Robust estimation in beta regression via maximum L$$_q$$-likelihood

A., Ribeiro, Terezinha K.; Ferrari, Silvia L. P.

doi:10.1007/s00362-022-01320-0

Cited by 7 publications

(7 citation statements)

References 24 publications

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“…It is established in an agile modeling framework under the parameterization of the beta law to describe a continuous response variable with values in a standard unit interval (0.1). We further exploited a robust estimation method of the beta regression, named the minimum density power divergence estimators (MDPDE) ( Ghosh, 2019 ), for dose-response estimation, with the tuning parameter optimized by a data-driven method ( Ribeiro and Ferrari, 2020 ). The technical details are provided in the Materials and methods.…”

Section: Resultsmentioning

confidence: 99%

“…The recommended α is around 0.3 to 0.4, but simply assigning a fixed α in [0.3, 0.4] is not applicable in many cases. Here we adopted a data-driven method ( Ribeiro and Ferrari, 2020 ) to identify the optimal α. The search for the optimal α starts with a grid of α, a pre-defined α max and grid size

, which generates a sequence of equally spaced

.…”

Section: Methodsmentioning

confidence: 99%

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Robust and Efficient Assessment of Potency (REAP) as a quantitative tool for dose-response curve estimation

Zhou

Liu

Fang

et al. 2022

eLife

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The median-effect equation has been widely used to describe the dose-response relationship and identify compounds that activate or inhibit specific disease targets in contemporary drug discovery. However, the experimental data often contain extreme responses, which may significantly impair the estimation accuracy and impede valid quantitative assessment in the standard estimation procedure. To improve the quantitative estimation of the dose-response relationship, we introduce a novel approach based on robust beta regression. Substantive simulation studies under various scenarios demonstrate solid evidence that the proposed approach consistently provides robust estimation for the median-effect equation, particularly when there are extreme outcome observations. Moreover, simulation studies illustrate that the proposed approach also provides a narrower confidence interval, suggesting a higher power in statistical testing. Finally, to efficiently and conveniently perform common lab data analyses, we develop a freely accessible web-based analytic tool to facilitate the quantitative implementation of the proposed approach for the scientific community.

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Section: Resultsmentioning

confidence: 99%

, which generates a sequence of equally spaced

.…”

Section: Methodsmentioning

confidence: 99%

Robust and Efficient Assessment of Potency (REAP) as a quantitative tool for dose-response curve estimation

Zhou

Liu

Fang

et al. 2022

eLife

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“…Robust beta regression : To overcome the drawbacks brought by the standard beta regression against outliers, Ghosh (2019) proposed a robust minimum density power divergence estimator (MDPDE) in beta regression by minimizing the average density power divergence due to its high asymptotic efficiency along with strong robustness. Similar to MDPDE, Ribeiro and Ferrari (2020) developed the surrogate maximum likelihood estimator (SMLE) by maximizing a reparameterized L q ‐likelihood. The L q ‐likelihood density is constructed first with a Box–Cox transformation

{L_q}

(Box & Cox, 1964).…”

Section: The Estimation Methods and Tools In Rmentioning

confidence: 99%

“…For the tuning parameter, based on simulations and real data analyses, MDPDE recommends the tuning parameter in the range of (0.3, 0.4). Ribeiro and Ferrari (2020) further improve the tuning parameter selection with a data‐driven algorithm by conducting a grid search to find the optimal tuning parameter that achieves sufficient stability.…”

Section: The Estimation Methods and Tools In Rmentioning

confidence: 99%

“…However, the development of the least squares method does not pay special attention to extreme cases, especially when the sample sizes are small. Recently, the beta regression model was introduced and incorporated into different statistical methods to yield robust estimation (Ghosh, 2019; Mayr et al., 2018; Niekerk et al., 2019; Ribeiro & Ferrari, 2020; Rigby & Stasinopoulos, 2005; Wood, 2017; Zhou et al., 2022). The construction of the beta regression itself is flexible enough to take on various shapes to account for nonnormality, asymmetry, and heteroskedasticity.…”

Section: Introductionmentioning

confidence: 99%

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A comparative study of in vitro dose–response estimation under extreme observations

Fang

Zhou

2023

Biometrical J

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Quantifying drug potency, which requires an accurate estimation of dose–response relationship, is essential for drug development in biomedical research and life sciences. However, the standard estimation procedure of the median–effect equation to describe the dose–response curve is vulnerable to extreme observations in common experimental data. To facilitate appropriate statistical inference, many powerful estimation tools have been developed in R, including various dose–response packages based on the nonlinear least squares method with different optimization strategies. Recently, beta regression‐based methods have also been introduced in estimation of the median–effect equation. In theory, they can overcome nonnormality, heteroscedasticity, and asymmetry and accommodate flexible robust frameworks and coefficients penalization. To identify a reliable estimation method(s) to estimate dose–response curves even with extreme observations, we conducted a comparative study to review 14 different tools in R and examine their robustness and efficiency via Monte Carlo simulation under a list of comprehensive scenarios. The simulation results demonstrate that penalized beta regression using the mgcv package outperforms other methods in terms of stable, accurate estimation, and reliable uncertainty quantification.

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Modeling tropical tuna shifts: An inflated power logit regression approach

Queiroz,

Ferrari

2024

Biometrical J

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We introduce a new class of zero‐or‐one inflated power logit (IPL) regression models, which serve as a versatile tool for analyzing bounded continuous data with observations at a boundary. These models are applied to explore the effects of climate changes on the distribution of tropical tuna within the North Atlantic Ocean. Our findings suggest that our modeling approach is adequate and capable of handling the outliers in the data. It exhibited superior performance compared to rival models in both diagnostic analysis and regarding the inference robustness. We offer a user‐friendly method for fitting IPL regression models in practical applications.

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Robust estimation in beta regression via maximum L$$_q$$-likelihood

Cited by 7 publications

References 24 publications

Robust and Efficient Assessment of Potency (REAP) as a quantitative tool for dose-response curve estimation

Robust and Efficient Assessment of Potency (REAP) as a quantitative tool for dose-response curve estimation

A comparative study of in vitro dose–response estimation under extreme observations

Modeling tropical tuna shifts: An inflated power logit regression approach

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