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Developments from analysis of variance through to generalized linear models and beyond

ANNALS OF APPLIED BIOLOGY 2014年第1期164卷 11-17页

作者： Payne, R. W. VSN Int Waterhouse 5 Hemel Hempstead HP1 1ES Herts England Rothamsted Res Harpenden Herts England

The collaborations between statisticians and biologists during the 100years since AAB was founded have led to a very impressive list of statistical techniques, whose use now goes well beyond agriculture and biology. One example is the maximum likelihood methodology for probit analysis, arising from the collaboration between Sir Ronald Fisher and Chester Bliss. Others include analysis of variance, design of experiments, generalized linear models and the residual, or restricted, maximum likelihood (REML) algorithm for fitting unbalanced linear mixed models.

关键词： Analysis of variance design of experiments generalized linear mixed models generalized linear models hierarchical generalized linear models probit analysis QTL REML t-test variance components

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generalized matrix factorization: efficient algorithms for fitting generalized linear latent variable models to large data arrays

The Journal of Machine Learning Research

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The Journal of Machine Learning Research 2022年第1期23卷 13211-13239页

作者： Łukasz Kidziński Francis K.C. Hui David I. Warton Trevor J. Hastie Department of Bioengineering Stanford University Stanford CA Research School of Finance Actuarial Studies and Statistics The Australian National University Canberra ACT Australia School of Mathematics and Statistics and Evolution & Ecology Research Centre The University of New South Wales Sydney NSW Australia Department of Statistics and Biomedical Data Science Stanford University Stanford CA

Unmeasured or latent variables are often the cause of correlations between multivariate measurements, which are studied in a variety of fields such as psychology, ecology, and medicine. For Gaussian measurements, there are classical tools such as factor analysis or principal component analysis with a well-established theory and fast algorithms. generalized linear Latent Variable models (GLLVMs) generalize such factor models to non-Gaussian responses. However, current algorithms for estimating model parameters in GLLVMs require intensive computation and do not scale to large data sets with thousands of observational units or responses. In this article, we propose a new approach for fitting GLLVMs to high-dimensional data sets, based on approximating the model using penalized quasi-likelihood and then using a Newton method and Fisher scoring to learn the model parameters. Computationally, our method is noticeably faster and more stable, enabling GLLVM fits to much larger matrices than previously possible. We apply our method on a data set of 48,000 observational units with over 2,000 observed species in each unit and find that most of the variability can be explained with a handful of factors. We publish an easy-to-use implementation of our proposed fitting algorithms.

关键词： generalized linear models generalized linear mixed-effect models nuclear norm penalized quasi-likelihood

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generalized Matrix Factorization: efficient algorithms for fitting generalized linear latent variable models to large data arrays

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JOURNAL OF MACHINE LEARNING RESEARCH 2022年 23卷

作者： Kidzinski, Lukasz Hui, Francis K. C. Warton, David I. Hastie, Trevor J. Stanford Univ Dept Bioengn Stanford CA 94305 USA Australian Natl Univ Res Sch Finance Actuarial Studies & Stat Canberra ACT 2601 Australia Univ New South Wales Sch Math & Stat Sydney NSW 2052 Australia Univ New South Wales Evolut & Ecol Res Ctr Sydney NSW 2052 Australia Stanford Univ Dept Stat & Biomed Data Sci Stanford CA 94305 USA

Unmeasured or latent variables are often the cause of correlations between multivariate measurements, which are studied in a variety of fields such as psychology, ecology, and medicine. For Gaussian measurements, there are classical tools such as factor analy-sis or principal component analysis with a well-established theory and fast algorithms. generalized linear Latent Variable models (GLLVMs) generalize such factor models to non-Gaussian responses. However, current algorithms for estimating model parameters in GLLVMs require intensive computation and do not scale to large data sets with thousands of observational units or responses. In this article, we propose a new approach for fitting GLLVMs to high-dimensional data sets, based on approximating the model using penalized quasi-likelihood and then using a Newton method and Fisher scoring to learn the model parameters. Computationally, our method is noticeably faster and more stable, enabling GLLVM fits to much larger matrices than previously possible. We apply our method on a data set of 48,000 observational units with over 2,000 observed species in each unit and find that most of the variability can be explained with a handful of factors. We publish an easy-to-use implementation of our proposed fitting algorithms.

关键词： generalized linear models generalized linear Mixed-effect models Nuclear Norm Penalized Quasi-Likelihood

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Improved likelihood inference in generalized linear models

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COMPUTATIONAL STATISTICS & DATA ANALYSIS 2014年第0期74卷 110-124页

作者： Vargas, Tiago M. Ferrari, Silvia L. P. Lemonte, Artur J. Univ Sao Paulo Dept Estat Sao Paulo Brazil Univ Fed Pernambuco Dept Estat Recife PE Brazil

We address the issue of performing testing inference in generalized linear models when the sample size is small. This class of models provides a straightforward way of modeling normal and non-normal data and has been widely used in several practical situations. The likelihood ratio, Wald and score statistics, and the recently proposed gradient statistic provide the basis for testing inference on the parameters in these models. We focus on the small-sample case, where the reference chi-squared distribution gives a poor approximation to the true null distribution of these test statistics. We derive a general Bartlett-type correction factor in matrix notation for the gradient test which reduces the size distortion of the test, and numerically compare the proposed test with the usual likelihood ratio, Wald, score and gradient tests, and with the Bartlett-corrected likelihood ratio and score tests, and bootstrap-corrected tests. Our simulation results suggest that the corrected test we propose can be an interesting alternative to the other tests since it leads to very accurate inference even for very small samples. We also present an empirical application for illustrative purposes(1) (C) 2014 Elsevier B.V. All rights reserved.

关键词： Bartlett correction Bootstrap generalized linear models Gradient statistic Likelihood ratio statistic Score statistic Bartlett-type correction Wald statistic

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Cross-realm transferability of species distribution models-Species characteristics and prevalence matter more than modelling methods applied

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ECOLOGICAL MODELLING 2025年 499卷

作者： Takolander, Antti Forsblom, Louise Hellsten, Seppo Ilmonen, Jari Jokinen, Ari-Pekka Kallio, Niko Koponen, Sampsa Vakeva, Sakari Virtanen, Elina Finnish Environm Inst Syke Latokartanonkaari 11 Helsinki 00790 Finland Metsahallitus Akselinkatu 8 Savonlinna 57130 Finland

Species Distribution models (SDMs) are frequently applied in ecological research, but geographic transferability of SDMs holds major uncertainties. Here, we assess the cross-realm (sea to lake) geographic transferability of four SDM methods: generalized linear models (GLMs), generalized Additive models (GAMs), Boosted Regression Trees (BRTs), and Bayesian Additive Regression Trees (BARTs) predicting occurrences of freshwater macrophytes from brackish water sea area (Bothnian Bay) to a freshwater lake environment in Finland. We found that the SDM method applied did not affect model transferability, and majority of the variation in transferability performance was associated with species. For most species model transferability was low, but reasonably good on one third of the species modelled, which had similar prevalences in both marine and freshwater data. These were emergent species or species growing close to shoreline, which presumably share similar environmental niche in terms of growing depth and water turbidity between the two environments. Generally, models which had high interpolation performance, also had higher transferability, but this relationship was not dependent on the SDM method applied. Our results suggest that species prevalence and species-specific characteristics, such as growth form, life history traits and ecological niche, are main contributors to geographic transferability of SDMs.

关键词： Species distribution models Macrophytes Model extrapolation Geographic transferability Spatial modelling Prevalence generalized linear models generalized additive models Boosted regression trees Bayesian additive regression trees

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Modeling and analyzing semiconductor yield with generalized linear mixed models

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APPLIED STOCHASTIC models IN BUSINESS AND INDUSTRY 2014年第6期30卷 691-707页

作者： Krueger, D. C. Montgomery, D. C. Kansas State Univ Manhattan KS 66506 USA Arizona State Univ Sch Comp Informat & Decis Syst Engn Tempe AZ 85287 USA

As the challenges and opportunities of using big data' expand, there is a need to explore different ways of analyzing large datasets. The semiconductor industry is a good example of a manufacturing process where many data are collected throughout the fabrication of the product. These massive datasets are used for various purposes, primarily to detect problems and determine root causes, control the process, and build models that predict yield. The yield predictions are used for process planning, optimization, and control. However, many current approaches to yield modeling are limited because the actual processes violate the model assumptions, limiting the power of the models' *** paper explores the use of generalized linear mixed models (GLMMs) to predict semiconductor yield and to provide significant information about the process using a large semiconductor yield dataset. Both batch-specific and population-averaged GLMM approaches are used and compared. Differences in link functions, sample sizes, and levels of aggregation (die-level and wafer-level models) are also compared with each other and with the results from generalized linear models (GLMs).The results of this study show that GLMMs are a reasonable approach to analyzing large datasets by providing additional insight into the fabrication process while maintaining or even improving prediction power compared with GLMs and some prior yield models found in the literature. This paper also provides a modeling strategy through suggestions regarding level of aggregation, link function, and sample size that are appropriate for different research goals. Copyright (c) 2014 John Wiley & Sons, Ltd.

关键词： semiconductor yield modeling generalized linear mixed models generalized linear models GLMM GLM big data

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Selective Inference with Distributed Data

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JOURNAL OF MACHINE LEARNING RESEARCH 2025年第12期26卷 1-44页

作者： Liu, Sifan Panigrahi, Snigdha Stanford Univ Dept Stat Stanford CA 94305 USA Univ Michigan Dept Stat Ann Arbor MI 48109 USA

When data are distributed across multiple sites or machines rather than centralized in one location, researchers face the challenge of extracting meaningful information without directly sharing individual data points. While there are many distributed methods for point estimation using sparse regression, few options are available for estimating uncertainties or conducting hypothesis tests based on the estimated sparsity. In this paper, we introduce a procedure for performing selective inference with distributed data. We consider a scenario where each local machine solves a lasso problem and communicates the selected predictors to a central machine. The central machine then aggregates these selected predictors to form a generalized linear model (GLM). Our goal is to provide valid inference for the selected GLM while reusing data that have been used in the model selection process. Our proposed procedure only requires low- dimensional summary statistics from local machines, thus keeping communication costs low and preserving the privacy of individual data sets. Furthermore, this procedure can be applied in scenarios where model selection is repeatedly conducted on randomly sub- sampled data sets, addressing the p-value lottery problem linked with model selection. We demonstrate the effectiveness of our approach through simulations and an analysis of a medical data set on ICU admissions.

关键词： carving data aggregation generalized linear models lasso post-selection inference selective inference selective likelihood

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Robust tests in generalized linear models with missing responses

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COMPUTATIONAL STATISTICS & DATA ANALYSIS 2013年 65卷 80-97页

作者： Bianco, Ana M. Boente, Graciela Rodrigues, Isabel M. Univ Buenos Aires Fac Ciencias Exactas & Nat RA-1053 Buenos Aires DF Argentina Consejo Nacl Invest Cient & Tecn RA-1033 Buenos Aires DF Argentina Tech Univ Lisbon TULisbon Dept Matemat Inst Super Tecn Lisbon Portugal Tech Univ Lisbon TULisbon CEMAT Inst Super Tecn Lisbon Portugal

In many situations, data follow a generalized linear model in which the mean of the responses is modelled, through a link function, linearly on the covariates. Robust estimators for the regression parameter in order to build test statistics for this parameter, when missing data occur in the responses, are considered. The asymptotic behaviour of the robust estimators for the regression parameter is obtained, under the null hypothesis and under contiguous alternatives. This allows us to derive the asymptotic distribution of the robust Wald-type test statistics constructed from the proposed estimators. The influence function of the test statistics is also studied. A simulation study allows us to compare the behaviour of the classical and robust tests, under different contamination schemes. Applications to real data sets enable to investigate the sensitivity of the p-value to the missing scheme and to the presence of outliers. (C) 2012 Elsevier B.V. All rights reserved.

关键词： Fisher-consistency generalized linear models Influence function Missing data Outliers Robust estimation Robust testing

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Temporal trends in estuarine-resident fishes: Functional traits and responses to environmental and climatic variability

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MARINE ENVIRONMENTAL RESEARCH 2025年 205卷 107019页

作者： Escamade, Nuno Mussa M. U. Lemos, Valeria Marques Garcia, Alexandre Miranda Fed Univ Rio Grande FURG Inst Oceanog Lab Ichthyol Ave Italia S-N Km 8 Rio Grande Brazil

Extreme climatic events, such as El Nino, are becoming increasingly intense and frequent, driving hydrodynamic changes in estuaries and significantly affecting their structure and biodiversity. Using long-term data (22 years) obtained from standardized surveys, we analyzed the abundance of three estuarine-resident species (Atherinella brasiliensis, Jenynsia lineata, Ctenogobius shufeldti) with distinct functional traits (related to reproductive strategy, feeding, and habitat use) and their relationships with local, regional, and climatic environmental factors in a subtropical estuary. We investigated the following hypotheses: (i) there is a long-term declining trend in the abundance of these estuarine-resident species;(ii) reductions in their abundance are associated with El Nino events;(iii) the abundance of species with different functional traits responds similarly to the effects of El Nino events. The analysis revealed a consistent decline in the abundance of all three estuarine-resident species, driven by local and regional factors and climatic variations, despite differences in their functional traits. generalized linear models showed that El Nino events impact species in distinct ways, with more pronounced effects on oviparous species (A. brasiliensis and C. shufeldti) compared to viviparous ones (J. lineata). These findings provide empirical evidence of decadal changes decline in the abundance of estuarine-resident fishes regardless of their distinct functional traits, raising concerns to the conservation of ecological functions and ecosystem services in subtropical estuaries under increasing anthropogenic and climatic pressures.

关键词： Climatic impacts Abundance generalized linear models Patos lagoon estuary B-LTER El Nino

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Simultaneous Optimization of Robust Parameter and Tolerance Design Based on generalized linear models

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QUALITY AND RELIABILITY ENGINEERING INTERNATIONAL 2013年第8期29卷 1107-1115页

作者： Shen, Lijuan Yang, Jun Zhao, Yu Beihang Univ Sch Reliabil & Syst Engn Beijing 100191 Peoples R China China Elect Power Res Inst Beijing 100192 Peoples R China

Robust parameter design (RPD) and tolerance design (TD) are two important stages in design process for quality improvement. Simultaneous optimization of RPD and TD is well established on the basis of linear models with constant variance assumption. However, little attention has been paid to RPD and TD with non-constant variance of residuals or non-normal responses. In order to obtain further quality improvement and cost reduction, a hybrid approach for simultaneous optimization of RPD and TD with non-constant variance or non-normal responses is proposed from generalized linear models (GLMs). First, the mathematical relationship among the process mean, process variance and control factors, noise factors and tolerances is derived from a dual-response approach based on GLMs, and the quality loss function integrating with tolerance is developed. Second, the total cost model for RPD-TD concurrent optimization based on GLMs is proposed to determine the best control factors settings and the optimal tolerance values synchronously, which is solved by genetic algorithm in detail. Finally, the proposed approach is applied into an example of electronic circuit design with non-constant variance, and the results show that the proposed approach performs better on quality improvement and cost reduction. Copyright (c) 2012 John Wiley & Sons, Ltd.

关键词： robust parameter design tolerance design simultaneous optimization generalized linear models genetic algorithm

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