Bayesian modeling and prior sensitivity analysis for zero–one augmented beta regression models with an application to psychometric data

2020 ◽  
Vol 34 (2) ◽  
pp. 304-322
Author(s):  
Danilo Covaes Nogarotto ◽  
Caio Lucidius Naberezny Azevedo ◽  
Jorge Luis Bazán
Keyword(s):  
Sensitivity Analysis ◽  
Bayesian Modeling ◽  
Regression Models ◽  
Beta Regression ◽  
Psychometric Data

A class of beta regression models with multiplicative log-normal measurement errors

2017 ◽  
Vol 47 (1) ◽  
pp. 229-248 ◽  
Author(s):  
Eveliny Barroso Da Silva ◽  
Carlos Alberto Ribeiro Diniz ◽  
Jalmar Manuel Farfan Carrasco ◽  
Mário De Castro
Keyword(s):  
Measurement Errors ◽  
Regression Models ◽  
Beta Regression ◽  
Normal Measurement ◽  
Log Normal

Flexible quasi-beta regression models for continuous bounded data

2018 ◽  
Vol 19 (6) ◽  
pp. 617-633 ◽  
Author(s):  
Wagner H Bonat ◽  
Ricardo R Petterle ◽  
John Hinde ◽  
Clarice GB Demétrio
Keyword(s):  
Regression Model ◽  
Regression Models ◽  
Beta Regression ◽  
Estimating Function ◽  
Dispersion Parameters ◽  
Linear Predictor ◽  
Mean And Variance ◽  
The Mean ◽  
Bounded Data ◽  
Beta Regression Model

We propose a flexible class of regression models for continuous bounded data based on second-moment assumptions. The mean structure is modelled by means of a link function and a linear predictor, while the mean and variance relationship has the form [Formula: see text], where [Formula: see text], [Formula: see text] and [Formula: see text] are the mean, dispersion and power parameters respectively. The models are fitted by using an estimating function approach where the quasi-score and Pearson estimating functions are employed for the estimation of the regression and dispersion parameters respectively. The flexible quasi-beta regression model can automatically adapt to the underlying bounded data distribution by the estimation of the power parameter. Furthermore, the model can easily handle data with exact zeroes and ones in a unified way and has the Bernoulli mean and variance relationship as a limiting case. The computational implementation of the proposed model is fast, relying on a simple Newton scoring algorithm. Simulation studies, using datasets generated from simplex and beta regression models show that the estimating function estimators are unbiased and consistent for the regression coefficients. We illustrate the flexibility of the quasi-beta regression model to deal with bounded data with two examples. We provide an R implementation and the datasets as supplementary materials.

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 Improved estimators for a general class of beta regression models

2010 ◽  
Vol 54 (2) ◽  
pp. 348-366 ◽  
Author(s):  
Alexandre B. Simas ◽  
Wagner Barreto-Souza ◽  
Andréa V. Rocha
Keyword(s):  
General Class ◽  
Regression Models ◽  
Beta Regression ◽  
Improved Estimators
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