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Modelling death rates due to COVID-19: A Bayesian approach
(Cornell University, 2020-04-06)
Objective: To estimate the number of deaths in Peru due to COVID-19. Design: With a priori information obtained from the daily number of deaths due to CODIV-19 in China and data from the Peruvian authorities, we constructed a predictive Bayesian non-linear model for the number of deaths in Peru. Exposure: COVID-19. Outcome: Number of deaths. Results: Assuming an intervention level similar to the one implemented in China, the total number of deaths in Peru is expected to be 612 (95%CI: 604.3 - 833.7) persons. Sixty four days after the first reported death, the 99% of expected deaths will be observed. The inflexion point in the number of deaths is estimated to be around day 26 (95%CI: 25.1 - 26.8) after the first reported death. Conclusion: These estimates can help authorities to monitor the epidemic and implement strategies in order to manage the COVID-19 pandemic.
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Screening for aberrant school performances in high-stakes assessments using in influential analysis
(Inderscience Publishers, 2020-01-01)
A method is proposed to screen for aberrant school performances in large-scale, high-stakes assessments using influential analysis under a Bayesian approach. Proportions of low and high achievers within a school were modelled via the beta inflated mean regression model (Bayes and Valdivieso, 2016) using school performances in previous years as predictors. The general measure of ϕ-divergence proposed by Peng and Dey (1995) was used to determine aberrancy. A simulation study revealed that the method could recover previously distorted school performances as aberrant. The proposed technique was applied to a Peruvian national reading assessment in grade 4th of primary education for which the government provided a school performance incentive bonus.
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Robust beta regression modeling with errors-in-variables: a Bayesian approach and numerical applications
(Springer Science+Business Media, 2021-09-14)
Beta regression models have become a popular tool for describing and predicting limited-range continuous data such as rates and proportions. However, these models can be severely affected by outlying observations that the beta distribution does not handle well. A robust alternative to the modeling with the beta distribution is considering the rectangular beta (RB) distribution, which is an extension of the former one. The RB distribution can deal with heavy tails and is therefore more flexible than the beta distribution. Regression modeling where covariates are measured with error is a frequent issue in different areas. This paper derives robust regression modeling for proportions with errors-in-variables using the RB distribution under a new parametrization recently proposed in the literature. We use a Bayesian approach to estimate the model parameters with a specification of prior distributions and a computational implementation carried out via the Gibbs sampling. Monte Carlo simulations allow us to conduct numerical evaluation to detect the statistical performance of the approach considered. Then, an illustration with real-world data is presented to show its potential uses.
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A robust regression model for bounded count health data
(SAGE Publications Ltd, 2024-08-01)
Bounded count response data arise naturally in health applications. In general, the well-known beta-binomial regression model form the basis for analyzing this data, specially when we have overdispersed data. Little attention, however, has been given to the literature on the possibility of having extreme observations and overdispersed data. We propose in this work an extension of the beta-binomial regression model, named the beta-2-binomial regression model, which provides a rather flexible approach for fitting a regression model with a wide spectrum of bounded count response data sets under the presence of overdispersion, outliers, or excess of extreme observations. This distribution possesses more skewness and kurtosis than the beta-binomial model but preserves the same mean and variance form of the beta-binomial model. Additional properties of the beta-2-binomial distribution are derived including its behavior on the limits of its parametric space. A penalized maximum likelihood approach is considered to estimate parameters of this model and a residual analysis is included to assess departures from model assumptions as well as to detect outlier observations. Simulation studies, considering the robustness to outliers, are presented confirming that the beta-2-binomial regression model is a better robust alternative, in comparison with the binomial and beta-binomial regression models. We also found that the beta-2-binomial regression model outperformed the binomial and beta-binomial regression models in our applications of predicting liver cancer development in mice and the number of inappropriate days a patient spent in a hospital.
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