Bayesian Reference Analysis for the Generalized Normal Linear Regression Model

Tomazella, Vera; Jesus, Sandra Rego de; Gazon, Amanda Buosi; Louzada, Francisco; Nadarajah, Saralees; Nascimento, Dejair Caitano do; Rodrigues, Francisco A.; Ramos, Pedro Luiz

doi:10.3390/sym13050856

Cited by 3 publications

(2 citation statements)

References 28 publications

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“…We calculate the K-L divergence estimates for each observation i and j to determine whether y ij under regression model R is influential, that is, identifying data points that significantly affect the parameter estimates. Following the approach of Tomazella et al (2021), we consider y ij an outlier if 0.5…”

Section: Conflict Of Interestmentioning

confidence: 99%

A robust mixed‐effects parametric quantile regression model for continuous proportions: Quantifying the constraints to vitality in cushion plants

Burger

Merwe

Lesaffre

et al. 2023

Statistica Neerlandica

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There is no literature on outlier‐robust parametric mixed‐effects quantile regression models for continuous proportion data as an alternative to systematically identifying and eliminating outliers. To fill this gap, we formulate a robust method by extending the recently proposed fixed‐effects quantile regression model based on the heavy‐tailed Johnson‐ distribution for continuous proportion data to the mixed‐effects modeling context, using a Bayesian approach. Our proposed method is motivated by and used to model the extreme quantiles of the vitality of cushion plants to provide insights into the ecology of the system in which the plants are dominant. We conducted a simulation study to assess the new method's performance and robustness to outliers. We show that the new model has good accuracy and confidence interval coverage properties and is remarkably robust to outliers. In contrast, our study demonstrates that the current approach in the literature for modeling hierarchically structured bounded data's quantiles is susceptible to outliers, especially when modeling the extreme quantiles. We conclude that the proposed model is an appropriate robust alternative to the current approach for modeling the quantiles of correlated continuous proportions when outliers are present in the data.

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Section: Conflict Of Interestmentioning

confidence: 99%

A robust mixed‐effects parametric quantile regression model for continuous proportions: Quantifying the constraints to vitality in cushion plants

Burger

Merwe

Lesaffre

et al. 2023

Statistica Neerlandica

View full text Add to dashboard Cite

show abstract

“…The second article, "Bayesian Reference Analysis for the Generalized Normal Linear Regression Model", by Tomazella et al [2] suggests using the Bayesian reference analysis to estimate the generalized normal linear regression model's parameters. The reference prior produced the correct posterior distribution, whereas the Jeffreys prior produced the incorrect one, as the study demonstrates.…”

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confidence: 99%