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Practical variable selection for generalized additive models

COMPUTATIONAL STATISTICS & DATA ANALYSIS 2011年第7期55卷 2372-2387页

作者： Marra, Giampiero Wood, Simon N. UCL Dept Stat Sci London WC1E 6BT England Univ Bath Dept Math Sci Bath BA2 7AY Avon England

The problem of variable selection within the class of generalized additive models, when there are many covariates to choose from but the number of predictors is still somewhat smaller than the number of observations, is considered. Two very simple but effective shrinkage methods and an extension of the nonnegative garrote estimator are introduced. The proposals avoid having to use nonparametric testing methods for which there is no general reliable distributional theory. Moreover, component selection is carried out in one single step as opposed to many selection procedures which involve an exhaustive search of all possible models. The empirical performance of the proposed methods is compared to that of some available techniques via an extensive simulation study. The results show under which conditions one method can be preferred over another, hence providing applied researchers with some practical guidelines. The procedures are also illustrated analysing data on plasma beta-carotene levels from a cross-sectional study conducted in the United States. (C) 2011 Elsevier B.V. All rights reserved.

关键词： generalized additive model Nonnegative garrote estimator Penalized thin plate regression spline Practical variable selection Shrinkage smoother

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Linking livestock snow disastermortality and environmental stressors in the Qinghai-Tibetan Plateau: Quantification based on generalized additive models

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SCIENCE OF THE TOTAL ENVIRONMENT 2018年 625卷 87-95页

作者： Li, Yijia Ye, Tao Liu, Weihang Gao, Yu Beijing Normal Univ Fac Geog Sci State Key Lab Earth Surface Proc & Resource Ecol Key Lab Environm Change & Nat DisasterMinist Edu Beijing 100875 Peoples R China East China Normal Univ Sch Geog Sci Shanghai 200241 Peoples R China

Livestock snowdisaster occurswidely in Central-to-Eastern Asian temperate and alpine grasslands. The effects of snowdisaster on livestock involve a complex interaction between precipitation, vegetation, livestock, and herder communities. Quantifying the relationship among livestock mortality, snow hazard intensity, and seasonal environmental stressors is of great importance for snow disaster early warning, risk assessments, and adaptation strategies. Using a wide-spatial extent, long-time series, and event-based livestock snow disaster dataset, this study quantified those relationships and established a quantitative model of livestock mortality for prediction purpose for the Qinghai-Tibet Plateau region. Estimations using generalized additive models (GAMs) were shown to accurately predict livestock mortality and mortality rate due to snow disaster, with adjusted-R-2 up to 0.794 and 0.666, respectively. These results showed that a longer snow disaster duration, lower temperatures during the disaster, and a drier summer with less vegetation all contribute significantly and non-linearly to higher mortality ( rate), after controlling for elevation and socioeconomic conditions. These results can be readily applied to risk assessment and risk-based adaptation actions. (c) 2017 Elsevier B.V. All rights reserved.

关键词： Livestock snow disaster Snow hazard intensity Environmental stressors generalized additive model Qinghai-Tibet Plateau

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Near-road air pollutant concentrations of CO and PM_2.5: A comparison of MOBILE6.2/CALINE4 and generalized additive models

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ATMOSPHERIC ENVIRONMENT 2010年第14期44卷 1740-1748页

作者： Zhang, Kai Batterrnan, Stuart Univ Michigan Ann Arbor MI 48109 USA

The contribution of vehicular traffic to air pollutant concentrations is often difficult to establish. This paper utilizes both time-series and simulation models to estimate vehicle contributions to pollutant levels near roadways. The time-series model used generalized additive models (GAMs) and fitted pollutant observations to traffic counts and meteorological variables. A one year period (2004) was analyzed on a seasonal basis using hourly measurements of carbon monoxide (CO) and particulate matter less than 2.5 mu m in diameter (PM2.5) monitored near a major highway in Detroit. Michigan, along with hourly traffic counts and local meteorological data. Traffic counts showed statistically significant and approximately linear relationships with CO concentrations in fall, and piecewise linear relationships in spring, summer and winter. The same period was simulated using emission and dispersion models (Motor Vehicle Emissions Factor model/MOBILE6.2;California Line Source Dispersion model/CALINE4). CO emissions derived from the GAM were similar, on average, to those estimated by MOBILE6.2. The same analyses for PM2.5 showed that GAM emission estimates were much higher (by 4-5 times) than the dispersion model results, and that the traffic-PM2.5 relationship varied seasonally. This analysis suggests that the simulation model performed reasonably well for CO, but it significantly underestimated PM2.5 concentrations, a likely result of underestimating PM2.5 emission factors. Comparisons between statistical and simulation models can help identify model deficiencies and improve estimates of vehicle emissions and near-road air quality. (C) 2010 Elsevier Ltd. All rights reserved.

关键词： Traffic counts CO PM2.5 MOBILE6.2 CALINE4 generalized additive model Dispersion modeling

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The burden associated with ambient PM_2.5 and meteorological factors in Guangzhou, China, 2012-2016: A generalized additive modeling of temporal years of life lost

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CHEMOSPHERE 2018年 212卷 705-714页

作者： Lin, Xiao Liao, Yu Hao, Yuantao Sun Yat Sen Univ Sch Publ Hlth Dept Med Stat & Epidemiol Guangzhou 510080 Guangdong Peoples R China Sun Yat Sen Univ Sun Yat Sen Global Hlth Inst Guangzhou 510080 Guangdong Peoples R China

Background: Daily exposure to ambient particulate matter with aerodynamic diameter <2.5 Am (PM2.5) increases deaths and is an important contributor to burden of disease in population. To better understand the disease burden associated with PM2.5, we examined the effects of PM2.5 on daily years of life lost (YLL) in Guangzhou, China. Methods: Using Guangzhou death registry, air pollution and meteorological database, we applied generalized additive models (GAM) to the relationships between YLL and PM2.5. We then adjusted the models for age, gender, seasonality and meteorological variables. We also conducted within -data prediction of YLL while setting 2012-2014 as baseline. Results: Over 2 million YLLs (800,137 YLLs for females and 1,212,040 YLLs for males) were observed during 2012-2016. YLL was higher for the elderly people. Mean daily average PM2.5 concentration was 47.3 mu g/m(3). In model comparisons, the GAM with six meteorological variables (sunshine hours, relative humidity, precipitation, atmospheric pressure, wind speed, evaporation) outperformed the others. The R-2 and total deviance were 0.542 and 53.0%, respectively. Non-linear trends were observed for PM2.5 and meteorological variables. Fitted daily YLL increased to the highest level, when PM2.5 concentration reached 134.3 g/m(3) and atmospheric pressure reached 99.4 kPa. Within-data prediction supported the fitted GAM, where low mean absolute percentage errors were observed. Conclusions: Daily PM2.5 exposure has a nonlinear effect on YLL and increased levels of PM2.5 may lead to increased YLL. This study highlights the urge to reduce ambient PM2.5 pollution in Guangzhou, in order to promote environmental health. (C) 2018 The Authors. Published by Elsevier Ltd. This is an open access article under the CC BY-NC-ND license

关键词： Disease burden Years of life lost PM2.5 Meteorological factor generalized additive model

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Statistical modelling of roadside and urban background ultrafine and accumulation mode particle number concentrations using generalized additive models

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SCIENCE OF THE TOTAL ENVIRONMENT 2020年第0期703卷 134570-000页

作者： Gerling, Lars Loeschau, Gunter Wiedensohler, Alfred Weber, Stephan Tech Univ Carolo Wilhelmina Braunschweig Inst Geoecol Climatol & Environm Meteorol Langer Kamp 19c D-38106 Braunschweig Germany Saxon State Off Environm Agr & Geol LfULG Pillnitzer Pl 3 D-01326 Dresden Germany Leibniz Inst Tropospher Res TROPOS Permoserstr 15 D-04318 Leipzig Germany

Quantification of the exposure of urban residents to ultrafine particle number concentrations (UFP) is challenging due to its high spatial and temporal variability. Hence, statistical models, e.g. generalized additive models (GAM), may be used to estimate time series or spatial characteristics of UFP. The GAM approach allows the representation of non-linear relations of a response variable with explanatory variables without the need to pre-define model functions. Up to now, GAMs were usually fitted to UFP data from a single site or from mobile measurement campaigns with limited temporal coverage. In this study, GAMs were used to determine UFP, accumulation mode particle (ACC) and total number concentration (TNC) at five urban sites in the cities of Leipzig and Dresden, Germany for the period 2011-2013. As explanatory variables, reanalysis data sets of meteorological quantities, urban geometry and traffic volume data were evaluated. Variables causing concurvity, which is the equivalent to collinearity in nonlinear model approaches, were neglected to guarantee the interpretability of the final models. The models were then validated in a ten-fold cross-validation approach. The final models contained smooth functions for the building surface fraction, planetary boundary layer height, traffic volume, air temperature, wind direction, atmospheric pressure, relative humidity, global radiation and precipitation. Adjusted coefficients of determination (R-adj(2).) for the final models were R-adj(2) = 0.44 for UFP, R-adj(2) = 0.51 for ACC and R-adj(2) = 0.48 for TNC. Coefficients of determination of the cross-validation were in a similar range (0.44 for UFP, 0.51 for ACC, 0.49 for TNC). Finally, our study shows that GAMs are able to represent important processes that contribute to the particle number concentration from the smooth functions, i.e. emission, dilution, nucleation, deposition and long-range transport. (C) 2019 Elsevier B.V. All rights reserved.

关键词： Ultrafine particles Accumulation mode particles Particle number concentration Urban air quality generalized additive model Statistical model

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Use of generalized additive models and cokriging of spatial residuals to improve land-use regression estimates of nitrogen oxides in Southern California

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ATMOSPHERIC ENVIRONMENT 2012年 55卷 220-228页

作者： Li, Lianfa Wu, Jun Wilhelm, Michelle Ritz, Beate Univ Calif Irvine Program Publ Hlth Coll Hlth Sci Irvine CA 92697 USA Chinese Acad Sci State Key Lab Resources & Environm Informat Syst Inst Geog Sci & Nat Resources Res Beijing 100864 Peoples R China Univ Calif Los Angeles Sch Publ Hlth Dept Epidemiol Los Angeles CA 90024 USA

Land-use regression (LUR) models have been developed to estimate spatial distributions of traffic-related pollutants. Several studies have examined spatial autocorrelation among residuals in LUR models, but few utilized spatial residual information in model prediction, or examined the impact of modeling methods, monitoring site selection, or traffic data quality on LUR performance. This study aims to improve spatial models for traffic-related pollutants using generalized additive models (GAM) combined with cokriging of spatial residuals. Specifically, we developed spatial models for nitrogen dioxide (NO2) and nitrogen oxides (NOx) concentrations in Southern California separately for two seasons (summer and winter) based on over 240 sampling locations. Pollutant concentrations were disaggregated into three components: local means, spatial residuals, and normal random residuals. Local means were modeled by GAM. Spatial residuals were cokriged with global residuals at nearby sampling locations that were spatially auto-correlated. We compared this two-stage approach with four commonly-used spatial models: universal kriging, multiple linear LUR and GAM with and without a spatial smoothing term. Leave-one-out cross validation was conducted for model validation and comparison purposes. The results show that our GAM plus cokriging models predicted summer and winter NO2 and NOx concentration surfaces well, with cross validation R-2 values ranging from 0.88 to 0.92. While local covariates accounted for partial variance of the measured NO2 and NOx concentrations, spatial autocorrelation accounted for about 20% of the variance. Our spatial GAM model improved R-2 considerably compared to the other four approaches. Conclusively, our two-stage model captured summer and winter differences in NO2 and NOx spatial distributions in Southern California well. When sampling location selection cannot be optimized for the intended model and fewer covariates are available as predictors for t

关键词： Land-use regression Spatial residuals generalized additive model Cokriging Traffic air pollution

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Comparative performance of generalized additive models and multivariate adaptive regression splines for statistical modelling of species distributions

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ECOLOGICAL modelLING 2006年第2期199卷 188-196页

作者： Leathwick, J. R. Elith, J. Hastie, T. Natl Inst Water & Atmospher Res Hamilton New Zealand Univ Melbourne Sch Bot Parkville Vic 3052 Australia Stanford Univ Dept Stat Stanford CA 94305 USA

Two statistical modelling techniques, generalized additive models (GAM) and multivariate adaptive regression splines (MARS), were used to analyse relationships between the distributions of 15 freshwater fish species and their environment. GAM and MARS models were fitted individually for each species, and a MARS multiresponse model was fitted in which the distributions of all species were analysed simultaneously. model performance was evaluated using changes in deviance in the fitted models and the area under the receiver operating characteristic curve (ROC), calculated using a bootstrap assessment procedure that simulates predictive performance for independent data. Results indicate little difference between the performance of GAM and MARS models, even when MARS models included interaction terms between predictor variables. Results from MARS models are much more easily incorporated into other analyses than those from GAM models. The strong performance of a MARS multiresponse model, particularly for species of low prevalence, suggests that it may have distinct advantages for the analysis of large datasets. Its identification of a parsimonious set of environmental correlates of community composition, coupled with its ability to robustly model species distributions in relation to those variables, can be seen as converging strongly with the purposes of traditional ordination techniques. (c) 2006 Elsevier B.V All rights reserved.

关键词： distribution environment fish freshwater generalized additive model multivariate adaptive regression splines

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Fast Automatic Smoothing for generalized additive models

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JOURNAL OF MACHINE LEARNING RESEARCH 2019年第1期20卷 1-27页

作者： El-Bachir, Yousra Davison, Anthony C. Ecole Polytech Fed Lausanne FSB MATH STAT Stn 8 CH-1015 Lausanne Switzerland

generalized additive models (GAMs) are regression models wherein parameters of probability distributions depend on input variables through a sum of smooth functions, whose degrees of smoothness are selected by L-2 regularization. Such models have become the de-facto standard nonlinear regression models when interpretability and flexibility are required, but reliable and fast methods for automatic smoothing in large data sets are still lacking. We develop a general methodology for automatically learning the optimal degree of L-2 regularization for GAMs using an empirical Bayes approach. The smooth functions are penalized by hyper-parameters that are learned simultaneously by maximization of a marginal likelihood using an approximate expectation-maximization algorithm. The latter involves a double Laplace approximation at the E-step, and leads to an efficient M-step. Empirical analysis shows that the resulting algorithm is numerically stable, faster than the best existing methods and achieves state-of-the-art accuracy. For illustration, we apply it to an important and challenging problem in the analysis of extremal data.

关键词： Automatic L-2 Regularization Empirical Bayes Expectation-maximization Algorithm generalized additive model Laplace Approximation Marginal Maximum Likelihood

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modeling and Fault Monitoring of Bioprocess Using generalized additive models （GAMs） and Bootstrap

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Chinese Journal of Chemical Engineering 2012年第6期20卷 1180-1183页

作者：郑蓉建周林成潘丰 Key Laboratory of Advanced Process Control for Light Industry (Ministry of Education) Jiangnan University Wuxi 214122 China Faculty of Electrical Engineering Huaiyin Institute of Technology Huai'an 223003 China

Fault monitoring of bioprocess is important to ensure safety of a reactor and maintain high quality of products. It is difficult to build an accurate mechanistic model for a bioprocess, so fault monitoring based on rich historical or online database is an effective way. A group of data based on bootstrap method could be resampling stochastically, improving generalization capability of model. In this paper, online fault monitoring of generalized additive models （GAMs） combining with bootstrap is proposed for glutamate fermentation process. GAMs and bootstrap are first used to decide confidence interval based on the online and off-line normal sampled data from glutamate fermentation experiments. Then GAMs are used to online fault monitoring for time, dissolved oxygen, oxygen uptake rate, and carbon dioxide evolution rate. The method can provide accurate fault alarm online and is helpful to provide useful information for removing fault and abnormal phenomena in the fermentation.

关键词： bioprocess fault monitoring generalized additive model glutamic acid fermentation bootstrap modeling

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Weather impacts on various types of road crashes: a quantitative analysis using generalized additive models

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EUROPEAN TRANSPORT RESEARCH REVIEW 2022年第1期14卷 1-18页

作者： Becker, Nico Rust, Henning W. Ulbrich, Uwe Free Univ Berlin Inst Meteorol Carl Heinrich Becker Weg 6-10 D-12165 Berlin Germany Hans Ertel Ctr Weather Res Berlin Germany

Adverse weather conditions can have different effects on different types of road crashes. We quantify the combined effects of traffic volume and meteorological parameters on hourly probabilities of 78 different crash types using generalized additive models. Using tensor product bases, we model non-linear relationships and combined effects of different meteorological parameters. We evaluate the increase in relative risk of different crash types in case of precipitation, sun glare and high wind speeds. The largest effect of snow is found in case of single-truck crashes, while rain has a larger effect on single-car crashes. Sun glare increases the probability of multi-car crashes, in particular at higher speed limits and in case of rear-end crashes. High wind speeds increase the probability of single-truck crashes and, for all vehicle types, the risk of crashes with objects blown on the road. A comparison of the predictive power of models with and without meteorological variables shows an improvement of scores of up to 24%, which makes the models suitable for applications in real-time traffic management or impact-based warning systems. These could be used by authorities to issue weather-dependent driving restrictions or situation-specific on-board warnings to improve road safety.

关键词： Road crashes Crash type Traffic volume Weather Precipitation Sun glare Wind speed generalized additive model Relative risk Impact model

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