Geoadditive regression modeling of stream biological condition

Schmid, Matthias; Hothorn, Torsten; Maloney, Kelly O.; Weller, Donald E.; Potapov, Sergej

doi:10.1007/s10651-010-0158-4

Cited by 28 publications

(22 citation statements)

References 47 publications

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“…Exceptions are Ridgeway (2002) and Sexton and Laake (2012), who study boosting algorithms for fitting density functions. Lu and Li (2008), Schmid and Hothorn (2008) and Schmid, Hothorn, Maloney, Weller, and Potapov (2011) proposed boosting algorithms for transformation models that treat the transformation function h Y as a nuisance parameter. In the same model framework, Tutz and Groll (2013) propose a likelihood-boosting approach for fitting cumulative and sequential models for ordinal responses.…”

Section: Discussionmentioning

confidence: 99%

Conditional Transformation Models

Hothorn

Kneib

Bühlmann

2013

Journal of the Royal Statistical Society Series B: Statistical Methodology

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100

143

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The ultimate goal of regression analysis is to obtain information about the conditional distribution of a response given a set of explanatory variables. This goal is, however, seldom achieved because most established regression models only estimate the conditional mean as a function of the explanatory variables and assume that higher moments are not affected by the regressors. The underlying reason for such a restriction is the assumption of additivity of signal and noise. We propose to relax this common assumption in the framework of transformation models. The novel class of semiparametric regression models proposed herein allows transformation functions to depend on explanatory variables. These transformation functions are estimated by regularised optimisation of scoring rules for probabilistic forecasts, e.g. the continuous ranked probability score. The corresponding estimated conditional distribution functions are consistent. Conditional transformation models are potentially useful for describing possible heteroscedasticity, comparing spatially varying distributions, identifying extreme events, deriving prediction intervals and selecting variables beyond mean regression effects. An empirical investigation based on a heteroscedastic varying coefficient simulation model demonstrates that semiparametric estimation of conditional distribution functions can be more beneficial than kernel-based non-parametric approaches or parametric generalised additive models for location, scale and shape.

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Section: Discussionmentioning

confidence: 99%

Conditional Transformation Models

Hothorn

Kneib

Bühlmann

2013

Journal of the Royal Statistical Society Series B: Statistical Methodology

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100

143

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“…In this study, the residual information is computed with the component-wise gradient boosting algorithm of Bühlmann and Hothorn (2007), using the negative gradient vector of the loss-function from the current model. For ordinal response variables such as lvp, the loss-function is defined by the log-likelihood of the proportional odds model of Agresti (2003;Schmid et al 2011). After the fitting of the new tree, its paths are aggregated to the paths of the previously grown ones, albeit with a shrinkage parameter to grow the model slowly, which improves the fit relative to single trees (James et al 2014).…”

Section: Random Forestmentioning

confidence: 99%

Forecasting Low-Visibility Procedure States with Tree-Based Statistical Methods

Dietz

Kneringer

Mayr

et al. 2018

Pure Appl. Geophys.

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Abstract-Low-visibility conditions at airports can lead to capacity reductions and, therefore, to delays or cancelations of arriving and departing flights. Accurate visibility forecasts are required to keep the airport capacity as high as possible. We generate probabilistic nowcasts of low-visibility procedure (lvp) states, which determine the reduction of the airport capacity due to low visibility. The nowcasts are generated with tree-based statistical models based on highly-resolved meteorological observations at the airport. Short computation times of these models ensure the instantaneous generation of new predictions when new observations arrive. The tree-based ensemble method boosting provides the highest benefit in forecast performance. For lvp forecasts with lead times shorter than 1 h variables with information of the current lvp state, ceiling, and horizontal visibility are most important. With longer lead times, visibility information of the airport's vicinity and standard meteorological variables such as humidity also become relevant.

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“…These functions depend on the coordinates of the site locations and are added to the other functions specified in (5) and (6) (cf. [15], [24]). To estimate the shapes of the surface functions, we use P-spline tensor product surfaces depending on the NAD83 coordinates of the lakes.…”

Section: Methodsmentioning

confidence: 99%

“…In many applications, predictor-response relationships are nonlinear in nature [15], [16]. This means that the linear predictor of the classical beta regression model needs to be replaced by a more flexible function that allows for an appropriate quantification of nonlinear predictor effects.…”

Section: Introductionmentioning

confidence: 99%

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Boosted Beta Regression

Schmid

Wickler²,

Maloney³

et al. 2013

PLoS ONE

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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 AIC-based 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 non-binomial variance structures.

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Geoadditive regression modeling of stream biological condition

Cited by 28 publications

References 47 publications

Conditional Transformation Models

Conditional Transformation Models

Forecasting Low-Visibility Procedure States with Tree-Based Statistical Methods

Boosted Beta Regression

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