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generalized additive models with unknown link function including variable selection

JOURNAL OF APPLIED STATISTICS 2016年第15期43卷 2866-2885页

作者： Tutz, Gerhard Petry, Sebastian Univ Munich Akad Str 1 Munich Germany

The generalized additive model is a well established and strong tool that allows modelling smooth effects of predictors on the response. However, if the link function, which is typically chosen as the canonical link, is misspecified, estimates can be biased. A procedure is proposed that simultaneously estimates the form of the link function and the unknown form of the predictor functions including selection of predictors. The procedure is based on boosting methodology, which obtains estimates by using a sequence of weak learners. It strongly dominates fitting procedures that are unable to modify a given link function if the true link function deviates from the fixed function. The performance of the procedure is shown in simulation studies and illustrated by real world examples.

关键词： Variable selection generalized additive models single index models link function estimation

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Spatial downscaling of soil prediction models based on weighted generalized additive models in smallholder farm settings

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ENVIRONMENTAL MONITORING AND ASSESSMENT 2017年第10期189卷 502-502页

作者： Xu, Yiming Smith, Scot E. Grunwald, Sabine Abd-Elrahman, Amr Wani, Suhas P. Nair, Vimala D. Beijing Technol & Business Univ Dept Environm Sci & Engn Beijing 100048 Peoples R China Univ Florida Sch Nat Resource & Environm 103 Black HallPOB 116455 Gainesville FL 32611 USA Univ Florida Sch Forest Resources & Conservat Geomat Program 301 Reed LabPOB 110565 Gainesville FL 32611 USA Univ Florida Soil & Water Sci Dept Pedometr Landscape Anal & GIS Lab 2181 McCarty HallPOB 110290 Gainesville FL 32611 USA Univ Florida Gulf Coast REC Sch Forest Resources & Conservat Geomat Program 1200 N Pk Rd Plant City FL 33563 USA Int Crops Res Inst Semi Arid Trop Patancheru 502324 Andhra Pradesh India Univ Florida Soil & Water Sci Dept 2181 McCarty HallPOB 110290 Gainesville FL 32611 USA

Digital soil mapping (DSM) is gaining momentum as a technique to help smallholder farmers secure soil security and food security in developing regions. However, communications of the digital soil mapping information between diverse audiences become problematic due to the inconsistent scale of DSM information. Spatial downscaling can make use of accessible soil information at relatively coarse spatial resolution to provide valuable soil information at relatively fine spatial resolution. The objective of this research was to disaggregate the coarse spatial resolution soil exchangeable potassium (K-ex) and soil total nitrogen (TN) base map into fine spatial resolution soil downscaled map using weighted generalized additive models (GAMs) in two smallholder villages in South India. By incorporating fine spatial resolution spectral indices in the downscaling process, the soil downscaled maps not only conserve the spatial information of coarse spatial resolution soil maps but also depict the spatial details of soil properties at fine spatial resolution. The results of this study demonstrated difference between the fine spatial resolution downscaled maps and fine spatial resolution base maps is smaller than the difference between coarse spatial resolution base maps and fine spatial resolution base maps. The appropriate and economical strategy to promote the DSM technique in smallholder farms is to develop the relatively coarse spatial resolution soil prediction maps or utilize available coarse spatial resolution soil maps at the regional scale and to disaggregate these maps to the fine spatial resolution downscaled soil maps at farm scale.

关键词： Spatial downscaling Soil nutrients Digital soil mapping generalized additive models Remote sensing Geographic information system Smallholder farms

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Study of the association of atmospheric temperature and relative humidity with bulk tank milk somatic cell count in dairy herds using generalized additive mixed models

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RESEARCH IN VETERINARY SCIENCE 2017年 114卷 511-517页

作者： Testa, Francesco Marano, Giuseppe Ambrogi, Federico Boracchi, Patrizia Casula, Antonio Biganzoli, Elia Moroni, Paolo Univ Milan Dipartimento Sci Vet Salute Prod Anim & Sicurezza Via Celoria 10 I-20133 Milan Italy Univ Milan Dept Clin Sci & Community Hlth Via Vanzetti 5 I-20133 Milan Italy Univ Milan Dipartimento Med Vet Via Celoria 10 I-20133 Milan Italy Fdn IRCCS Ist Nazl Tumori Unit Med Stat & Biometry Via Venezian 1 I-20133 Milan Italy Cornell Univ Anim Hlth Diagnost Ctr Qual Milk Prod Serv 240 Farrier Rd Ithaca NY 14853 USA

Elevated bulk tank milk somatic cell count (BMSCC) has a negative impact on milk production, milk quality, and animal health. Seasonal increases in herd level somatic cell count (SCC) are commonly associated with elevated environmental temperature and humidity. The Temperature Humidity Index (THI) has been developed to measure general environmental stress in dairy cattle;however, additional work is needed to determine a specific effect of the heat stress index on herd-level SCC. generalized additive Model methods were used for a flexible exploration of the relationships between daily temperature, relative humidity, and bulk milk somatic cell count. The data consist of BMSCC and meteorological recordings collected between March 2009 and October 2011 of 10 dairy farms. The results indicate that, an average increase of 0.16% of BMSCC is expected for an increase of 1 degrees C degree of temperature. A complex relationship was found for relative humidity. For example, increase of 0.099%, 0.037% and 0.020% are expected in correspondence to an increase of relative humidity from 50% to 51%, 80% to 81%;and 90% to 91%, respectively. Using this model, it will be possible to provide evidence-based advice to dairy farmers for the use of THI control charts created on the basis of our statistical model.

关键词： Bovine Somatic cell count Temperature Humidity Index generalized additive models

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Rank-Based Estimation for generalized additive models

Rank-Based Estimation for Generalized Additive Models

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作者： Hannah Elizabeth Correia Auburn University

学位级别：硕士

This thesis focuses on the improvement of generalized additive models (GAMs) using rank estimators. We introduce estimation of the smoothing functions in GAMs via backfitting in a local scoring algorithm using maximization of the expected log likelihood function with weights. Improvements of GAM estimation have focused on the smoothers used in the local scoring algorithm, but poor prediction for non-Gaussian data motivates the need for robust estimation of GAMs. Rank-based estimation as a robust and efficient alternative to the likelihood-based estimation of GAMs is proposed, and it is shown that rank GAM estimators can be restructured as iteratively reweighted GAM estimators. Simulations further support the use of rank-based GAM estimation for heavy-tailed or contaminated sources of data common in climate studies. Successful application of rank GAM estimation is employed for fisheries data, a field which commonly uses GAMs for their high degree of flexibility in modeling complex systems and could benefit from improved model prediction performance for non-Gaussian data. Cross-validation shows improved prediction performance for rank GAMs over GAMs, and improved adjusted R-squared values highlight the better fit of rank GAMs for the given data.

关键词： generalized additive models smoothing spline robust estimation

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generalized additive models for estimating motorcycle collisions on collector roads 5

Generalized additive models for estimating motorcycle collis...

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5th Euro Asia Civil Engineering Forum (EACEF)

作者： Machsus, Machsus Basuki, Rachmad Mawardi, Amalia Firdaus Inst Teknol Sepuluh Nopember Diploma Program Civil Engn Surabaya 60294 East Java Indonesia

In the recent years, the frequency of motorcycle collision in Indonesia, especially in Surabaya, is constantly increasing. This article will explain the use of the generalized additive models (GAMs) to estimate motorcycle collision on collector roads in Surabaya. This study uses GAMs with Gaussian distribution and logarithmic link function, as well as application of software R in data processing. The case study takes place on urban roads in Surabaya, Indonesia. In this study, 69 roads of 120 collector roads in Surabaya are selected. The final model of this study indicates the relationship between the frequency of motorcycle collision on collector roads with explanatory variables which consists of traffic volume, road length, accessibility, road width, number of lanes, and traffic speed. Increasing values of explanatory variables in the prediction model lead to increased risk of accidents. These findings are expected to be considered in programs planned to reduce motorcycle collision on collector roads in Surabaya and other cities. (C) 2015 The Authors. Published by Elsevier Ltd.

关键词： motorcycle collision generalized additive models Gaussian distribution logarithmic link function collector road access road

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generalized additive and index models with shape constraints

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JOURNAL OF THE ROYAL STATISTICAL SOCIETY SERIES B-STATISTICAL METHODOLOGY 2016年第4期78卷 729-754页

作者： Chen, Yining Samworth, Richard J. Univ Cambridge Cambridge CB2 1TN England

We study generalized additive models, with shape restrictions (e.g. monotonicity, convexity and concavity) imposed on each component of the additive prediction function. We show that this framework facilitates a non-parametric estimator of each additive component, obtained by maximizing the likelihood. The procedure is free of tuning parameters and under mild conditions is proved to be uniformly consistent on compact intervals. More generally, our methodology can be applied to generalized additive index models. Here again, the procedure can be justified on theoretical grounds and, like the original algorithm, has highly competitive finite sample performance. Practical utility is illustrated through the use of these methods in the analysis of two real data sets. Our algorithms are publicly available in the R package scar, short for shape-constrained additive regression.

关键词： generalized additive models Index models Non-parametric maximum likelihood estimation Shape constraints

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generalized additive models for Estimating Motorcycle Collisions on Collector Roads

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Procedia Engineering 2015年 125卷 411-416页

作者： Machsus Machsus Rachmad Basuki Amalia Firdaus Mawardi The Diploma Program of Civil Engineering Institut Teknologi Sepuluh Nopember Surabaya East Java 60294 Indonesia

关键词： motorcycle collision generalized additive models Gaussian distribution logarithmic link function collector road access road

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generalized additive models OF HOSPITAL ADMISSIONS WITH RESPIRATORY DISEASE AND METEOROLOGY 3

GENERALIZED ADDITIVE MODELS OF HOSPITAL ADMISSIONS WITH RESP...

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3rd IEEE International Conference on Cloud Computing and Intelligence Systems (CCIS)

作者： An, Lei Kang, Hongyu Xin, Yi Hu, Xiaoming Li, Qin Ling, Yin Gu, Heng Beijing Inst Technol Sch Life Sci Dept Biomed Engn Beijing Peoples R China Chinese Peoples Liberat Army Gen Hosp Telemed Ctr Beijing Peoples R China Beijing Univ Posts & Telecommun Beijing 100876 Peoples R China

ISBN: (纸本)9781479947195

Clinicians are very interested in researching what are important determinants of hospitalization for respiratory disease. In this paper, a general model to explain the relationship between the risk of respiratory disease and several meteorological variables will be presented by the framework of generalized additive models (GAMs) and its predictive effects will be evaluated. By using 9655 medical records with respiratory disease in a county in central China and daily meteorological data, a reasonably good fit was obtained. The result shows that the general method which was presented by this paper to discover the relationship between the meteorological factors and the hospitalization rate for respiratory disease is can explain most of the variation in the daily counts of hospital admissions.

关键词： generalized additive models hospital admissions respiratory disease

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Modeling the Effect of Environmental Factors on the Ricker Stock-Recruitment Relationship for North Pacific Albacore Using generalized additive models

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TERRESTRIAL ATMOSPHERIC AND OCEANIC SCIENCES 2014年第4期25卷 581-590页

作者： Shih, Chia-Lung Chen, Yi-Hsiu Hsu, Chien-Chung Natl Taiwan Univ Coll Sci Inst Oceanog Taipei 10764 Taiwan

This study investigates how the inclusion of El Nino episodes affects the modeling of recruitment in North Pacific albacore. The relationship between spawning stock size and recruitment for the 1976 - 2004 period, including environmental variables (Southern Oscillation Index and sea surface temperature anomalies), was conducted by general linear and generalized additive models (GAM). The results indicate that the Southern Oscillation Index and the interaction between spawning stock size and sea surface temperature anomalies have significant effects on the recruitment of North Pacific albacore. GAM fit the original data better than general linear models, according to the Akaike information criterion. The recruitment declined when El Nino episodes occurred, but increased when La Nino episodes occurred. The recruitment also increased when the spawning stock size density was above 11.21 million tons with a -0.3 degrees C sea surface temperature anomaly. El Nino was observed to have both long-period (above 10 - 15 years) and short-period (1 - 2 years) effects on North Pacific recruitment.

关键词： El Nino generalized additive models La Nino Southern oscillation index

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Interpretable generalized additive neural networks

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EUROPEAN JOURNAL OF OPERATIONAL RESEARCH 2024年第2期317卷 303-316页

作者： Kraus, Mathias Tschernutter, Daniel Weinzierl, Sven Zschech, Patrick FAU Erlangen Nurnberg Lange Gasse 20 D-90403 Nurnberg Germany Swiss Fed Inst Technol Weinbergstr 56-58 CH-8092 Zurich Switzerland

We propose Interpretable generalized additive Neural Networks (IGANN), a novel machine learning model that uses gradient boosting and tailored neural networks to obtain high predictive performance while being interpretable to humans. We derive an efficient training algorithm based on the theory of extreme learning machines, that allows reducing the training process to solving a sequence of regularized linear regressions. We analyze the algorithm theoretically, provide insights into the rate of change of so-called shape functions, and show that the computational complexity of the training process scales linearly with the number of samples in the training dataset. We implement IGANN in PyTorch, which allows the model to be trained on graphics processing units (GPUs) to speed up training. We demonstrate favorable results in a variety of numerical experiments and showcase IGANN's value in three real-world case studies for productivity prediction, credit scoring, and criminal recidivism prediction. (c) 2023 The Author(s). Published by Elsevier B.V. This is an open access article under the CC BY license ( http://***/licenses/by/4.0/ )

关键词： Analytics generalized additive models Gradient boosting Interpretable machine learning Neural networks

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