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A generalized linear mixed models approach for detecting incident clusters of disease in small areas, with an application to biological terrorism

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AMERICAN JOURNAL OF EPIDEMIOLOGY 2004年第3期159卷 217-224页

作者： Kleinman, K Lazarus, R Platt, R Harvard Univ Sch Med Dept Ambulatory Care & Prevent Boston MA 02215 USA Harvard Pilgrim Hlth Care Boston MA USA Harvard Vanguard Med Associates Boston MA USA Ctr Dis Control & Prevent Eastern Massachusetts Prevent Epictr Boston MA USA HMO Res Network Ctr Educ & Res Therapeut Boston MA USA Brigham & Womens Hosp Boston MA 02115 USA Univ Sydney Sch Publ Hlth Sydney NSW 2006 Australia

Since the intentional dissemination of anthrax through the US postal system in the fall of 2001, there has been increased interest in surveillance for detection of biological terrorism. More generally, this could be described as the detection of incident disease clusters. In addition, the advent of affordable and quick geocoding allows for surveillance on a finer spatial scale than has been possible in the past. Surveillance for incident clusters of disease in both time and space is a relatively undeveloped arena of statistical methodology. Surveillance for bioterrorism detection, in particular, raises unique issues with methodological relevance. For example, the bioterrorism agents of greatest concern cause initial symptoms that may be difficult to distinguish from those of naturally occurring disease. In this paper, the authors propose a general approach to evaluating whether observed counts in relatively small areas are larger than would be expected on the basis of a history of naturally occurring disease. They implement the approach using generalized linear mixed models. The approach is illustrated using data on health-care visits (1996-1999) from a large Massachusetts managed care organization/multispecialty practice group in the context of syndromic surveillance for anthrax. The authors argue that there is great value in using the geographic data.

关键词： bioterrorism communicable diseases epidemiologic methods generalized linear mixed model population surveillance spatial analysis

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A MARGINAL QUASI-LIKELIHOOD APPROACH TO THE ANALYSIS OF POISSON VARIABLES WITH generalized linear mixed modelS

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GENETICS SELECTION EVOLUTION 1993年第1期25卷 101-107页

作者： FOULLEY, JL IM, S INRA BIOMETRIE INTELLIGENCE ARTIFICIELLE STNF-31326 CASTANET TOLOSANFRANCE

This paper extends to Poisson variables the approach of Gilmour, Anderson and Rae (1985) for estimating fixed effects by maximum quasi-likelihood in the analysis of threshold discrete data with a generalized linear mi... 详细信息

关键词： DISCRETE VARIABLE POISSON DISTRIBUTION generalized linear mixed model QUASI-LIKELIHOOD

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Using generalized linear mixed models to predict the number of roadway accidents: A case study in Hamilton county, Tennessee

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Open Transportation Journal 2020年 14卷 1-13页

作者： Laflamme, Eric M. Way, Peter Roland, Jeremiah Sartipi, Mina Department of Mathematics Plymouth State University Plymouth NH 03264 United Kingdom College of Engineering and Computer Science University of Tennessee at Chattanooga Chattanooga 37403 TN United States

Introduction: A method for identifying significant predictors of roadway accident counts has been presented. This process is applied to real-world accident data collected from roadways in Hamilton County, TN. Methods: In preprocessing, an aggregation procedure based on segmenting roadways into fixed lengths has been introduced, and then accident counts within each segment have been observed according to predefined weather conditions. Based on the physical roadway characteristics associated with each individual accident record, a collection of roadway features is assigned to each segment. A mixed-effects Negative Binomial regression form is assumed to approximate the relationship between accident counts and several explanatory variables including roadway characteristics, weather conditions, and several interactions between them. Standard diagnostics and a validation procedure show that our model form is properly specified and suitably fits the data. Results: Interpreting interaction terms leads to the follow findings: 1) rural roads with cloudy conditions are associated with relative increases in accident frequency;2) lower/moderate AADT and rainy weather are associated with relative decreases in accident frequency, while high AADT and rain are associated with relative increases in accident frequency;3) higher AADT and wider pavements are associated with relative increases in accident frequency;and 4) higher speed limits in residential areas are associated with relative increases in accident frequency. Conclusion: Results illustrate the complicated relationship between accident frequency and both roadway features and weather. Therefore, it is not sufficient to observe the effects of weather and roadway features independently as these variables interact with one another. © 2020 Laflamme et al.

关键词： Accident frequency model generalized linear mixed model Negative binomial regression Railways Roadway features Weather

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Bayesian inference for generalized linear mixed models of portfolio credit risk

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Journal of Empirical Finance 2007年第2期14卷 131-149页

作者： McNeil, Alexander J. Wendin, Jonathan P. Department of Mathematics ETH Zurich 8092 Zurich Switzerland

The aims of this paper are threefold. First, we highlight the usefulness of generalized linear mixed models (GLMMs) in the modelling of portfolio credit default risk. The GLMM-setting allows for a flexible specification of the systematic portfolio risk in terms of observed fixed effects and unobserved random effects, in order to explain the phenomena of default dependence and time-inhomogeneity in historical default data. Second, we show that computational Bayesian techniques such as the Gibbs sampler can be successfully applied to fit models with serially correlated random effects, which are special instances of state space models. Third, we provide an empirical study using Standard and Poor's data on U.S. firms. A model incorporating rating category and sector effects, and a macroeconomic proxy variable for state-of-the-economy suggests the presence of a residual, cyclical, latent component in the systematic risk. © 2006 Elsevier B.V. All rights reserved.

关键词： Bayesian inference Credit risk generalized linear mixed model State space model

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Monte Carlo Likelihood Approximation for generalized linear mixed models

Monte Carlo Likelihood Approximation for Generalized Linear ...

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作者： Knudson, Christina University of Minnesota

学位级别：Ph.D.

Frequentist likelihood-based inference for generalized linear mixed models is often difficult to perform. Because the likelihood cannot depend on unobserved data (such as random effects), the likelihood for a generalized linear mixed model is an integral that is often high-dimensional and intractable. The method of Monte Carlo likelihood approximation (MCLA) approximates the entire likelihood function using random effects simulated from an importance sampling distribution. The resulting Monte Carlo likelihood approximation can be used for any frequentist likelihood-based inference. Due to the challenge of finding an importance sampling distribution that works well in practice, very little publicly-available MCLA software existed prior to 2015. I present an importance sampling distribution to be used in implementing MCLA for generalized linear mixed models; establish its theoretical validity; implement it in the R package glmm; and demonstrate how to use the package to perform maximum likelihood, test hypotheses, and calculate confidence intervals.

关键词： generalized linear mixed model likelihood likelihood approximation likelihood-based inference Monte Carlo

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Goodness-of-Fit Test Issues in generalized linear mixed models

Goodness-of-Fit Test Issues in Generalized Linear Mixed Mode...

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作者： Chen, Nai-Wei Texas A&M University

linear mixed models and generalized linear mixed models are random-effects models widely applied to analyze clustered or hierarchical data. Generally, random effects are often assumed to be normally distributed in the context of mixed models. However, in the mixed-effects logistic model, the violation of the assumption of normally distributed random effects may result in inconsistency for estimates of some fixed effects and the variance component of random effects when the variance of the random-effects distribution is large. On the other hand, summary statistics used for assessing goodness of fit in the ordinary logistic regression models may not be directly applicable to the mixed-effects logistic models. In this dissertation, we present our investigations of two independent studies related to goodness-of-fit tests in generalized linear mixed models. First, we consider a semi-nonparametric density representation for the random effects distribution and provide a formal statistical test for testing normality of the random-effects distribution in the mixed-effects logistic models. We obtain estimates of parameters by using a non-likelihood-based estimation procedure. Additionally, we not only evaluate the type I error rate of the proposed test statistic through asymptotic results, but also carry out a bootstrap hypothesis testing procedure to control the inflation of the type I error rate and to study the power performance of the proposed test statistic. Further, the methodology is illustrated by revisiting a case study in mental health. Second, to improve assessment of the model fit in the mixed-effects logistic models, we apply the nonparametric local polynomial smoothed residuals over within-cluster continuous covariates to the unweighted sum of squares statistic for assessing the goodness-of-fit of the logistic multilevel models. We perform a simulation study to evaluate the type I error rate and the power performance for detecting a missing quadratic or intera

关键词： generalized linear mixed model generalized estimating equations robust score test misspecification of the random-effect distribution parametric bootstrap. Thesis

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Technical note: An R package for fitting generalized linear mixed models in animal breeding

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JOURNAL OF ANIMAL SCIENCE 2010年第2期88卷 497-504页

作者： Vazquez, A. I. Bates, D. M. Rosa, G. J. M. Gianola, D. Weigel, K. A. Univ Wisconsin Dept Dairy Sci Madison WI 53706 USA Univ Wisconsin Dept Stat Madison WI 53706 USA Univ Wisconsin Dept Anim Sci Madison WI 53706 USA

mixed models have been used extensively in quantitative genetics to study continuous and discrete traits. A standard quantitative genetic model proposes that the effects of levels of some random factor ( e. g., sire) are correlated accordingly with their relationships. For this reason, routines for mixed models available in standard packages cannot be used for genetic analysis. The pedigreemm package of R was developed as an extension of the lme4 package, and allows mixed models with correlated random effects to be fitted for Gaussian, binary, and count responses. Following the method of Harville and Callanan (1989), a correlation between levels of the grouping factor (e. g., sire) is induced by post-multiplying the incidence matrix of the levels of this random factor by the Cholesky factor of the corresponding (co) variance matrix (e. g., the numerator relationship matrix between sires). Estimation methods available in pedigreemm include approximations to maximum likelihood and REML. This note describes the classes of models that can be fitted using pedigreemm and presents examples that illustrate its use.

关键词： animal model correlated random effect generalized linear mixed model quantitative genetics R package sire model

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Analyzing dynamic species abundance distributions using generalized linear mixed models

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ECOLOGY 2022年第9期103卷 e3742-e3742页

作者： Solbu, Erik Blystad van der Veen, Bert Herfindal, Ivar Hovstad, Knut Anders Norwegian Inst Bioecon Res NIBIO Dept Landscape & Biodivers Trondheim Norway Norwegian Univ Sci & Technol NTNU Dept Math Trondheim Norway Norwegian Univ Sci & Technol NTNU Ctr Biodivers Dynam Dept Biol Trondheim Norway Norwegian Biodivers Informat Ctr Trondheim Norway

Understanding the mechanisms of ecological community dynamics and how they could be affected by environmental changes is important. Population dynamic models have well known ecological parameters that describe key characteristics of species such as the effect of environmental noise and demographic variance on the dynamics, the long-term growth rate, and strength of density regulation. These parameters are also central for detecting and understanding changes in communities of species;however, incorporating such vital parameters into models of community dynamics is challenging. In this paper, we demonstrate how generalized linear mixed models specified as intercept-only models with different random effects can be used to fit dynamic species abundance distributions. Each random effect has an ecologically meaningful interpretation either describing general and species-specific responses to environmental stochasticity in time or space, or variation in growth rate and carrying capacity among species. We use simulations to show that the accuracy of the estimation depends on the strength of density regulation in discrete population dynamics. The estimation of different covariance and population dynamic parameters, with corresponding statistical uncertainties, is demonstrated for case studies of fish and bat communities. We find that species heterogeneity is the main factor of spatial and temporal community similarity for both case studies.

关键词： environmental variance generalized linear mixed model Poisson lognormal population dynamics spatial and temporal correlation species abundance distribution species heterogeneity variance partitioning

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A method to evaluate the combined effect of tree species composition and woodland structure on indicator birds

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ECOLOGICAL INDICATORS 2015年 55卷 44-51页

作者： Dondina, O. Orioli, V. Massimino, D. Pinoli, G. Bani, L. Univ Milano Bicocca Dept Earth & Environm Sci I-20126 Milan Italy British Trust Ornithol Thetford IP24 2PU Norfolk England Agr Gen Directorate I-20124 Milan Italy

Providing quantitative management guidelines is essential for an effective conservation of forest-dependent animal communities. Traditional forest practices at the stand scale simultaneously alter both physical and floristic features with a negative effect on ecosystem processes. Thus, we tested and proposed a method to define forestry prescriptions taking into account the combined effect of woodland structure and tree species composition on the presence of four bird indicator species (Marsh Tit Poecile palustris, European Nuthatch Sitta europaea, Short-toed Tree-creeper Certhya brachydactyla and Blue Tit Cyanistes caeruleus). The study was carried out in Lombardy (Northern Italy), from 2002 to 2005. By using a stratified cluster sampling design, we recorded Basal Area, one hundred tree trunk diameters at breast height (DBH) and tree species in 160 sampling plots, grouped in 23 sampling areas. In each plot we also performed a bird survey using the point count method. We analyzed data using Multimodel Inference and model Averaging on generalized linear mixed models, with species presence/absence as the response variable, sampling area as a random factor and forest covariates as fixed factors. In order to test our method, we compared it with other two traditional approaches, which consider structural and tree floristic variables separately. model comparison showed that our method performed better than traditional ones, in both the evaluation and validation processes. Based on our main results, in deciduous mixed forest where the exploitation demand is limited, we recommend maintaining at least 65 trees/ha with DBH > 45 cm. In particular, we advise keeping 70 trees/ha with DBH >50 cm in chestnut forests and 300 trees/ha with DBH 20-30 cm in oak forests. Conversely, in more exploited oak forests, we advise maintaining at least 670 trees/ha with DBH 15-30 cm in chestnut forests and 100 trees/ha with DBH 10-15 cm. (C) 2015 Elsevier Ltd. All rights reserved.

关键词： Basal area (BA) Diameters at breast height (DBH) Exploited forests generalized linear mixed model model comparison Secondary cavity-nesters

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Effect of cleaning methods in mixed pine-deciduous stands on moose damage to Scots pines in southern Finland

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SCANDINAVIAN JOURNAL OF FOREST RESEARCH 2008年第6期23卷 491-500页

作者： Harkonen, Sauli Miina, Jari Saksa, Timo Finnish Forest Res Inst Joensuu Res Unit FI-80101 Joensuu Finland Finnish Forest Res Inst Suonenjoki Res Unit Suonenjoki Finland

The effect of different cleaning treatments on moose (Alces alces L.) damage to Scots pines (Pinus sylvestris L.) was examined using a generalized linear mixed model (GLMM) with a binomial response (logit-link function). The treatments were the following: no cleaning, point-cleaning of broadleaves (mainly birch, Betula pendula Roth and B. pubescens Ehrh.) within a radius of 1 m from the pine, point-cleaning delayed 2 years, topping of competing broadleaves (main stem cut at a height of 1.3 m) and total cleaning of broadleaves. A randomized complete block design with three replicates was established in three planted pine stands (mean height of pines 1.5 m). Measurements taken four growing seasons later (mean height of pines 3.5 m) showed that all cleaning treatments reduced moose damage, although the difference was not significant (p = 0.078) in the case of topping. The proportion of damaged pines was predicted as a function of the characteristics of pines and broadleaves in two untreated, planted pine stands with a height of 3 m. Within these untreated stands the number of damaged pines increased in plots with a higher number of broadleaves and taller broadleaves. In conclusion, the results show that on relatively fertile growing sites of pine cleaning treatments reduced moose damage on pine. It is recommended that cleaning is performed before broadleaved trees occur as overgrowth above pines.

关键词： Alces alces cleaning damage generalized linear mixed model moose Pinus sylvestris

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