Topic
Beta rectangular distribution
About: Beta rectangular distribution is a research topic. Over the lifetime, 4 publications have been published within this topic receiving 160 citations.
Papers
TL;DR: In this paper, a new regression model for proportions is presented by considering the Beta rectangular distribution proposed by Hahn (2008), which includes the Beta regression model introduced by Ferrari and Cribari-Neto (2004) and the variable dispersion Beta regression models introduced by Smithson and Verkuilen (2006) as particular cases.
Abstract: A new regression model for proportions is presented by considering the Beta rectangular distribution proposed by Hahn (2008). This new model includes the Beta regression model introduced by Ferrari and Cribari-Neto (2004) and the variable dispersion Beta regression model introduced by Smithson and Verkuilen (2006) as particular cases. Like Branscum, Johnson, and Thurmond (2007), a Bayesian inference approach is adopted using Markov Chain Monte Carlo (MCMC) algorithms. Simulation studies on the influence of outliers by considering contaminated data under four perturbation patterns to generate outliers were carried out and confirm that the Beta rectangular regression model seems to be a new robust alternative for modeling proportion data and that the Beta regression model shows sensitivity to the estimation of regression coefficients, to the posterior distribution of all parameters and to the model comparison criteria considered. Furthermore, two applications are presented to illustrate the robustness of the Beta rectangular model.
127 citations
TL;DR: It is argued that the tail-area decay of an activity time distribution is a key factor which has been insufficiently considered previously and can be integrated into the PERT framework such that the classic PERT results represent an important special case of the method presented here.
108 citations
TL;DR: A joint modeling framework is proposed to address the issues from the following data features: multiple correlated PROs; the presence of the boundary values of zeros and ones; extreme outliers and heavy tails; and the PRO-dependent terminal events such as death and dropout.
Abstract: Many longitudinal studies (e.g. observational studies and randomized clinical trials) have collected multiple rating scales at each visit in the form of patient-reported outcomes (PROs) in the close unit interval [0,1]. We propose a joint modeling framework to address the issues from the following data features: (1) multiple correlated PROs; (2) the presence of the boundary values of zeros and ones; (3) extreme outliers and heavy tails; (4) the PRO-dependent terminal events such as death and dropout. Our modeling framework consists of a multivariate augmented mixed-effects sub-model based on Beta rectangular distributions for the multiple longitudinal outcomes and a Cox model for the terminal events. The simulation studies suggest that in the presence of outliers, heavy tails, and dependent terminal event, our proposed models provide more accurate parameter estimates than the joint model based on Beta distributions. The proposed models are applied to the motivating Long-term Study-1 (LS-1 study, n = 1741)...
14 citations
TL;DR: This work proposes a mixed effects model using Beta rectangular distribution and augment it with the probabilities of zero and one and suggests that the regression models based on Beta rectangular distributions improve the accuracy of parameter estimates in the presence of outliers and heavy tails.
Abstract: Mixed effects Beta regression models based on Beta distributions have been widely used to analyze longitudinal percentage or proportional data ranging between zero and one. However, Beta distributions are not flexible to extreme outliers or excessive events around tail areas, and they do not account for the presence of the boundary values zeros and ones because these values are not in the support of the Beta distributions. To address these issues, we propose a mixed effects model using Beta rectangular distribution and augment it with the probabilities of zero and one. We conduct extensive simulation studies to assess the performance of mixed effects models based on both the Beta and Beta rectangular distributions under various scenarios. The simulation studies suggest that the regression models based on Beta rectangular distributions improve the accuracy of parameter estimates in the presence of outliers and heavy tails. The proposed models are applied to the motivating Neuroprotection Exploratory Trials in Parkinson's Disease (PD) Long-term Study-1 (LS-1 study, n = 1741), developed by The National Institute of Neurological Disorders and Stroke Exploratory Trials in Parkinson's Disease (NINDS NET-PD) network.
Related Topics (5)
Performance Metrics
| Year | Papers |
|---|---|
| 2017 | 1 |
| 2016 | 1 |
| 2012 | 1 |
| 2008 | 1 |