
Author(s):  
Anwar Fitrianto
Keyword(s):  
Mortality Rate ◽  
Regression Model ◽  
Count Data ◽  
Bayesian Information Criterion ◽  
Regression Models ◽  
Negative Binomial ◽  
Negative Binomial Regression ◽  
Information Criterion ◽  
Poisson Regression Model ◽  
Binomial Regression

This paper discusses how overdispersed count data to be fit. Poisson regression model, Negative Binomial 1 regression model (NEGBIN 1) and Negative Binomial regression 2 (NEGBIN 2) model were proposed to fit mortality rate data. The method used is comparing the values of Akaike Information Criterion (AIC) and Bayesian Information Criterion (BIC) to find out which method suits the data the most. The results show that the data indeed display higher variability. Among the three models, the model preferred is NEGBIN 1 model.

scholarly journals Parametric regression model for response time in clinical trials – a bayesian approach

2017 ◽  
Vol 7 (1) ◽  
pp. 1-7 ◽  
Author(s):  
SUNDARAM N
Keyword(s):  
Clinical Trials ◽  
Monte Carlo ◽  
Regression Model ◽  
Survival Data ◽  
Regression Models ◽  
Bayesian Regression ◽  
The Other ◽  
Mcmc Methods ◽  
Censored Survival Data ◽  
Parametric Regression

In this paper an attempt has been made to model the censored survival data using Bayesian regressions with Markov Chain Monte Carlo (MCMC) methods. Bayesian LogNormal (LN) regression model are found to be providing better fit than the other Bayesian regression models namely Exponential (E), Generalized Exponential (GE), Webull (W), LogLogistic (LL) and Gamma (G).

scholarly journals Ruminal pH and N-NH3 behavior: a Bayesian approach

2016 ◽  
Vol 37 (1) ◽  
pp. 311
Author(s):  
Osvaldo Martins Souza ◽  
Elias Nunes Martins ◽  
Robson Marcelo Rossi ◽  
Carlos Antonio Lopes de Oliveira ◽  
Sílvia Cristina de Aguiar ◽  
...  
Keyword(s):  
Bayesian Approach ◽  
Regression Models ◽  
Correlated Data ◽  
Linear Functions ◽  
A Posteriori ◽  
Ruminal Ph ◽  
Estimated Parameters ◽  
A Posteriori Estimates ◽  
Least Squares Estimates ◽  
The Bayesian Approach

In this work, we present the Bayesian approach as an alternative to frequentist analysis regarding correlated data of pH and N-NH3 in the Holstein cow rumen. It was observed that for pH and N-NH3 data, a posteriori estimates of coefficients of the regression models were significant, which was not observed for least-squares estimates. Thus, the Bayesian approach allowed inferences that were directly linked to the sampling of parameters of interest and statistical comparisons of non-linear functions of the estimated parameters.

A Theoretical Framework for Estimating Swarm Success Probability Using Scouts

2012 ◽  
pp. 277-307
Author(s):  
Antons Rebguns ◽  
Diana F. Spears ◽  
Richard Anderson-Sprecher ◽  
Aleksey Kletsov
Keyword(s):  
Bayesian Approach ◽  
Mean Squared Error ◽  
Success Probability ◽  
Ground Truth ◽  
Theoretical Framework ◽  
Experimental Results ◽  
Squared Error ◽  
The Mean ◽  
The Bayesian Approach ◽  
Bayesian Formula

This paper presents a novel theoretical framework for swarms of agents. Before deploying a swarm for a task, it is advantageous to predict whether a desired percentage of the swarm will succeed. The authors present a framework that uses a small group of expendable “scout” agents to predict the success probability of the entire swarm, thereby preventing many agent losses. The scouts apply one of two formulas to predict – the standard Bernoulli trials formula or the new Bayesian formula. For experimental evaluation, the framework is applied to simulated agents navigating around obstacles to reach a goal location. Extensive experimental results compare the mean-squared error of the predictions of both formulas with ground truth, under varying circumstances. Results indicate the accuracy and robustness of the Bayesian approach. The framework also yields an intriguing result, namely, that both formulas usually predict better in the presence of (Lennard-Jones) inter-agent forces than when their independence assumptions hold.

scholarly journals Analysis of a dose-response assay in Scaptotrigona bipunctata bees, Lepeletier, 1836 (Hymenoptera: Apidae) using the logistic regression model under the Bayesian approach

2021 ◽  
Vol 43 ◽  
pp. e57781
Author(s):  
Breno Gabriel da Silva ◽  
Paula Ribeiro Santos ◽  
Cristian Marcelo Villegas Lobos ◽  
Tamiris de Oliveira Diniz ◽  
Naiara Climas Pereira ◽  
...  
Keyword(s):  
Logistic Regression ◽  
Regression Model ◽  
Bayesian Approach ◽  
Dose Response ◽  
Lead Time ◽  
Logistic Regression Model ◽  
Prior Information ◽  
Alternative Approach ◽  
Dose Response Study ◽  
The Bayesian Approach

This paper shows the results of a dose-response study in Scaptotrigona bipunctata bees, Lepeletier, 1836 (Hymenoptera: Apidae) exposed to the insecticide Fastac Duo. The aim was to evaluate the lethal concentration that causes the death of 50% of bees (LC50) and investigate the odd of mortality after exposure to different concentrations, using the logistic regression model under the Bayesian approach. In this approach, it is possible to incorporate a prior information and gives more accurate inferential results. Three independent dose-response experiments were analyzed, dissimilar in their lead time according to guidelines from the Organisation for Economic Co-operation and Development (OECD), in which each assay contained four replicates at the concentration levels investigated, including control. Observing exposure to the agrochemical, it was identified that the higher the concentration, the greater the odd of mortality. Regarding the estimated lethal concentrations for each experiment, the following values were found, 0.03 g a.i. L-1, for 24 hours, 0.04 g a.i. L-1, for 48 hours and 0.06 g a.i. L-1 for 72 hours, showing that in experiments with longer exposure times there was an increase in LC50. Concluding, the study showed an alternative approach to classical methods for dose-response studies in Scaptotrigona bipunctata bees exposed to the insecticide Fastac Duo.

How a Bayesian Might Estimate the Distribution of Cronbach’s Alpha From Ordinal-Dynamic Scaled Data

Methodology ◽  
2010 ◽  
Vol 6 (2) ◽  
pp. 71-82 ◽  
Author(s):  
Byron J. Gajewski ◽  
Diane K. Boyle ◽  
Sarah Thompson
Keyword(s):  
Confidence Intervals ◽  
Bayesian Approach ◽  
Mean Squared Error ◽  
Cronbach’S Alpha ◽  
Interval Estimates ◽  
Response Options ◽  
Practical Advice ◽  
Cronbach's Alpha ◽  
Squared Error ◽  
The Bayesian Approach

We demonstrate the utility of a Bayesian-based approach for calculating intervals of Cronbach’s alpha from a psychological instrument having ordinal responses with a dynamic scale. A small number of response options on an instrument will cause traditional-based interval estimates to be biased. Ordinal-based solutions are problematic because there is no clear mechanism for handling the dynamic scale. One way to remedy the bias is to adjust with a Bayesian approach. The Bayesian approach adjusts the bias and allows theoretically simple calculations of Cronbach’s alpha and intervals. We demonstrate the calculations of the Bayesian approach while at the same time offer a comparison to more traditional-based methods using both credible (or confidence) intervals and mean squared error. Practical advice is offered.

Robustness against outliers: A new variance inflated regression model for proportions

2019 ◽  
Vol 20 (3) ◽  
pp. 274-309
Author(s):  
Agnese Maria Di Brisco ◽  
Sonia Migliorati ◽  
Andrea Ongaro
Keyword(s):  
Regression Model ◽  
Bayesian Approach ◽  
Regression Models ◽  
The Other ◽  
Regression Coefficients ◽  
Posterior Distributions ◽  
New Model ◽  
Model Based ◽  
Regression Curves ◽  
New Distribution

This article addresses the issue of building regression models for bounded responses, which are robust in the presence of outliers. To this end, a new distribution on (0,1) and a regression model based on it are proposed and some properties are derived. The distribution is a mixture of two beta components. One of them, showing a higher variance (variance inflated) is expected to capture outliers. Within a Bayesian approach, an extensive robustness study is performed to compare the new model with three competing ones present in the literature. A broad range of inferential tools are considered, aimed at measuring the influence of various outlier patterns from diverse perspectives. It emerges that the new model displays a better performance in terms of stability of regression coefficients’ posterior distributions and of regression curves under all outlier patterns. Moreover, it exhibits an adequate behaviour under all considered settings, unlike the other models.

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