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Joint distribution and marginal distribution methods for checking assumptions of generalized linear model

COMMUNICATIONS IN STATISTICS-THEORY AND METHODS 2021年第6期50卷 1456-1476页

作者： Dong, Junyi Yu, Qiqing St Ambrose Univ Math & Stat Dept Davenport IA USA SUNY Binghamton Dept Math Sci Binghamton NY 13902 USA

In this article, we consider the model diagnostic plot and test of the generalized linear model. There exist several commonly used plotting methods and tests for checking the regression model assumptions. However, the existing plots and tests require certain constraints on the joint cumulative distribution function of the response variable Y and the covariate Z and thus are invalid when the real data set does not satisfy those constraints. In particular, in the latter case, the p-values provided by these tests are false. In this article, we propose a new method to check the model assumptions. This method compares two estimators of the marginal distribution of Y (or the joint distribution of (Y, Z)): one is the non-parametric maximum likelihood estimator and the other is an estimator based on the null hypothesis. This method is called the marginal distribution (MD) method or the joint distribution (JD) method. Their asymptotic properties are studied. The simulation results suggest both the diagnostic plots and the hypothesis tests using the new methods provide satisfactory results and the JD method is always consistent even when the existing methods fail.

关键词： generalized linear models joint distribution marginal distribution diagnostic plotting hypothesis testing

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SuRF: A new method for sparse variable selection, with application in microbiome data analysis

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STATISTICS IN MEDICINE 2021年第4期40卷 897-919页

作者： Liu, Lihui Gu, Hong Van Limbergen, Johan Kenney, Toby Dalhousie Univ Dept Math & Stat Halifax NS Canada Dalhousie Univ Dept Pediat Halifax NS Canada

In this article, we present a new variable selection method for regression and classification purposes, particularly for microbiome analysis. Our method, called subsampling ranking forward selection (SuRF), is based on LASSO penalized regression, subsampling and forward-selection methods. SuRF offers major advantages over existing variable selection methods in terms of both sparsity of selected models and model inference. We provide an R package that can implement our method for generalized linear models. We apply our method to classification problems from microbiome data, using a novel agglomeration approach to deal with the special tree-like correlation structure of the variables. Existing methods arbitrarily choose a taxonomic level a priori before performing the analysis, whereas by combining SuRF with these aggregated variables, we are able to identify the key biomarkers at the appropriate taxonomic level, as suggested by the data. We present simulations in multiple sparse settings to demonstrate that our approach performs better than several other popularly used existing approaches in recovering the true variables. We apply SuRF to two microbiome datasets: one about prediction of pouchitis and another for identifying samples from two healthy individuals. We find that SuRF can provide a better or comparable prediction with other methods while controlling the false positive rate of variable selection.

关键词： forward selection generalized linear models identifying biomarkers LASSO microbiome stability selection SuRF variable selection

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Online stochastic gradient descent on non-convex losses from high-dimensional inference

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JOURNAL OF MACHINE LEARNING RESEARCH 2021年第1期22卷 1-51页

作者： Ben Arous, Gerard Gheissari, Reza Jagannath, Aukosh NYU Courant Inst Math Sci New York NY 10012 USA Univ Calif Berkeley Dept Stat Berkeley CA 94720 USA Univ Calif Berkeley Dept EECS Berkeley CA 94720 USA Univ Waterloo Dept Stat Waterloo ON Canada Univ Waterloo Dept Actuarial Sci & Appl Math Waterloo ON Canada

Stochastic gradient descent (SGD) is a popular algorithm for optimization problems arising in high-dimensional inference tasks. Here one produces an estimator of an unknown parameter from independent samples of data by iteratively optimizing a loss function. This loss function is random and often non-convex. We study the performance of the simplest version of SGD, namely online SGD, from a random start in the setting where the parameter space is high-dimensional. We develop nearly sharp thresholds for the number of samples needed for consistent estimation as one varies the dimension. Our thresholds depend only on an intrinsic property of the population loss which we call the information exponent. In particular, our results do not assume uniform control on the loss itself, such as convexity or uniform derivative bounds. The thresholds we obtain are polynomial in the dimension and the precise exponent depends explicitly on the information exponent. As a consequence of our results, we find that except for the simplest tasks, almost all of the data is used simply in the initial search phase to obtain non-trivial correlation with the ground truth. Upon attaining non-trivial correlation, the descent is rapid and exhibits law of large numbers type behavior. We illustrate our approach by applying it to a wide set of inference tasks such as phase retrieval, and parameter estimation for generalized linear models, online PCA, and spiked tensor models, as well as to supervised learning for single-layer networks with general activation functions.

关键词： stochastic gradient descent parameter estimation non-convex optimization supervised learning generalized linear models tensor PCA

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Prediction and model-assisted estimation of diameter distributions using Norwegian national forest inventory and airborne laser scanning data

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CANADIAN JOURNAL OF FOREST RESEARCH 2021年第10期51卷 1521-1533页

作者： Raty, Janne Astrup, Rasmus Breidenbach, Johannes Norwegian Inst Bioecon Res NIBIO Div Forest & Forest Resources Natl Forest Inventory Hogskoleveien 8 N-1433 As Norway

Diameter at breast height (DBH) distributions offer valuable information for operational and strategic forest management decisions. We predicted DBH distributions using Norwegian national forest inventory and airborne laser scanning data and compared the predictive performances of linear mixed-effects (PPM), generalized linear-mixed (GLM), and k nearest-neighbor (NN) models. While GLM resulted in smaller prediction errors than PPM, both were clearly outperformed by NN. We therefore studied the ability of the NN model to improve the precision of stem frequency estimates by DBH classes in the 8.7 Mha study area using a model-assisted (MA) estimator suitable for systematic sampling. MA estimates yielded greater than or approximately equal efficiencies as direct estimates using field data only. The relative efficiencies (REs) associated with the MA estimates ranged between 0.95-1.47 and 0.96-1.67 for 2 and 6 cm DBH class widths, respectively, when dominant tree species were assumed to be known. The use of a predicted tree species map, instead of the observed information, decreased the REs by up to 10%.

关键词： generalized linear models linear mixed-effects models most similar neighbor approach number of stems systematic sampling

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Prediction of body weight of Curraleiro Pé-Duro cattle based on morphometric measurements

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TROPICAL ANIMAL HEALTH AND PRODUCTION 2024年第1期56卷 42-42页

作者： Rocha-Silva, Merik Britto, Fabio Barros da Silva, Dinnara Layza Souza Oliveira do, Alan O. da Silva, Leiliane Alves Soares de Oliveira, Max Brandao de Araujo, Claudio Vieira Carvalho, Geraldo Magela Cortes Sarmento, Jose Lindenberg Rocha Univ Estadual Piaui Ctr Agr Sci Teresina Piaui Brazil Univ Fed Piaui Anim Sci Dept Teresina Piaui Brazil Univ Fed Piaui Biol Dept Teresina Piaui Brazil Univ Fed Piaui Dept Stat Teresina Piaui Brazil Univ Fed Mato Grosso Anim Sci Dept Sinop Mato Grosso Brazil Empresa Brasileira Pesquisa Agr Teresina Piaui Brazil

Cattle weight development is highly correlated with some body measurements. Based on the relationship between morphometric measurements and body mass, our aim was to develop regression equations to estimate the body weight of Curraleiro Pe-Duro (CPD) cattle to be used in farms that lack access to weighting scales. Data from 1023 animals from four farms on withers height (WH), body length (BL), body score (BS), heart girth (HG), permanent teeth (PT), scrotal perimeter (SP), and live weight were used. The animals were classified into five categories depending on age and/or sex: newborns (NB), calves, weaned animals, cows, and bulls. The best models are GLM with Gamma, Gamma, inverse Gaussian, Gaussian, and Gamma distributions for NB, calves, weaned animals, cows, and bulls, respectively. Predictive modeling for bulls was the best performing overall, with a correlation of 0.97 between the estimated by the model and the obtained with a weighting scale. For NB, calves, weaned animals, and cows, the correlation (r) was 0.85, 0.90, 0.95, and 0.87, respectively. The evaluated models are adequate to be used as a technical solution to estimate weight in a cattle production system.

关键词： Scale Tape measure Gamma generalized linear models StepWise

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Modelling the habitat preferences of the NE-Atlantic Sea cucumber Holothuria forskali: Demographics and abundance

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ECOLOGICAL INFORMATICS 2024年 80卷

作者： Felix, P. M. Azevedo e Silva, F. Simoes, T. Pombo, A. Marques, T. A. Rocha, C. Sousa, J. Venancio, E. Brito, A. C. Univ Lisbon Fac Ciencias MARE Marine & Environm Sci Ctr ARNET Aquat Res Network Lisbon Portugal ARNET Aquat Res Network Polytech Inst Leiria MARE Marine & Environm Sci Ctr ESTM Leiria Portugal Univ Lisbon Fac Ciencias CEAUL Ctr Estat & Aplicac Lisbon Portugal Univ St Andrews Ctr Res Ecol & Environm Modelling The Observatory St Andrews Scotland Univ Lisbon Fac Ciencias Dept Biol Anim Lisbon Portugal Univ Lisbon Fac Ciencias Dept Estat & Invest Operac Lisbon Portugal Univ Lisbon Fac Ciencias Dept Biol Vegetal Lisbon Portugal

Sea cucumbers' historical demand, together with the depletion of several traditional species in the market, has popularized new target species from new fishing grounds. Holothuria forskali is one of those emergent species in the trade market. However, it is a species for which there is no relevant information to allow sustainable stock management. Fundamental knowledge of the populations' structure and habitat preferences are key elements without which any measure is inconsequent. This work aims to fill that gap by modelling temporal and spatial patterns of abundance and demographic structure of this species in a NE -Atlantic area, as a function of environmental features. For a period of 15 months, nine regular sampling campaigns collected data on density, individual length, individual conditions of occurrence (e.g. sheltered, on sand, on algae cover) and environmental parameters (water column, sediment, substrate cover and type), using random transects throughout a costal rocky -reef, considering habitat heterogeneity and substrate types. To determine the species' habitat preferences generalized linear models were used to model density and demographic structure of the species as a function of environmental conditions. The models revealed that the main drivers shaping the distribution of H. forskali are neither abiotic nor biotic parameters of the water column, but physical stressors, like current intensity and depth, and substrate type in a patchy distribution pattern. Estuarine conditions are generally avoided, although with a size -dependent opportunistic strategy. Larger individuals show temporal and spatial displacement patterns towards suitable reproductive conditions (pre -breeding aggregation) and favourable feeding grounds and smaller size -classes tend to aggregate in higher numbers in more stable environments. Sustainable sources for market supply, like aquaculture, are still a long way from commercial production. So, these results are fundamental to supp

关键词： Holothuroidea Density Size -class Distribution patterns Environmental cues generalized linear models Portugal

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Learning latent heterogeneity for type 2 diabetes patients using longitudinal health markers in electronic health records

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STATISTICS IN MEDICINE 2021年第8期40卷 1930-1946页

作者： Lou, Jitong Wang, Yuanjia Li, Lang Zeng, Donglin Univ N Carolina Dept Biostat Chapel Hill NC 27599 USA Columbia Univ Dept Biostat New York NY USA Ohio State Univ Dept Biomed Informat Columbus OH USA

Electronic health records (EHRs) from type 2 diabetes (T2D) patients consist of longitudinally and sparsely measured health markers at clinical encounters. Our goal is to use such data to learn latent patterns that can inform patient's health status related to T2D while accounting for challenges in retrospectively collected EHRs. To handle challenges such as correlated longitudinal measurements, irregular and informative encounter times, and mixed marker types, we propose multivariate generalized linear models to learn latent patient subgroups. In our model, covariate effects were time-dependent and latent Gaussian processes were introduced to model between-marker correlations over time. Using inferred latent processes, we integrated the irregularly measured health markers of mixed types into composite scores and applied hierarchical clustering to learn latent subgroup structures among T2D patients. Application to an EHR dataset of T2D patients showed different trends of age, sex, and race effects on hypertension/high blood pressure, total cholesterol, glycated hemoglobin, high-density lipoprotein, and medications. The associations among these markers varied over time during the study window. Clustering results revealed four subgroups, each with distinct health status. The same patterns were further confirmed using new EHR records of the same cohort. We developed a novel latent model to integrate longitudinal health markers in EHRs and characterize patient latent heterogeneities. Analysis indicated that there were distinct subgroups of T2D patients, suggesting that effective healthcare managements for these patients should be performed separately for each subgroup.

关键词： electronic health records generalized linear models kernel smoothing latent process type 2 diabetes

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Assessment of Regression models With Discrete Outcomes Using Quasi-Empirical Residual Distribution Functions

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JOURNAL OF COMPUTATIONAL AND GRAPHICAL STATISTICS 2021年第4期30卷 1019-1035页

作者： Yang, Lu Univ Minnesota Sch Stat Minneapolis MN 55455 USA

Making informed decisions about model adequacy has been an outstanding issue for regression models with discrete outcomes. Standard assessment tools for such outcomes (e.g., deviance residuals) often show a large discrepancy from the hypothesized pattern even under the true model and are not informative, especially when data are highly discrete (e.g., binary). To fill this gap, we propose a quasi-empirical residual distribution function for general discrete (e.g., ordinal and count) outcomes that serves as an alternative to the empirical distribution function of Cox-Snell residuals. The assessment tool we propose is a principled approach and does not require injecting noise into the data. When at least one continuous covariate is available, we show asymptotically that the proposed function converges uniformly to the identity function under the correctly specified model, even with highly discrete outcomes. Through simulation studies, we demonstrate empirically that the proposed quasi-empirical residual distribution function outperforms commonly used residuals for various model assessment tasks, since it is close to the hypothesized pattern under the true model and significantly departs from this pattern under model misspecification, and is thus an effective assessment tool. for this article are available online.

关键词： Cox-Snell residuals generalized linear models Goodness of fit Insurance claim frequency m-asymptotics

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Drivers and implications of change in an inshore multi-species fishery

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ICES JOURNAL OF MARINE SCIENCE 2021年第5期78卷 1815-1825页

作者： Henly, Lauren Stewart, James E. Simpson, Stephen D. Univ Exeter Coll Life & Environm Sci Hatherly Labs Biosci Prince Wales Rd Exeter EX4 4PS Devon England Brixham Lab Devon & Severn Inshore Fisheries & Conservat Auth Brixham TQ5 8BA England

Inshore fisheries are an important source of employment and income across Europe. However, their sustainability and management efficacy are relatively understudied, particularly in a multispecies context. Management of these data-limited fisheries can be informed by assessments of standardized catch and landings per unit effort (CPUE and LPUE) data from fishery-dependent surveys. We demonstrate the utility of this approach in the first robust assessment of the sustainability and management of a multispecies inshore fishery for live wrasse (Labridae) in southern England. Our findings have wider ramifications for assessment and management of inshore fisheries, including international live wrasse fisheries, many of which are intensely exploited but have less stringent management than the fishery studied here. Using generalized linear models, we identified ecologically relevant drivers of variation in CPUE and LPUE, alongside interspecific variation in responses to fishing pressure during 2017-2019. We also highlight robust evidence of declines in the primary target species, a protogynous hermaphrodite, that are suggestive of fishery impacts driven by management-enabled selective removal of mature females. We demonstrate the need to consider ecologically similar species separately for management purposes, and account for ecogeographical variables in assessments;a failure to do so risks erroneous conclusions regarding inshore fisheries' sustainability.

关键词： generalized linear models Labridae live wrasse fishery multispecies fishery management selective harvesting standardized CPUE standardized LPUE

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Wind power curve modeling: A probabilistic Beta regression approach

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RENEWABLE ENERGY 2024年 223卷

作者： Capelletti, Marco Raimondo, Davide M. De Nicolao, Giuseppe Univ Pavia Dept Elect Comp & Biomed Engn Via A Ferrata5 I-27100 Pavia Italy Fdn IRCCS Policlin San Matteo Div Infect Diseases 1 Viale C Golgi19 I-27100 Pavia Italy

Wind turbine power curves play a key role in various aspects during the life of a wind farm. Typical uses range from wind power forecasting to wind turbine condition monitoring. This paper addresses the identification of probabilistic models of wind power curves from observed data. The main challenge is the need to handle a statistical distribution of wind energy whose shape not only may be highly skewed, but can also change with wind speed. To address these issues, we resort to the framework of generalized linear models (GLMs), proposing a Beta regression approach, with constant or variable dispersion and an appropriate preconditioning step. The proposed methodology was tested on three real SCADA measurements retrieved from public datasets, including a comparison with Quantile Regression Forests (QRFs), also in terms of robustness to outliers. The results suggest that Beta regression can be a valuable resource in the development of probabilistic models for wind energy, as it provides a high degree of flexibility while preserving an interpretable structure.

关键词： Wind turbines Wind power curves Statistical models generalized linear models

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