A beta inflated mean regression model for fractional response variables

Bayes, Cristian L.; Valdivieso, Luis

doi:10.1080/02664763.2015.1120711

Cited by 18 publications

(22 citation statements)

References 15 publications

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“…Furthermore, it should be noted that γ is restricted to the open interval (δ 1 , 1 − δ 0 ). An alternative to solve these problems is described in Bayes y Valdivieso (2016) where a reparametrization of (5.1) is proposed as follows:…”

Section: Alternative Parametrizationmentioning

confidence: 99%

“…where Y ∈ [0, 1] is the fractional response and N the sample size. The main disadvantage of these models is that extremely biased estimations can be obtained, as shown in Bayes y Valdivieso (2016).…”

Section: Introduction 11 Preliminary Considerationsmentioning

confidence: 99%

“…An important property of QMLE is the fact that it is consistent and asymptotically normal regardless of the distribution of the response variable conditional to covariates. On the other hand, Bayes y Valdivieso (2016) propose a beta inflated mean regression model which, based on a convenient reparameterization, allows to model directly the mean of the fractional bounded variable of interest; estimation of this model is carried out from a classical perspective. In this article we will try to extend this model to a mixed effect model since it is shown that in the transversal setting this model outperforms Papke y Wooldridge (1996) model in terms of root of mean squared error (RMSE), bias and information criteria.…”

Section: Introduction 11 Preliminary Considerationsmentioning

confidence: 99%

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A beta-inflated mean regression model with mixed effects for fractional response variables

Villegas

2018

Journal of Statistical Computation and Simulation

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ResumenEn este artículo proponemos un nuevo modelo de regresión con efectos mixtos para variables acotadas fraccionarias. Este modelo nos permite incorporar covariables directamente al valor esperado, de manera que podemos cuantficar exactamente la influencia de estas covariables en la media de la variable de interés en vez de en la media condicional. La estimación se llevó a cabo desde una perspectiva bayesiana y debido a la complejidad de la distribución aumentada a posteriori usamos un algoritmo de Monte Carlo Hamiltoniano, el muestreador No-U-Turn, que se encuentra implementado en el software Stan. Se realizó un estudio de simulación que compara, en términos de sesgo y RMSE, el modelo propuesto con otros modelos tradicionales longitudinales para variables acotadas, resultando que el primero tiene un mejor desempeño. Finalmente, aplicamos nuestro modelo de regresión Beta Inflacionada con efectos mixtos a datos reales los cuales consistían en información de la utilización de las líneas de crédito en el sistema financiero peruano.Palabras-clave: proporciones, variables fraccionarias, distribución Beta Inflacionada, inferencia bayesiana, métodos MCMC, Monte Carlo Hamiltoniano, modelos mixtos, RStan.iv AbstractIn this article we propose a new mixed effects regression model for fractional bounded response variables. Our model allows us to incorporate covariates directly to the expected value, so we can quantify exactly the influence of these covariates in the mean of the variable of interest rather than to the conditional mean. Estimation is carried out from a bayesian perspective and due to the complexity of the augmented posterior distribution we use a Hamiltonian Monte Carlo algorithm, the No-U-Turn sampler, implemented using Stan software. A simulation study for comparison, in terms of bias and RMSE, was performed showing that our model has a better performance than other traditional longitudinal models for bounded variables. Finally, we applied our Beta Inflated mixed-effects regression model to real data which consists of utilization of credit lines in the peruvian financial system.

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Section: Alternative Parametrizationmentioning

confidence: 99%

Section: Introduction 11 Preliminary Considerationsmentioning

confidence: 99%

Section: Introduction 11 Preliminary Considerationsmentioning

confidence: 99%

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A beta-inflated mean regression model with mixed effects for fractional response variables

Villegas

2018

Journal of Statistical Computation and Simulation

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“…[ 8 ] introduced a general class of zero or one inflated beta regression models, which is a natural extension of the beta regression model [ 11 ] to model variables that assume values in (0, 1] or [0, 1). [ 12 ] proposed an inflated beta regression model based on a reparametrization of the inflated beta distribution. This model accommodates mixed random variable responses, with non-negligible probabilities of assuming zeros and/or ones and continuous values in the interval (0, 1) that follows a beta distribution.…”

Section: Introductionmentioning

confidence: 99%

“…This model accommodates mixed random variable responses, with non-negligible probabilities of assuming zeros and/or ones and continuous values in the interval (0, 1) that follows a beta distribution. The inflated beta regression model introduced by [ 12 ] may be useful for developing model-based control charts for monitoring inflated beta distributed processes as it considers an interesting parametrization in terms of the response variable mean. However, the model proposed by [ 12 ] does not consider a regression structure for the precision parameter.…”

Section: Introductionmentioning

confidence: 99%

Process monitoring using inflated beta regression control chart

et al. 2020

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This paper provides a general framework for controlling quality characteristics related to control variables and limited to the intervals (0, 1], [0, 1), or [0, 1]. The proposed control chart is based on the inflated beta regression model considering a reparametrization of the inflated beta distribution indexed by the response mean, which is useful for modeling fractions and proportions. The contribution of the paper is twofold. First, we extend the inflated beta regression model by allowing a regression structure for the precision parameter. We also present closed-form expressions for the score vector and Fisher’s information matrix. Second, based on the proposed regression model, we introduce a new model-based control chart. The control limits are obtained considering the estimates of the inflated beta regression model parameters. We conduct a Monte Carlo simulation study to evaluate the performance of the proposed regression model estimators, and the performance of the proposed control chart is evaluated in terms of run length distribution. Finally, we present and discuss an empirical application to show the applicability of the proposed regression control chart.

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Pre‐fire grazing and herbicide treatments can affect post‐fire vegetation in a Great Basin rangeland

Gornish

Guo

Porensky

et al. 2023

Ecol Sol and Evidence

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Management of wildfire associated with spread of the highly invasive annual grass Bromus tectorum (cheatgrass) is a critical need in the western U.S. We investigated the utility of coupling common rangeland management strategies pre‐fire to modify post‐fire plant community outcomes. We used a long‐term, large‐scale experiment to test the separate and combined effects of pre‐fire targeted grazing (spring and fall), native plant seeding (seeding rate, seed coating and spatial seeding arrangement) and herbicide (glyphosate followed by 2 years of imazapic) on post‐fire plant community outcomes in a highly invaded system in the Great Basin, U.S. We found grazing and herbicide effects were consistent across cheatgrass biomass, count, and cover. Spring grazing reduced cheatgrass more effectively than fall grazing; however, this effect was detected primarily outside of the seeding treatments. Herbicide overall and in conjunction with grazing reduced cheatgrass and fuel loads. Among seeding treatments, seed mixtures proved more effective than monocultures for reducing both cheatgrass count and cover, particularly when combined with low seed rate. However, many seeding approaches resulted in higher cheatgrass dominance, and thus higher fuel loads. This work suggests that effects of pre‐fire herbicide for reducing cheatgrass abundance can persist post‐fire. Grazing, however, might not produce consistent results, and season of grazing can affect outcomes. Employing pre‐fire management strategies to interrupt the cheatgrass‐fire cycle may have utility. Some of our treatments were able to reduce cheatgrass abundance after fire, but despite our intensive interventions, we did not find a strategy that led to full restoration of native perennial species.

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A beta inflated mean regression model for fractional response variables

Cited by 18 publications

References 15 publications

A beta-inflated mean regression model with mixed effects for fractional response variables

A beta-inflated mean regression model with mixed effects for fractional response variables

Process monitoring using inflated beta regression control chart

Pre‐fire grazing and herbicide treatments can affect post‐fire vegetation in a Great Basin rangeland

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