NONPARAMETRIC ESTIMATION AND TESTING OF INTERACTION IN ADDITIVE 
MODELS

We consider an additive model with second-order interaction terms. Both marginal integration estimators and a combined backfitting-integration estimator are proposed for all components of the model and their derivatives. The corresponding asymptotic distributions are derived. Moreover, two test statistics for testing the presence of interactions are proposed. Asymptotics for the test functions and local power results are obtained. Because direct implementation of the test procedure based on the asymptotics would produce inaccurate results unless the number of observations is very large, a bootstrap procedure is provided, which is applicable for small or moderate sample sizes. Further, based on these methods a general test for additivity is developed. Estimation and testing methods are shown to work well in simulation studies. Finally, our methods are illustrated on a five-dimensional production function for a set of Wisconsin farm data. In particular, the separability hypothesis for the production function is discussed.

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Predicting Malaria Transmission Dynamics in Dangassa, Mali: A Novel Approach Using Functional Generalized Additive Models

International Journal of Environmental Research and Public Health ◽

10.3390/ijerph17176339 ◽

2020 ◽

Vol 17 (17) ◽

pp. 6339

Author(s):

François Freddy Ateba ◽

Manuel Febrero-Bande ◽

Issaka Sagara ◽

Nafomon Sogoba ◽

Mahamoudou Touré ◽

...

Keyword(s):

Wind Speed ◽

Malaria Incidence ◽

Generalized Additive Models ◽

Community Health Center ◽

Additive Model ◽

Additive Models ◽

Functional Regression ◽

Novel Approach ◽

Malaria Incidence Rate ◽

Mean Wind Speed

Mali aims to reach the pre-elimination stage of malaria by the next decade. This study used functional regression models to predict the incidence of malaria as a function of past meteorological patterns to better prevent and to act proactively against impending malaria outbreaks. All data were collected over a five-year period (2012–2017) from 1400 persons who sought treatment at Dangassa’s community health center. Rainfall, temperature, humidity, and wind speed variables were collected. Functional Generalized Spectral Additive Model (FGSAM), Functional Generalized Linear Model (FGLM), and Functional Generalized Kernel Additive Model (FGKAM) were used to predict malaria incidence as a function of the pattern of meteorological indicators over a continuum of the 18 weeks preceding the week of interest. Their respective outcomes were compared in terms of predictive abilities. The results showed that (1) the highest malaria incidence rate occurred in the village 10 to 12 weeks after we observed a pattern of air humidity levels >65%, combined with two or more consecutive rain episodes and a mean wind speed <1.8 m/s; (2) among the three models, the FGLM obtained the best results in terms of prediction; and (3) FGSAM was shown to be a good compromise between FGLM and FGKAM in terms of flexibility and simplicity. The models showed that some meteorological conditions may provide a basis for detection of future outbreaks of malaria. The models developed in this paper are useful for implementing preventive strategies using past meteorological and past malaria incidence.

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Principal component regression in GAMLSS applied to Greek–German government bond yield spreads

Statistical Modelling ◽

10.1177/1471082x211022980 ◽

2021 ◽

pp. 1471082X2110229

Author(s):

D. Stasinopoulos Mikis ◽

A. Rigby Robert ◽

Georgikopoulos Nikolaos ◽

De Bastiani Fernanda

Keyword(s):

Additive Model ◽

Principal Component Regression ◽

Principal Component ◽

Complex Nature ◽

Government Bond ◽

German Government ◽

Yield Spreads ◽

Explanatory Variables ◽

Interaction Terms ◽

Bond Yield

A solution to the problem of having to deal with a large number of interrelated explanatory variables within a generalized additive model for location, scale and shape (GAMLSS) is given here using as an example the Greek–German government bond yield spreads from 25 April 2005 to 31 March 2010. Those were turbulent financial years, and in order to capture the spreads behaviour, a model has to be able to deal with the complex nature of the financial indicators used to predict the spreads. Fitting a model, using principal components regression of both main and first order interaction terms, for all the parameters of the assumed distribution of the response variable seems to produce promising results.

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ADDITIVE-VETO MODELS FOR CHOICE AND RANKING MULTICRITERIA DECISION PROBLEMS

Asia Pacific Journal of Operational Research ◽

10.1142/s0217595913500267 ◽

2013 ◽

Vol 30 (06) ◽

pp. 1350026 ◽

Cited By ~ 11

Author(s):

ADIEL TEIXEIRA DE ALMEIDA

Keyword(s):

High Performance ◽

Additive Model ◽

Additive Models ◽

Numerical Application ◽

Multicriteria Decision ◽

Decision Methods ◽

Overall Evaluation ◽

Low Performance ◽

Ranking Problems ◽

Multicriteria Decision Problems

Using additive models for aggregation of criteria is an important procedure in many multicriteria decision methods. This compensatory approach, which scores the alternatives straightforwardly, may have significant drawbacks. For instance, the Decision Maker (DM) may prefer not to select alternatives which have a very low performance in whatever criterion. In contrast, such an alternative may have the best overall evaluation, since the additive model may compensate this low performance in one of the criteria as a result of high performance in other criteria. Thus, additive-veto models are proposed with a view to considering the possibility of vetoing alternatives in such situations, particularly for choice and ranking problems. A numerical application illustrates the use of such models, with a detailed discussion related to real practical problems. Moreover, the results obtained from a numerical simulation show that it is not so rare for a veto of the best alternative to occur in the additive model. This is of considerable relevance depending on the DM's preference structure.

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A generalized additive model-based data-driven solution for lithium-ion battery capacity prediction and local effects analysis

Transactions of the Institute of Measurement and Control ◽

10.1177/01423312211057981 ◽

2021 ◽

pp. 014233122110579

Author(s):

Tao Chen ◽

Ciwei Gao ◽

Hongxun Hui ◽

Qiushi Cui ◽

Huan Long

Keyword(s):

Energy Storage ◽

Lithium Ion Battery ◽

Lithium Ion ◽

Additive Models ◽

Data Driven ◽

Local Effects ◽

Interaction Terms ◽

Battery Capacity ◽

Formulation Parameters ◽

Capacity Prediction

Lithium-ion battery-based energy storage systems have been widely utilized in many applications such as transportation electrification and smart grids. As a key health status indicator, battery performance would highly rely on its capacity, which is easily influenced by various electrode formulation parameters within a battery. Due to the strongly coupled electrical, chemical, thermal dynamics, predicting battery capacity, and analysing the local effects of interested parameters within battery is significantly important but challenging. This article proposes an effective data-driven method to achieve effective battery capacity prediction, as well as local effects analysis. The solution is derived by using generalized additive models (GAM) with different interaction terms. Comparison study illustrate that the proposed GAM-based solution is capable of not only performing satisfactory battery capacity predictions but also quantifying the local effects of five important battery electrode formulation parameters as well as their interaction terms. Due to data-driven nature and explainability, the proposed method could benefit battery capacity prediction in an efficient manner and facilitate battery control for many other energy storage system applications.

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p.Arg72Pro polymorphism of P53 and Breast Cancer Risk: A meta-analysis of case-control studies

10.21203/rs.2.18400/v3 ◽

2020 ◽

Author(s):

Brehima Diakite ◽

Yaya Kassogue ◽

Guimogo Dolo ◽

Jun Wang ◽

Erin Neuschler ◽

...

Keyword(s):

Breast Cancer ◽

Breast Cancer Risk ◽

Cancer Risk ◽

Meta Analysis ◽

Additive Model ◽

P53 Gene ◽

Case Control ◽

Additive Models ◽

Case Control Studies ◽

Genotype Frequencies

Abstract Background :The effect of the p.Arg72Pro variant of the P53 gene on the risk of developmentof breast cancer remains variable in populations. However, the use of strategiessuchas pooling age-matched controls with disease cases may provide a solid meta-analysis. Our goal was to perform a meta-analysis in order to assessthe association of p.Arg72Provariant of P53 gene with breast cancer risk. Methods : Databases such as PubMed, Genetics Medical Literature, Harvard University Library, Web of Science and Genesis Library were used to search articles. Age-matched case-control studies on breast cancer that have evaluated the genotype frequencies of the p.Arg72Pro of P53 gene were selected. The fixed and random effects (Mantel-Haenszel) were calculated using pooled odds ratio of 95% CI to determine the risk of disease. Inconsistency was calculated to determine heterogeneity among the studies. The publication bias was estimated using the funnel plot. Results : Twenty-one publications with cases age-matched controls including7841disease cases and 8876controls were evaluated in this meta-analysis. Overall, our results suggested that p.Arg72ProP53 was associated with a risk for breast cancer for the dominant model (OR= 1.09, 95% CI = 1.02-1.16; P= 0.01) and the additive model (OR= 1.09, 95% CI = 1.01-1.17; P= 0.03), but not in the recessive model (OR = 1.07, 95% CI = 0.97-1.16; P= 0.19). According to the ethnic group, allele Pro has been associated with breast cancer risk in Europeans for the dominant and additive models. Conclusions : This meta-analysis found a significant association between p.Arg72Pro in the P53 gene and the risk of breast cancer. Individuals carrying at least one Pro allele of the P53 gene are more likely to have breast cancer with dominant and additive models than individualsharboringthe Arg allele.

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Experimental Design for Optimization of Orthogonal Projection Pursuit Models

Proceedings of the AAAI Conference on Artificial Intelligence ◽

10.1609/aaai.v34i06.6585 ◽

2020 ◽

Vol 34 (06) ◽

pp. 10235-10242

Author(s):

Mojmir Mutny ◽

Johannes Kirschner ◽

Andreas Krause

Keyword(s):

Experimental Design ◽

Orthogonal Projection ◽

Optimization Problems ◽

Additive Model ◽

Projection Pursuit ◽

Parameter Tuning ◽

Additive Models ◽

Function Optimization ◽

Bayesian Optimization ◽

Additive Structure

Bayesian optimization and kernelized bandit algorithms are widely used techniques for sequential black box function optimization with applications in parameter tuning, control, robotics among many others. To be effective in high dimensional settings, previous approaches make additional assumptions, for example on low-dimensional subspaces or an additive structure. In this work, we go beyond the additivity assumption and use an orthogonal projection pursuit regression model, which strictly generalizes additive models. We present a two-stage algorithm motivated by experimental design to first decorrelate the additive components. Subsequently, the bandit optimization benefits from the statistically efficient additive model. Our method provably decorrelates the fully additive model and achieves optimal sublinear simple regret in terms of the number of function evaluations. To prove the rotation recovery, we derive novel concentration inequalities for linear regression on subspaces. In addition, we specifically address the issue of acquisition function optimization and present two domain dependent efficient algorithms. We validate the algorithm numerically on synthetic as well as real-world optimization problems.

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Hierarchical generalized additive models: an introduction with mgcv

10.7287/peerj.preprints.27320v1 ◽

2018 ◽

Cited By ~ 1

Author(s):

Eric J Pedersen ◽

David L. Miller ◽

Gavin L. Simpson ◽

Noam Ross

Keyword(s):

Hierarchical Model ◽

Generalized Additive Model ◽

Generalized Additive Models ◽

Additive Model ◽

Additive Models ◽

Complex Structures ◽

Ecological Data ◽

Nonlinear Functional ◽

Functional Relationships ◽

Statistical Issues

In this paper, we discuss an extension to two popular approaches to modelling complex structures in ecological data: the generalized additive model (GAM) and the hierarchical model (HGLM). The hierarchical GAM (HGAM), allows modelling of nonlinear functional relationships between covariates and outcomes where the shape of the function itself varies between different grouping levels. We describe the theoretical connection between these models, HGLMs and GAMs, explain how to model different assumptions about the degree of inter-group variability in functional response, and show how HGAMs can be readily fitted using existing GAM software, the mgcv package in R. We also discuss computational and statistical issues with fitting these models, and demonstrate how to fit HGAMs on example data.

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On the mechanistic foundation and limit of Liebig’s law of the minimum

10.5194/ismc2021-16 ◽

2021 ◽

Author(s):

Jinyun Tang ◽

William Riley

Keyword(s):

Additive Model ◽

Additive Models ◽

Mass Action ◽

Substrate Uptake ◽

Law Of Mass Action ◽

Growth Data ◽

Biological Growth ◽

Elemental Stoichiometry ◽

The Law ◽

Parameter Values

In ecosystem biogeochemistry, Liebig&#8217;s law of the minimum (LLM) is one of the most widely used rules to model and interpret biological growth. Although it is intuitively accepted as being true, its mechanistic foundation has never been clearly presented. We here first show that LLM can be derived from the law of mass action, the state of art theory for modeling biogeochemical reactions. We further show that there are (at least) another two approximations (the synthesizing unit (SU) model and additive model) that are more accurate than LLM in approximating the law of mass action. We then evaluated the LLM, SU, and additive models against growth data of algae and plants. For algae growth, we found all three models are equally accurate, albeit with different parameter values. For plants, LLM failed to accurately model one dataset, and achieved equally good results for other datasets with very different parameters. We also find that LLM does not allow flexible elemental stoichiometry, which is an oft-observed characteristic of plants, when an organism&#8217;s growth is modeled as a function of substrate uptake flux. In summary, we caution the use of LLM for modeling biological growth if one is interested in representing the organisms&#8217; capability in adapting to different nutrient conditions.&#160;&#160;&#160;

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Specification tests for covariance structures in high-dimensional statistical models

Biometrika ◽

10.1093/biomet/asaa073 ◽

2020 ◽

Author(s):

X Guo ◽

C Y Tang

Keyword(s):

Statistical Models ◽

Nuisance Parameter ◽

Additive Model ◽

Covariance Structure ◽

Real Data ◽

Theoretical Development ◽

High Dimensional ◽

Test Statistics ◽

Estimation Errors ◽

The Impact

Summary We consider testing the covariance structure in statistical models. We focus on developing such tests when the random vectors of interest are not directly observable and have to be derived via estimated models. Additionally, the covariance specification may involve extra nuisance parameters which also need to be estimated. In a generic additive model setting, we develop and investigate test statistics based on the maximum discrepancy measure calculated from the residuals. To approximate the distributions of the test statistics under the null hypothesis, new multiplier bootstrap procedures with dedicated adjustments that incorporate the model and nuisance parameter estimation errors are proposed. Our theoretical development elucidates the impact due to the estimation errors with high-dimensional data and demonstrates the validity of our tests. Simulations and real data examples confirm our theory and demonstrate the performance of the proposed tests.

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Estimating the impact of vaccination using age–time-dependent incidence rates of hepatitis B

Epidemiology and Infection ◽

10.1017/s0950268807008692 ◽

2007 ◽

Vol 136 (3) ◽

pp. 341-351 ◽

Cited By ~ 9

Author(s):

N. HENS ◽

M. AERTS ◽

Z. SHKEDY ◽

P. KUNG'U KIMANI ◽

M. KOJOUHOROVA ◽

...

Keyword(s):

Hepatitis B ◽

Generalized Additive Models ◽

Additive Model ◽

Penalized Regression ◽

Incidence Rates ◽

Additive Models ◽

Time Dependent ◽

Model Framework ◽

Penalized Regression Splines ◽

The Impact

SUMMARYThe objective of this study was to model the age–time-dependent incidence of hepatitis B while estimating the impact of vaccination. While stochastic models/time-series have been used before to model hepatitis B cases in the absence of knowledge on the number of susceptibles, this paper proposed using a method that fits into the generalized additive model framework. Generalized additive models with penalized regression splines are used to exploit the underlying continuity of both age and time in a flexible non-parametric way. Based on a unique case notification dataset, we have shown that the implemented immunization programme in Bulgaria resulted in a significant decrease in incidence for infants in their first year of life with 82% (79–84%). Moreover, we have shown that conditional on an assumed baseline susceptibility percentage, a smooth force-of-infection profile can be obtained from which two local maxima were observed at ages 9 and 24 years.

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