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modelling current status data using generalized additive models with flexible link: the additive gamma-logit model

INTERNATIONAL JOURNAL OF APPLIED MATHEMATICS & STATISTICS 2011年第11A期24卷 2-19页

作者： Papoila, Ana Luisa Rocha, Cristina S. Univ Nova Lisboa Fac Med Sci CEAUL Campo Martires Patria 130 P-1169056 Lisbon Portugal Univ Lisbon Fac Sci CEAUL Campo Grande P-1749016 Lisbon Portugal

When using generalized Linear models (GLMs), misspecification of the link is very likely to occur due to the fact that the information, necessary to correctly choose this function, is usually unavailable. To overcome this problem, new developments emerged which also gave rise to more flexible models. As a result, survival analysis has also benefited from this new line of research due to the correspondence that can be established between models in binary regression analysis and in survival analysis. In fact, the gamma-logit survival model may be viewed as a GLM with binary response and unknown link function belonging to the one-parameter Aranda-Ordaz family of transformations. We believe a greater flexibility can be achieved by also allowing non linear covariate effects. Hence, we propose the use of flexible parametric link families in generalized additive models (GAMs) with binary response. If we now consider the referred Aranda-Ordaz transformations family, a generalization of the gamma-logit model will be obtained, which we will denote by additive gamma-logit model. Based on the local scoring algorithm, the estimation procedure minimizes the deviance through the use of a deviance profile plot. A quality evaluation of the link parameter estimates, as well as the comparison of the performance of the proposed GAM with that of the GLM with the same parametric link, were carried out for simulated data. The proposed methodology was applied to a real current status data set.

关键词： Current status data Gamma-logit model generalized additive model Survival analysis Unknown link function

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Buckley-James estimation of generalized additive accelerated lifetime model with ultrahigh-dimensional data

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STATISTICAL ANALYSIS AND DATA MINING 2023年第3期16卷 305-312页

作者： Li, Zichang Zhao, Xuejing Renmin Univ China Sch Stat Beijing Peoples R China Lanzhou Univ Ctr Data Sci Sch Math & Stat Lanzhou Peoples R China

High-dimensional covariates in lifetime data is a challenge in survival analysis, especially in gene expression profile. The objective of this paper is to propose an efficient algorithm to extend the generalized additive model to survival data with high-dimensional covariates. The algorithm is combined of generalized additive (GAM) model and Buckley-James estimation, which makes a nonparametric extension to the nonlinear model, where the GAM is exploited to illustrate the nonlinear effect of the covariates and the Buckley-James estimation is used to address the regression model with right-censored response. In addition, we use maximal-information-coefficient (MIC)-type variable screening and weighted p-value to reduce dimension in high-dimensional situations. The performance of the proposed algorithm is compared with the three benchmark models: Cox proportional hazards regression model, random survival forest, and BJ-AFT on a simulated dataset and two real survival datasets. The results, evaluated by concordance index (C-index) as well as modified mean squared error (mMSE), illustrated the superiority of the proposed algorithm.

关键词： accelerated lifetime model Buckley-James estimation feature screening generalized additive model ultrahigh dimension

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Bayesian Analysis of the generalized additive Proportional Hazards model: Asymptotic Studies

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BAYESIAN ANALYSIS 2024年第4期19卷 1225-1243页

作者： Kim, Gwangsu Yoo, Chang D. Kim, Yongdai Jeonbuk Natl Univ Inst Appl Stat Dept Stat 567 Baekje Daero Jeonju Si Jeollabuk Do South Korea Korea Adv Inst Sci & Technol Sch Elect Engn 291 Daehak Ro Daejeon South Korea Seoul Natl Univ Dept Stat 1 Gwanak Ro Seoul South Korea

In this paper, we study Bayesian asymptotic properties of the proportional hazards model where the link function is modeled by the generalized additive model. As the standard generalized additive model is, the generalized additive proportional hazards model is a useful tool in finding the nonlinearity of covariate effects to survival times. We develop a data-dependent sieve prior for the generalized additive link function and use the Bayesian bootstrap prior for the baseline hazard function. We prove that the posterior contraction rate of the generalized additive link function is minimax optimal up to a log n term when the prior is carefully selected. By analyzing simulated as well as real data, we verify our theoretical results and compare with exisiting algorithms for the generalized additive proportional hazards model to illustrate that the proposed Bayesian model is a useful inference tool.

关键词： b-spline generalized additive model partial likelihood posterior contraction rate proportional hazards model

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A Flexible Approach to Age Dependence in Organizational Mortality: Comparing the Life Duration for Cooperative and Non-Cooperative Enterprises Using a Bayesian generalized additive Discrete Time Survival model

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JOURNAL OF QUANTITATIVE ECONOMICS 2019年第4期17卷 829-855页

作者： Rousseliere, Damien INRA AGROCAMPUS OUEST SMART LERECO F-49045 Angers France

This paper proposes a new estimation model to capture the complex effect of age on organization survival. Testing various theoretical propositions on organizational mortality, we study the survival of French agricultural cooperatives in comparison with other firms with which they compete. The relationship between age and mortality in organizations is analyzed using a Bayesian generalized discrete-time semi-parametric hazard model incorporating unobserved heterogeneity, isolating the various effects of time and identifying within-effects and between-effects of the time-varying covariates. This analysis emphasizes the specificity of the temporal dynamics of cooperatives in relation to their special role in agriculture.

关键词： Bayesian estimation Bayesian model selection Cooperatives Hybrid model generalized additive model Survival analysis C11 C41 Q13 L25

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Global maize yield responses to essential climate variables: Assessment using atmospheric reanalysis and future climate scenarios

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COMPUTERS AND ELECTRONICS IN AGRICULTURE 2025年 232卷

作者： Zhao, Zhi-Wei Leng, Pei Han, Xiao-Jing Shang, Guo-Fei Chinese Acad Agr Sci Inst Agr Resources & Reg Planning State Key Lab Efficient Utilizat Arable Land China Beijing 100081 Peoples R China Hebei GEO Univ Hebei Int Joint Res Ctr Remote Sensing Agr Drought Sch Land Sci & Space Planning Shijiazhuang 050031 Peoples R China Chinese Acad Agr Sci Inst Agr Econ & Dev Beijing 100101 Peoples R China

Maize is recognized as one of the four major crops in the world and plays an important role in global agri-food systems. Therefore, understanding how maize yield responds to climate change is essential for addressing the challenges of exponential population growth and food security. In this study, maize yield data in 77 countries from 1982 to 2016 and seven essential climate variables (ECVs) were collected to assess the effects of climate change on maize yield variation. To this end, potential ECVs were first divided into three groups: energy availability (net surface solar radiation, air temperature and land surface temperature), water availability (soil moisture and precipitation), and exchange efficiency (relative humidity and wind speed), which are closely related to crop growth. Correlation analysis was conducted to determine the best ECVs for further investigation. Furthermore, the generalized additive model (GAM) was used to express yield as function to the ECVs in each country. Specifically, the first-order difference in maize yield and ECVs were considered in data process to maximize the effects of reductions from other factors such as crop management and cultivars. Finally, the performance of the proposed approach was compared with that of widely used multiple regression method. The results indicate that: (1) a global average of 46% of maize yield variability can be explained by ECVs variability, yet significant discrepancies exist for different countries;(2) over 73% of countries are dominated by more than two groups of ECVs;(3) GAM generally outperforms the traditional multiple regression method in more than 80% of the investigated countries. This study offers a fresh perspective for investigating maize yield responses to climate change.

关键词： Maize yield Essential climate variables Climate change generalized additive model

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Integrating machine learning regression and classification for enhanced interpretability in optimizing the Fenton process for real wastewater treatment conditions

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SEPARATION AND PURIFICATION TECHNOLOGY 2025年 363卷

作者： Ergan, Basak Temur Yucel, Ozgun Gengec, Erhan Aydin, Ebubekir Siddik Gebze Tech Univ Dept Chem Engn TR-41400 Kocaeli Turkiye Kocaeli Univ Dept Environm Protect & Control TR-41380 Kocaeli Turkiye Sivas Univ Sci & Technol Dept Chem Engn TR-58000 Sivas Turkiye

The Fenton process is an important process used in treating textile wastewater such as Jeans-wash wastewater (JWW). Predicting the results of this process according to Fenton parameters is a critical step to evaluating the treatment performance. One of the important ways to improve treatment performance is to use machine learning methods. Therefore, machine learning methods using experimental Fenton treatment data were proposed to mathematically demonstrate the effect of the hydrogen peroxide (H2O2) and iron sulfate (FeSO4) dosage on dye and total organic carbon (TOC) concentration within this research. To increase the predictive capability of machine learning methods, in addition to concentration of H2O2 and FeSO4 inputs, dye and TOC initial concentration values were used as inputs in the machine learning methods. Four regression techniques were used to forecast the dye and TOC concentration outputs of Fenton process, namely Random Forest Regression (RFR), Gaussian Process Regression (GPR), Decision Tree Regression (DTR), and generalized additive model (GAM) in this study. Hold-out and k-fold cross-validation were used in combination to examine the effectiveness of the suggested regression techniques. Among these machine learning methods, GPR was more successful than the other proposed models with predicted the dye concentration as R-2 > 0.97 and TOC concentration as R-2 > 0.86. Finally, illustration of decision tree classifiers indicating the process operation were placed with interpretable machine learning. With these trees, the input-range/target result relationship depending on the input parameters of the process was established to eliminate the side reactions that occur due to the nature of the Fenton process.

关键词： Fenton process Random forest regression Gaussian process regression Decision tree regression generalized additive model Machine learning methods

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modelling vegetation phenology in alpine grasslands of North-East Italy integrating microclimatic and meteorological Drivers: A 23-Years Time-Series analysis

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COMPUTERS AND ELECTRONICS IN AGRICULTURE 2025年 232卷

作者： Pinna, Daniele Sozzi, Marco Pornaro, Cristina Macolino, Stefano Pezzuolo, Andrea Marinello, Francesco Univ Padua Dept Land Environm Agr & Forestry I-35020 Legnaro Italy Univ Padua Dept Agron Food Nat Resources Anim & Environm I-35020 Legnaro Italy

Grasslands in mountainous regions often exhibit unique variations in the amplitude and timing of their growing seasons in response to microclimatic and meteorological variability. This study investigates the environmental drivers of vegetation phenology in the Alpine grasslands of North-East Italy using a 23-year MODIS NDVI time series (2001-2023), harmonic regression, and generalized additive models (GAMs). Results highlight a strong negative correlation between altitude and NDVI metrics, with higher elevations exhibiting lower vegetation cover, greater seasonal variability, and shorter growing seasons. Slope similarly constrains vegetation growth, while aspect influences microclimatic conditions but shows weaker overall effects. Temperature and solar radiation positively influence NDVI, enhancing vegetation vigor and extending the growing season, while precipitation plays a more limited role, with limited variability across the region. Wind exposure shortens the growing season, reducing NDVI values, while snowfall significantly delays and shortens vegetation growth, increasing seasonal variability. Soil properties, particularly water-holding capacity, pH, and texture, strongly influence vegetation dynamics, with silt-rich soils favoring longer and more stable growing periods. The developed GAMs demonstrated high predictive accuracy (R2 = 0.70-0.91), effectively estimating phenological transitions, including the start and end of the vegetative season, with an accuracy of approximately 11 days. These findings enhance our understanding of the complex interactions shaping alpine pasture ecosystems and provide valuable tools for sustainable management, conservation, and climate adaptation strategies.

关键词： Grassland generalized additive model Harmonic regression NDVI MODIS Pasture Time-Series

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Improved confidence intervals for nonlinear mixed-effects and nonparametric regression models

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ANNALS OF THE INSTITUTE OF STATISTICAL MATHEMATICS 2025年第1期77卷 105-126页

作者： Zheng, Nan Cadigan, Noel Mem Univ Newfoundland Dept Math & Stat St John NF A1C 5S7 Canada Mem Univ Newfoundland Fisheries & Marine Inst Ctr Fisheries Ecosyst Res St John NF A1C 5R3 Canada

Statistical inference for high-dimensional parameters (HDPs) can leverage their intrinsic correlations, as spatially or temporally close parameters tend to have similar values. This is why nonlinear mixed-effects models (NMMs) are commonly used for HDPs. Conversely, in many practical applications, the random effects (REs) in NMMs are correlated HDPs that should remain constant during repeated sampling for frequentist inference. In both scenarios, the inference should be conditional on REs, instead of marginal inference by integrating out REs. We summarize recent theory of conditional inference for NMM, and then propose a bias-corrected RE predictor and confidence interval (CI). We also extend this methodology to accommodate the case where some REs are not associated with data. Simulation studies indicate our new approach leads to substantial improvement in the conditional coverage rate of RE CIs, including CIs for smooth functions in generalized additive models, compared to the existing method based on marginal inference.

关键词： Confidence interval Nonlinear mixed-effects model Prediction error State-space model generalized additive model Template model builder

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Spatial distributions, driving factors, and threshold effects of soil organic carbon stocks in the Tibetan Plateau

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SOIL & TILLAGE RESEARCH 2025年 248卷

作者： Sun, Zheng Liu, Feng Yang, Fei Wang, Decai Zhang, Gan-Lin Chinese Acad Sci Inst Soil Sci State Key Lab Soil & Sustainable Agr Nanjing 211135 Peoples R China Henan Agr Univ Coll Forestry Zhengzhou 450002 Peoples R China Nanjing Hydraul Res Inst Natl Key Lab Water Disaster Prevent Nanjing 210029 Peoples R China Nanjing Hydraul Res Inst Ctr Ecoenvironm Res Nanjing 210029 Peoples R China Univ Chinese Acad Sci Beijing 100049 Peoples R China Qinghai Normal Univ Sch Geog Sci Key Lab Phys Geog & Environm Proc Qinghai Prov Xining 312366 Peoples R China Chinese Acad Sci Nanjing Inst Geog & Limnol Key Lab Watershed Geog Sci Nanjing 210008 Peoples R China

The Tibetan Plateau (TP), known as the "Earth's Third Pole", has a fragile ecological environment, and is sensitive to global changes, which can easily lead to fluctuations of soil organic carbon (SOC). The spatial variations of soil organic carbon stocks (SOCS), and their driving factors in TP remain unclear. Here. we used quantile regression forest (QRF) model to map soil organic carbon density (SOCD) in TP at 90 m spatial resolution, and estimated the spatial uncertainty of the mapping. generalized additive model (GAM) was used to analyze the nonlinear responses of SOCD to the driving factors. The results showed that the QRF model can explain about 32 %-51 % of SOCD variation, and the explanatory power decreased with increasing depth. The SOCD decreased gradually from southeast to northwest, and showed a decreasing trend with increasing depth. The SOCS of 0-100 cm soil was 37.26 Pg C of the entire TP, where the grassland occupied 54.59 % of the total stock. Vegetation and land surface temperature were important environmental covariates at all depths. SOCD has obvious nonlinear responses and threshold effects on temperature (MAAT), precipitation (MAP) and aridity (1-AI). The results are of great significance for understanding the status of SOC sequestration, and the response of SOCS in TP to climate conditions.

关键词： Digital soil mapping Carbon pools Quantile regression forest generalized additive model

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A statistical framework for district energy long-term electric load forecasting

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APPLIED ENERGY 2025年 384卷

作者： Royal, Emily Bandyopadhyay, Soutir Newman, Alexandra Huang, Qiuhua Tabares-Velasco, Paulo Cesar Colorado Sch Mines Dept Elect Engn 1500 Illinois St Golden CO 80401 USA Colorado Sch Mines Dept Appl Math & Stat 1500 Illinois St Golden CO 80401 USA Colorado Sch Mines Dept Mech Engn 1500 Illinois St Golden CO 80401 USA

An accurate forecast of electric demand is essential for the optimal design of a generation system. For district installations, the projected lifespan may extend one or two decades. The reliance on a single-year forecast, combined with a fixed load growth rate, is the current industry standard, but does not support a multi-decade investment. Existing work on long-term forecasting focuses on annual growth rate and/or uses time resolution that is coarser than hourly. To address the gap, we propose multiple statistical forecast models, verified over as long as an 11-year horizon. Combining demand data, weather data, and occupancy trends results in a hybrid statistical model, i.e., generalized additive model (GAM) with a seasonal autoregressive integrated moving average (SARIMA) of the GAM residuals, a multiple linear regression (MLR) model, and a GAM with ARIMA errors model. We evaluate accuracy based on: (i) annual growth rates of monthly peak loads;(ii) annual growth rates of overall energy consumption;(iii) preservation of daily, weekly, and month-to-month trends that occur within each year, known as the "seasonality"of the data;and, (iv) realistic representation of demand fora full range of weather and occupancy conditions. For example, the models yield an 11-year forecast from a one-year training data set with a normalized root mean square error of 9.091%, a six-year forecast from a one-year training data set with a normalized root mean square error of 8.949%, and a one-year forecast from a 1.2-year training data set with a normalized root mean square error of 6.765%.

关键词： Electric demand forecasting District energy Renewable energy technologies Long-term load forecasting generalized additive model SARIMA

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