zoib: An R Package for Bayesian Inference for Beta Regression and Zero/One Inflated Beta Regression

Liu, Fang; Kong, Yunchuan

doi:10.32614/rj-2015-019

Cited by 90 publications

(82 citation statements)

References 22 publications

(31 reference statements)

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“…Beta regression, in which a logit link is coupled with a beta distribution observation model (Ferrari and Cribari-Neto 2004), can model proportions between zero and one, but cannot account for the zeros or ones themselves. Therefore, we fit zero/one inflated beta (ZOIB) hierarchical regression models (Ospina andFerrari 2012, Liu andKong 2015), which allow for zeros, ones, and continuous proportions between these bounds. Following the notation of Liu and Kong (2015), ZOIB models assume that the response data y (here, a proportion value for each burn severity metric, ranging from zero to one) for observation i follow a piecewise distribution such that…”

Section: Discussionmentioning

confidence: 99%

“…where p i represents the probability Pr(y i = 0), q i represents the conditional probability Prðy i ¼ 1jy i 6 ¼ 0Þ, and a i and b i represent the beta distribution shape parameters for y i 2 ð0; 1Þ. We can combine these components to derive the unconditional estimate of the response E(y i ) (Liu and Kong 2015) as…”

Section: Discussionmentioning

confidence: 99%

“…Beta regression, in which a logit link is coupled with a beta distribution observation model (Ferrari and Cribari‐Neto ), can model proportions between zero and one, but cannot account for the zeros or ones themselves. Therefore, we fit zero/one inflated beta (ZOIB) hierarchical regression models (Ospina and Ferrari , Liu and Kong ), which allow for zeros, ones, and continuous proportions between these bounds.…”

Section: Methodsmentioning

confidence: 99%

“…Following the notation of Liu and Kong (), ZOIB models assume that the response data y (here, a proportion value for each burn severity metric, ranging from zero to one) for observation i follow a piecewise distribution such that

f false(y_{i} false) = \{\begin{matrix} p_{i} & if y_{i} = 0, \\ false(1 - p_{i} false) q_{i} & if y_{i} = 1, \\ false(1 - p_{i} false) false(1 - q_{i} false) Beta false(a_{i}, b_{i} false) & if y_{i} \in false(0, 1 false), \end{matrix}

where p i represents the probability Pr( y i = 0), q i represents the conditional probability

Pr (y_{i} = 1 | y_{i} \neq 0)

, and a i and b i represent the beta distribution shape parameters for

y_{i} \in false(0, 1 false)

. We can combine these components to derive the unconditional estimate of the response E ( y i ) (Liu and Kong ) as

E false(y_{i} false) = false(1 - p_{i} false) (q_{i} + (1 - q_{i}) μ_{i}^{false(0, 1 false)}) .

…”

Section: Methodsmentioning

confidence: 99%

See 3 more Smart Citations

Incorporating biophysical gradients and uncertainty into burn severity maps in a temperate fire‐prone forested region

2019

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As forest fire activity increases worldwide, it is important to track changing patterns of burn severity (i.e., degree of fire‐caused ecological change). Satellite data provide critical information across space and time, yet how satellite indices relate to individual measures of burn severity on the ground (e.g., tree mortality or surface charring) and how these relationships change across biophysical gradients remain unclear. To address these knowledge gaps, we used Bayesian hierarchical zero‐one‐inflated beta (ZOIB) regression models with nearly 600 plots of individual field measures of burn severity distributed across the U.S. Rocky Mountains. We asked the following: How do three commonly used satellite indices of burn severity relate to individual field measures of canopy burn severity and forest‐floor burn severity (Q1)? Then, using the highest ranked satellite index, how is reliability affected by biophysical gradients that can be captured in accessible geospatial data (e.g., latitude, slope) (Q2) and stand‐structure data typically available only with field data (Q3)? The Relative differenced Normalized Burn Ratio (RdNBR) outperformed the differenced Normalized Burn Ratio (dNBR) and the Relative Burn Ratio (RBR) across canopy and forest‐floor measures of burn severity, but differences among index performances were minor. Overall, indices performed better for field measures of canopy burn severity than for forest‐floor measures. The relationship between RdNBR and individual field measures of burn severity changed across several biophysical gradients. For example, the same value of RdNBR corresponded to different field levels of burn severity depending on latitude, pre‐fire forest structure, and pre‐fire beetle outbreaks—and effects of biophysical gradients were often different for canopy vs. forest‐floor measures of burn severity. We show that estimating field measures of burn severity using satellite indices can be improved by including biophysical information, but if variables that are difficult to obtain without field data (e.g., pre‐fire beetle outbreak severity) are lacking, we suggest caution in interpreting satellite indices of burn severity across gradients of pre‐fire biophysical conditions. Finally, using an example fire, we illustrate contrasting maps of burn severity that arise from differences in the relationship between individual field measures of burn severity and RdNBR after accounting for error in those relationships.

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Section: Discussionmentioning

confidence: 99%

Section: Discussionmentioning

confidence: 99%

Section: Methodsmentioning

confidence: 99%

f false(y_{i} false) = \{\begin{matrix} p_{i} & if y_{i} = 0, \\ false(1 - p_{i} false) q_{i} & if y_{i} = 1, \\ false(1 - p_{i} false) false(1 - q_{i} false) Beta false(a_{i}, b_{i} false) & if y_{i} \in false(0, 1 false), \end{matrix}

where p i represents the probability Pr( y i = 0), q i represents the conditional probability

Pr (y_{i} = 1 | y_{i} \neq 0)

, and a i and b i represent the beta distribution shape parameters for

y_{i} \in false(0, 1 false)

. We can combine these components to derive the unconditional estimate of the response E ( y i ) (Liu and Kong ) as

E false(y_{i} false) = false(1 - p_{i} false) (q_{i} + (1 - q_{i}) μ_{i}^{false(0, 1 false)}) .

…”

Section: Methodsmentioning

confidence: 99%

See 2 more Smart Citations

Incorporating biophysical gradients and uncertainty into burn severity maps in a temperate fire‐prone forested region

2019

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“…The model was subsequently projected with the error associated with estimating potential limits set to zero, meaning that the predictions were weighted towards observations for which we had the greatest confidence. Finally, we also included a random‐effects term in the regression for the taxonomic family ( n = 222) (Liu & Kong, ) to account, in part, for potential phylogenetic similarities in thermal tolerance. All parameters used weak normally distributed priors, and the Markov chain Monte Carlo (MCMC) sample was generated from four chains run for 1 million iterations, with a burn‐in of 200,000, and thinned to every 100 steps (see Supporting Information Appendix 3 for model script and output summaries).…”

Section: Methodsmentioning

confidence: 99%

Truncation of thermal tolerance niches among Australian plants

Буш

Catullo

Mokany

et al. 2017

Global Ecol Biogeogr

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Aim: Despite recognition that realized distributions inherently underestimate species' physiological tolerances, we are yet to identify the extent of these differences within diverse taxonomic groups.The degree to which species could tolerate environmental conditions outside their observed distributions may have a significant impact on the perceived extinction risk in ecological models. More information on this potential error is required to improve our confidence in management strategies. Location: Australia.Time Period: 1983-2012.Major Taxa Studied: Plants. Methods:To quantify the scale and spatial patterns of this disparity, we estimated the existing tolerance to thermal extremes of 7,124 Australian plants, more than one-third of the native continental flora, using data from cultivated records at 128 botanical gardens and nurseries.Hierarchical Bayesian beta regression was used to assess whether factors such as realized niches, traits or phylogeny could predict the incidence or magnitude of niche truncation (underestimation of thermal tolerances), while controlling for sources of collection bias.Results: Approximately half of the cultivated species analysed could tolerate temperature extremes beyond those experienced in their native range. Niche truncation was predictable from the breadth and extremes of their realized niches and by traits such as plant growth form. Phylogenetic relationships with niche truncation were weak and appeared more suited to predicting thermal tolerances directly.Main conclusions: This study highlights a widespread disparity between realized and potential thermal limits that may have significant implications for species' capacity to persist in situ with a changing climate. Identifying whether thermal niche truncation is the result of biotic interactions, dispersal constraints or other environmental factors could provide significant insight into community assembly at macroecological scales. Estimating niche truncation may help to explain why certain ecological communities are more resilient to change and may potentially improve the reliability of model projections under climate change. K E Y W O R D Sadaptive capacity, biodiversity modelling, climate change, niche truncation, potential niche, realized niche, tolerance niche 22 |

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No evidence of a rural‐urban divide in prioritizing agricultural policy goals

El Benni,

Finger,

Irek

et al. 2024

Applied Eco Perspectives Pol

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Rural‐urban divides have been found in various policy fields, but it remains unclear if they exist in agricultural policy. We analyzed the policy preferences of 1542 Swiss respondents, ranging from very rural to very urban. Respondents prioritized different pairs of conflicting goals, that is, two economic goals versus four conflicting agri‐environmental goals. We find no evidence of a rural‐urban divide in the prioritization of agricultural policy goals. Respondents prioritize economic goals over environmental goals. Efforts to make agriculture more environmentally sustainable do not per se create a rural‐urban divide, but policies should focus on reducing trade‐offs between economic and environmental goals.

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zoib: An R Package for Bayesian Inference for Beta Regression and Zero/One Inflated Beta Regression

Cited by 90 publications

References 22 publications

Incorporating biophysical gradients and uncertainty into burn severity maps in a temperate fire‐prone forested region

Incorporating biophysical gradients and uncertainty into burn severity maps in a temperate fire‐prone forested region

Truncation of thermal tolerance niches among Australian plants

No evidence of a rural‐urban divide in prioritizing agricultural policy goals

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