Adjusted Pearson residuals in beta regression models

Anholeto, Tatiana; Sandoval, Mônica C.; Botter, Denise Aparecida

doi:10.1080/00949655.2012.736993

Cited by 18 publications

(19 citation statements)

References 3 publications

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“…When the difference involves the link function(s), a larger sample size is needed. 1 How do the J and MJ perform when the correct model is not among the competing models, i.e. when none of the models under consideration is the true model?…”

Section: Numerical Resultsmentioning

confidence: 99%

“…Ferrari and Cribari-Neto [21] introduced the class of beta regression models using an alternative parameterization for the density in Equation (1). Let μ = p/(p + q) and φ = p + q, then p = μφ and q = (1 − μ)φ.…”

Section: The Beta Regression Modelmentioning

confidence: 98%

“…Pereira and Cribari [43] developed small-sample adjustments to the LR and signed LR test statistics in inflated beta regressions. Anholeto et al [1] obtained adjusted Pearson residuals for the class of beta regression models.…”

Section: The Beta Regression Modelmentioning

confidence: 99%

“…The null hypothesis that the correct model is in the set of candidate models is rejected if MJ > χ 2 1−α,τ , where τ equals the number of degrees of freedom in the J test corresponding to the smallest J test statistic. For instance, in order to perform the MJ test using two candidate nonnested beta regression models (H 1 and H 2 ) which differ in both submodels, the J statistic associated to each model is computed and MJ = min{J 1 …”

Section: Nonnested Hypothesis Tests For Beta Regression Modelsmentioning

confidence: 99%

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Nonnested hypothesis testing in the class of varying dispersion beta regressions

Cribari‐Neto

Lucena

2014

Journal of Applied Statistics

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Oftentimes practitioners have at their disposal two or more competing models with different parametric structures. Whenever each model cannot be obtained as a particular case of the remaining models through a set of parametric restrictions the models are said to be nonnested. Tests that can be used to select a model from a set of nonnested linear regression models are available in the literature. Particularly, useful tests are the J and MJ tests. In this paper, we extend these two tests to the class of beta regression models, which is useful for modeling responses that assume values in the standard unit interval, (0, 1). We report Monte Carlo evidence on the finite sample behavior of the tests. Bootstrap-based testing inference is also considered. Overall, the best performing test is the bootstrap MJ test. Two empirical applications are presented and discussed.

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Section: Numerical Resultsmentioning

confidence: 99%

Section: The Beta Regression Modelmentioning

confidence: 98%

Section: The Beta Regression Modelmentioning

confidence: 99%

Section: Nonnested Hypothesis Tests For Beta Regression Modelsmentioning

confidence: 99%

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Nonnested hypothesis testing in the class of varying dispersion beta regressions

Cribari‐Neto

Lucena

2014

Journal of Applied Statistics

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“…The first three belongs to the class introduced in this paper, but using other residuals as r i instead of the quantile residual. We used the standardized weighted residual 1 (Espinheira et al, 2008), the standardized weighted residual 2 (Espinheira et al, 2008) and the adjusted standardized weighted residual 1 (Anholeto et al, 2014) For each of the observations and residuals, we calculated the percentage of the residuals smaller than −3, −2, −1 and greater than 1, 2, 3 among the 25, 000 replications. When y i = 0, the residuals are not defined and we considered that they are neither smaller than -1 and nor greater than 1.…”

Section: Simulation Studiesmentioning

confidence: 99%

A class of residuals for outlier identification in zero adjusted regression models

Pereira

Scudilio

Santos‐Neto

et al. 2019

Journal of Applied Statistics

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Zero adjusted regression models are used to fit variables that are discrete at zero and continuous at some interval of the positive real numbers. Diagnostic analysis in these models is usually performed using the randomized quantile residual, which is useful for checking the overall adequacy of a zero adjusted regression model. However, it may fail to identify some outliers. In this work, we introduce a residual for outlier identification in zero adjusted regression models. Monte Carlo simulation studies and an application suggest that the residual introduced here has good properties and detects outliers that are not identified by the randomized quantile residual.

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Residual‐based CUSUM beta regression control chart for monitoring double‐bounded processes

Rauber

Lima-Filho

Bayer

2022

Quality & Reliability Eng

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This paper proposes a control chart useful for detecting small shifts in the mean of a double‐bounded process, such as fractions and proportions, in the presence of control variables. For this purpose, we consider the cumulative sum (CUSUM) control chart applied to different residuals of the beta regression model. We conduct an extensive Monte Carlo simulation study to evaluate and compare the performance of the proposed control chart with two other control charts in the literature in terms of run length analysis. The numerical results show that the proposed control chart is more sensitive to detect changes in the process than its competitors and that the quantile residual is the most suitable residual to be used in our proposal. Finally, based on the quantile residual, we present and discuss applications to real and simulated data to show the applicability of the proposed control chart.

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Adjusted Pearson residuals in beta regression models

Cited by 18 publications

References 3 publications

Nonnested hypothesis testing in the class of varying dispersion beta regressions

Nonnested hypothesis testing in the class of varying dispersion beta regressions

A class of residuals for outlier identification in zero adjusted regression models

Residual‐based CUSUM beta regression control chart for monitoring double‐bounded processes

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