Extending Ordinal Regression with a Latent Zero-Augmented Beta Distribution

Irvine, Kathryn M.; Rodhouse, Thomas J.; Keren, Ilai N.

doi:10.1007/s13253-016-0265-2

Cited by 21 publications

(38 citation statements)

References 55 publications

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“…To account for differences between occurrence and cover, we used hurdle spatial models to explore the effect of covariates on both response variables. Hurdle models permit modeling of distribution (presence and absence) and cover of plant species in an integrated framework (Irvine, Rodhouse, & Keren, 2016). The hurdle model (Cragg, 1971) is a two-component model able to accommodate two different spatial processes and is often used to fit data coming from two distributions (Potts & Elith, 2006;Tarbox, Fiestas, & Caughlin, 2018).…”

Section: Hurdle Spatial Modelsmentioning

confidence: 99%

Integrating anthropogenic factors into regional‐scale species distribution models—A novel application in the imperiled sagebrush biome

Requena‐Mullor

Maguire

Shinneman

et al. 2019

Global Change Biology

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Species distribution models (SDMs) that rely on regional‐scale environmental variables will play a key role in forecasting species occurrence in the face of climate change. However, in the Anthropocene, a number of local‐scale anthropogenic variables, including wildfire history, land‐use change, invasive species, and ecological restoration practices can override regional‐scale variables to drive patterns of species distribution. Incorporating these human‐induced factors into SDMs remains a major research challenge, in part because spatial variability in these factors occurs at fine scales, rendering prediction over regional extents problematic. Here, we used big sagebrush (Artemisia tridentata Nutt.) as a model species to explore whether including human‐induced factors improves the fit of the SDM. We applied a Bayesian hurdle spatial approach using 21,753 data points of field‐sampled vegetation obtained from the LANDFIRE program to model sagebrush occurrence and cover by incorporating fire history metrics and restoration treatments from 1980 to 2015 throughout the Great Basin of North America. Models including fire attributes and restoration treatments performed better than those including only climate and topographic variables. Number of fires and fire occurrence had the strongest relative effects on big sagebrush occurrence and cover, respectively. The models predicted that the probability of big sagebrush occurrence decreases by 1.2% (95% CI: −6.9%, 0.6%) when one fire occurs and cover decreases by 44.7% (95% CI: −47.9%, −41.3%) if at least one fire occurred over the 36 year period of record. Restoration practices increased the probability of big sagebrush occurrence but had minimal effect on cover. Our results demonstrate the potential value of including disturbance and land management along with climate in models to predict species distributions. As an increasing number of datasets representing land‐use history become available, we anticipate that our modeling framework will have broad relevance across a range of biomes and species.

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Section: Hurdle Spatial Modelsmentioning

confidence: 99%

Integrating anthropogenic factors into regional‐scale species distribution models—A novel application in the imperiled sagebrush biome

Requena‐Mullor

Maguire

Shinneman

et al. 2019

Global Change Biology

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“…A continuous, proportion‐type response variable (bounded between 0 and 1) that also includes true zeros, such as visually estimated percent canopy cover within a predefined areal plot, is appropriately analysed using ZAB regression (Ospina & Ferrari, ). This model is a hurdle‐at‐zero model where we assume the ecological mechanism for generating an absence of a species within a plot is independent of the ecological process leading to non‐zero cover values for a species (see Irvine, Rodhouse, & Keren, for more discussion of hurdle‐at‐zero models for plant cover). Assuming no observation errors and a single observation per plot, a ZAB model for plots i = 1, …, n is as follows,

false[Z_{i} false] \sim Bernoulli false(normalψ false),

and

false[Y_{i} ∣ Z_{i} = 1 false] \sim Beta false(normalα, normalβ false),

where Z i represents an indicator for whether the focal species is present (1) or absent (0) in plot i and Y i describes the proportional coverage of a plot by that species given it is present.…”

Section: Methodsmentioning

confidence: 99%

Statistical design and analysis for plant cover studies with multiple sources of observation errors

et al. 2017

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Effective wildlife habitat management and conservation requires understanding the factors influencing distribution and abundance of plant species. Field studies, however, have documented observation errors in visually estimated plant cover including measurements which differ from the true value (measurement error) and not observing a species that is present within a plot (detection error). Unlike the rapid expansion of occupancy and N‐mixture models for analysing wildlife surveys, development of statistical models accounting for observation error in plants has not progressed quickly. Our work informs development of a monitoring protocol for managed wetlands within the National Wildlife Refuge System. Zero‐augmented beta (ZAB) regression is the most suitable method for analysing areal plant cover recorded as a continuous proportion but assumes no observation errors. We present a model extension that explicitly includes the observation process thereby accounting for both measurement and detection errors. Using simulations, we compare our approach to a ZAB regression that ignores observation errors (naïve model) and an “ad hoc” approach using a composite of multiple observations per plot within the naïve model. We explore how sample size and within‐season revisit design affect the ability to detect a change in mean plant cover between 2 years using our model. Explicitly modelling the observation process within our framework produced unbiased estimates and nominal coverage of model parameters. The naïve and “ad hoc” approaches resulted in underestimation of occurrence and overestimation of mean cover. The degree of bias was primarily driven by imperfect detection and its relationship with cover within a plot. Conversely, measurement error had minimal impacts on inferences. We found >30 plots with at least three within‐season revisits achieved reasonable posterior probabilities for assessing change in mean plant cover. For rapid adoption and application, code for Bayesian estimation of our single‐species ZAB with errors model is included. Practitioners utilizing our R‐based simulation code can explore trade‐offs among different survey efforts and parameter values, as we did, but tuned to their own investigation. Less abundant plant species of high ecological interest may warrant the additional cost of gathering multiple independent observations in order to guard against erroneous conclusions.

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“…Statistical models appropriate for such data are available (e.g., cumulative link models, Agresti, ; Warton, Foster, De’ath, Stoklosa, & Piers, ), but recently an ordinal zero‐augmented beta model (OZAB) was proposed as a way to directly link the cover classes to the partially observed percent cover of a plot (Herpigny & Gosselin, ; Irvine, Rodhouse, & Keren, ). The OZAB model allows for investigating the drivers of distribution (presence/absence) separate from environmental factors governing abundance and provides a more appealing interpretation of model parameters in terms of changes in mean percent cover compared to cumulative odds ratios (Irvine et al, ). Here we expand the OZAB model to account for imperfect detection and measurement errors in plant cover class data.…”

Section: Introductionmentioning

confidence: 99%

Cohesive framework for modelling plant cover class data

et al. 2019

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The study of plant distribution and abundance is a fundamental pursuit in ecology and conservation biology. Measuring plant abundance by visually assessing percent cover and recording a cover class is a common field method that yields ordinal data. Statistical models for ordinal data exist but entail cumbersome interpretations and sometimes restrictive assumptions. We propose a Bayesian hierarchical framework for analysing cover class data that allows for linking ordinal observations to a latent beta distribution and accounts for zero inflation. Harnessing a latent beta distribution supports interpreting changes in abundance in terms of mean percent cover rather than odds ratios of cumulative cover classes as for cumulative link models. The zero augmentation allows for simultaneous inferences on both occurrence (distribution) and abundance. We show how our model can account for true and false zeros, misclassification of cover classes, multiple species and hierarchical sampling designs, using empirical examples and simulations. Simulated observation errors, when ignored, led to models overestimating abundance and underestimating occurrence. Based on simulations, we found no substantial difference between mean percent cover estimates when analyzing ordinal cover classes versus continuous percent cover as the response. Our empirical datasets displayed high probability of detection (>0.85 on average for all species), likely due to the sampling design used and training of observers. Probability of occurrence was slightly underestimated for bare ground, Artemisia tridentata, Elycap medusae, and Poa secunda using a model that ignored imperfect detection. Estimated mean percent cover was not substantially impacted by ignoring measurement error for five plant species and bare ground. Our modelling framework for cover class data allows for an explicit separation of distribution from abundance and, importantly, allows for interpreting species–environment relationships in terms of variation in mean percent cover as compared to cumulative odds ratios. The beta distribution inherently accommodates heteroscedasticity and skewness, statistical properties that are a consequence of spatially aggregated patterns common to plant survey data. Recording cover classes provides a reliable, efficient way to measure plants and our simulations suggest little loss of information compared to assuming continuous percent cover. We provide JAGS and Stan model code for implementation.

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Extending Ordinal Regression with a Latent Zero-Augmented Beta Distribution

Cited by 21 publications

References 55 publications

Integrating anthropogenic factors into regional‐scale species distribution models—A novel application in the imperiled sagebrush biome

Integrating anthropogenic factors into regional‐scale species distribution models—A novel application in the imperiled sagebrush biome

Statistical design and analysis for plant cover studies with multiple sources of observation errors

Cohesive framework for modelling plant cover class data

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