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46
Beta Regression in R
"... The class of beta regression models is commonly used by practitioners to model variables that assume values in the standard unit interval (0, 1). It is based on the assumption that the dependent variable is betadistributed and that its mean is related to a set of regressors through a linear predict ..."
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The class of beta regression models is commonly used by practitioners to model variables that assume values in the standard unit interval (0, 1). It is based on the assumption that the dependent variable is betadistributed and that its mean is related to a set of regressors through a linear predictor with unknown coefficients and a link function. The model also includes a precision parameter which may be constant or depend on a (potentially different) set of regressors through a link function as well. This approach naturally incorporates features such as heteroskedasticity or skewness which are commonly observed in data taking values in the standard unit interval, such as rates or proportions. This paper describes the betareg package which provides the class of beta regressions in the R system for statistical computing. The underlying theory is briefly outlined, the implementation discussed and illustrated in various replication exercises.
Alternative estimating and testing empirical strategies for fractional regression models
, 2009
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A general class of zeroorone inflated beta regression models
 Computational Statistics & Data Analysis
, 2012
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Modelbased prediction of sequence alignment quality
 Bioinformatics
, 2008
"... Motivation: Multiple sequence alignment (MSA) is an essential prerequisite for many sequence analysis methods and valuable tool itself for describing relationships between protein sequences. Since the success of the sequence analysis is highly dependent on the reliability of alignments, measures f ..."
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Motivation: Multiple sequence alignment (MSA) is an essential prerequisite for many sequence analysis methods and valuable tool itself for describing relationships between protein sequences. Since the success of the sequence analysis is highly dependent on the reliability of alignments, measures for assessing the quality of alignments are highly requisite. Results: We present a statistical modelbased alignment quality score. Unlike other quality scores, it does not require several parallel alignments for the same set of sequences or additional structural information. Our quality score is based on measuring the conservation level of reference alignments in Homstrad database. Reference sequences were realigned with the Mafft, Muscle and Probcons alignment programs, and a sumofpairs (SP) score was used to measure the quality of the realignments. Statistical modelling of the SP score as a function of conservation level and other alignment characteristics makes it possible to predict the SP score for any global MSA. The predicted SP scores are highly correlated with the correct SP scores, when tested on the Homstrad and SABmark databases. The results are comparable to that of MOS and better than those of NorMD and NiRMSD alignment quality criteria. Furthermore, the predicted SP score is able to detect alignments with badly aligned or unrelated sequences.
Estimating riparian understory vegetation cover with beta regression and copula models.
 For. Sci.,
, 2011
"... Abstract: Understory vegetation communities are critical components of forest ecosystems. As a result, the importance of modeling understory vegetation characteristics in forested landscapes has become more apparent. Abundance measures such as shrub cover are bounded between 0 and 1, exhibit hetero ..."
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Abstract: Understory vegetation communities are critical components of forest ecosystems. As a result, the importance of modeling understory vegetation characteristics in forested landscapes has become more apparent. Abundance measures such as shrub cover are bounded between 0 and 1, exhibit heteroscedastic error variance, and are often subject to spatial dependence. These distributional features tend to be ignored when shrub cover data are analyzed. The beta distribution has been used successfully to describe the frequency distribution of vegetation cover. Beta regression models ignoring spatial dependence (BR) and accounting for spatial dependence (BRdep) were used to estimate percent shrub cover as a function of topographic conditions and overstory vegetation structure in riparian zones in western Oregon. The BR models showed poor explanatory power (pseudoR 2 Յ 0.34) but outperformed ordinary leastsquares (OLS) and generalized leastsquares (GLS) regression models with logittransformed response in terms of mean square prediction error and absolute bias. We introduce a copula (COP) model that is based on the beta distribution and accounts for spatial dependence. A simulation study was designed to illustrate the effects of incorrectly assuming normality, equal variance, and spatial independence. It showed that BR, BRdep, and COP models provide unbiased parameter estimates, whereas OLS and GLS models result in slightly biased estimates for two of the three parameters. On the basis of the simulation study, 9397% of the GLS, BRdep, and COP confidence intervals covered the true parameters, whereas OLS and BR only resulted in 84 88% coverage, which demonstrated the superiority of GLS, BRdep, and COP over OLS and BR models in providing standard errors for the parameter estimates in the presence of spatial dependence. FOR. SCI. 57(3):212221.
Modeling Percent Tree Canopy Cover: A Pilot Study
"... Tree canopy cover is a fundamental component of the landscape, and the amount of cover influences fire behavior, air pollution mitigation, and carbon storage. As such, efforts to empirically model percent tree canopy cover across the United States are a critical area of research. The 2001 nationals ..."
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Tree canopy cover is a fundamental component of the landscape, and the amount of cover influences fire behavior, air pollution mitigation, and carbon storage. As such, efforts to empirically model percent tree canopy cover across the United States are a critical area of research. The 2001 nationalscale canopy cover modeling and mapping effort was completed in 2006, and here we present results from a pilot study for a 2011 product. We examined the influence of two different modeling techniques (random forests and beta regression), two different Landsat imagery normalization processes, and eight different sampling intensities across five different pilot areas. We found that random forest outperformed beta regression techniques and that there was little difference between models developed based on the two different normalization techniques. Based on these results we present a prototype study design which will test canopy cover modeling approaches across a broader spatial scale.
Similar plastic responses to elevated temperature among different sized brook trout populations. Ecology 96:1010–1019.
, 2015
"... Abstract. The potential influence of population size on the magnitude of phenotypic plasticity, a key factor in adaptation to environmental change, has rarely been studied. Conventionally, small populations might exhibit consistently lower plasticity than large populations if small population habit ..."
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Abstract. The potential influence of population size on the magnitude of phenotypic plasticity, a key factor in adaptation to environmental change, has rarely been studied. Conventionally, small populations might exhibit consistently lower plasticity than large populations if small population habitats are generally poor in quality and if genetic diversity underpinning plasticity is lost as population size is reduced. Alternatively, small populations might exhibit (1) consistently higher plasticity as a response to the increased environmental variation that can accompany habitat fragment size reduction or (2) greater variability in plasticity, as fragmentation can increase variability in habitat types. We explored these alternatives by investigating plasticity to increasing temperature in a common garden experiment using eight fragmented populations of brook trout varying nearly 50fold in census size (1798416) and 10fold in effective number of breeders
Changes in verbal and nonverbal conversational behavior in longterm interaction
 In Proc. ICMI 2012
, 2012
"... ABSTRACT We present an empirical investigation of conversational behavior in dyadic interaction spanning multiple conversations, in the context of a developing interpersonal relationship between a health counselor and her clients. Using a longitudinal video corpus of behavior change counseling conv ..."
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ABSTRACT We present an empirical investigation of conversational behavior in dyadic interaction spanning multiple conversations, in the context of a developing interpersonal relationship between a health counselor and her clients. Using a longitudinal video corpus of behavior change counseling conversations, we show systematic changes in verbal and nonverbal behavior during greetings (within the first minute of conversations). Both the number of prior conversations and selfreported assessments of the strength of the interpersonal relationship are predictive of changes in verbal and nonverbal behavior. We present a model and implementation of nonverbal behavior generation for conversational agents that incorporates these findings, and discuss how the results can be applied to multimodal recognition of conversational behavior over time.
Boosted Beta Regression
, 2013
"... Regression analysis with a bounded outcome is a common problem in applied statistics. Typical examples include regression models for percentage outcomes and the analysis of ratings that are measured on a bounded scale. In this paper, we consider beta regression, which is a generalization of logit mo ..."
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Regression analysis with a bounded outcome is a common problem in applied statistics. Typical examples include regression models for percentage outcomes and the analysis of ratings that are measured on a bounded scale. In this paper, we consider beta regression, which is a generalization of logit models to situations where the response is continuous on the interval (0,1). Consequently, beta regression is a convenient tool for analyzing percentage responses. The classical approach to fit a beta regression model is to use maximum likelihood estimation with subsequent AICbased variable selection. As an alternative to this established yet unstable approach, we propose a new estimation technique called boosted beta regression. With boosted beta regression estimation and variable selection can be carried out simultaneously in a highly efficient way. Additionally, both the mean and the variance of a percentage response can be modeled using flexible nonlinear covariate effects. As a consequence, the new method accounts for common problems such as overdispersion and nonbinomial variance structures.
Estimating Litter Decomposition Rate in SinglePool Models Using Nonlinear Beta Regression
"... Litter decomposition rate (k) is typically estimated from proportional litter mass loss data using models that assume constant, normally distributed errors. However, such data often show nonnormal errors with reduced variance near bounds (0 or 1), potentially leading to biased k estimates. We compa ..."
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Litter decomposition rate (k) is typically estimated from proportional litter mass loss data using models that assume constant, normally distributed errors. However, such data often show nonnormal errors with reduced variance near bounds (0 or 1), potentially leading to biased k estimates. We compared the performance of nonlinear regression using the beta distribution, which is wellsuited to bounded data and this type of heteroscedasticity, to standard nonlinear regression (normal errors) on simulated and real litter decomposition data. Although the beta model often provided better fits to the simulated data (based on the corrected Akaike Information Criterion, AICc), standard nonlinear regression was robust to violation of homoscedasticity and gave equally or more accurate k estimates as nonlinear beta regression. Our simulation results also suggest that k estimates will be most accurate when study length captures mid to late stage decomposition (50–80 % mass loss) and the number of measurements through time is $5. Regression method and data transformation choices had the smallest impact on k estimates during mid and late stage decomposition. Estimates of k were more variable among methods and generally less accurate during early and end stage decomposition. With real data, neither model was predominately best; in most cases the models were indistinguishable based on AICc, and gave similar k estimates. However, when decomposition rates were high, normal and beta model k estimates often diverged substantially. Therefore, we recommend a pragmatic approach where both models are compared and the best is selected for a given data set.