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Marginal zero-inflated regression models for count data

JOURNAL OF APPLIED STATISTICS 2017年第10期44卷 1807-1826页

作者： Martin, Jacob Hall, Daniel B. Univ Georgia Dept Stat Athens GA 30602 USA

Data sets with excess zeroes are frequently analyzed in many disciplines. A common framework used to analyze such data is the zero-inflated (ZI) regression model. It mixes a degenerate distribution with point mass at zero with a non-degenerate distribution. The estimates from ZI models quantify the effects of covariates on the means of latent random variables, which are often not the quantities of primary interest. Recently, marginal zero-inflated Poisson (MZIP;Long etal. [A marginalized zero-inflated Poisson regression model with overall exposure effects. Stat. Med. 33 (2014), pp.5151-5165]) and negative binomial (MZINB;Preisser et al., 2016) models have been introduced that model the mean response directly. These models yield covariate effects that have simple interpretations that are, for many applications, more appealing than those available from ZI regression. This paper outlines a general framework for marginal zero-inflated models where the latent distribution is a member of the exponential dispersion family, focusing on common distributions for count data. In particular, our discussion includes the marginal zero-inflated binomial (MZIB) model, which has not been discussed previously. The details of maximum likelihood estimation via the EM algorithm are presented and the properties of the estimators as well as Wald and likelihood ratio-based inference are examined via simulation. Two examples presented illustrate the advantages of MZIP, MZINB, and MZIB models for practical data analysis.

关键词： Exponential dispersion family generalized linear models zero inflation marginal models EM algorithm

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BIBI: Bayesian inference of breed composition

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JOURNAL OF ANIMAL BREEDING AND GENETICS 2018年第1期135卷 54-61页

作者： Martinez, C. A. Khare, K. Elzo, M. A. Univ Florida Dept Anim Sci Gainesville FL 32611 USA Univ Florida Dept Stat Gainesville FL 32611 USA

The aim of this paper was to develop statistical models to estimate individual breed composition based on the previously proposed idea of regressing discrete random variables corresponding to counts of reference alleles of biallelic molecular markers located across the genome on the allele frequencies of each marker in the pure (base) breeds. Some of the existing regression-based methods do not guarantee that estimators of breed composition will lie in the appropriate parameter space, and none of them account for uncertainty about allele frequencies in the pure breeds, that is, uncertainty about the design matrix. To overcome these limitations, we proposed two Bayesian generalized linear models. For each individual, both models assume that the counts of the reference allele at each marker locus follow independent Binomial distributions, use the logit link and pose a Dirichlet prior over the vector of regression coefficients (which corresponds to breed composition). This prior guarantees that point estimators of breed composition such as the posterior mean pertain to the appropriate space. The difference between these models is that model termed BIBI does not account for uncertainty about the design matrix, while model termed BIBI2 accounts for such an uncertainty by assigning independent Beta priors to the entries of this matrix. We implemented these models in a data set from the University of Florida's multibreed Angus-Brahman population. Posterior means were used as point estimators of breed composition. In addition, the ordinary least squares estimator proposed by Kuehn etal. () (OLSK) was also computed. BIBI and BIBI2 estimated breed composition more accurately than OLSK, and BIBI2 had a 7.69% improvement in accuracy as compared to BIBI.

关键词： Bayes estimators generalized linear models genomic data individual breed composition

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Does the hydrodynamic, morphometric and sedimentary environment explain the structure of soft-bottom benthic assemblages in the Eastern Bay of Seine (English Channel)?

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ESTUARINE COASTAL AND SHELF SCIENCE 2017年 189卷 156-172页

作者： Dauvin, Jean-Claude Lucas, Sabrina Navon, Maxime Lesourd, Sandric Mear, Yann Poizot, Emmanuel Alizier, Sandrine Normandie Univ UNICAEN UNIROUEN Lab Moiphodynam Continentale & CotiereCNRSUMR 6 24 Rue Tilleuls F-14000 Caen France INTECHMER CNAM BP 324 F-50103 Octeville France LUSAC EA 4253 BP 324 F-50103 Octeville France Univ Lille 1 Stn Marine Lab Oceanol & Geosci UMR LOG 8187 28 Ave FochBP 80 F-62930 Wimereux France

It has been traditionally assumed that the distribution of the macrofauna is mainly related to the nature of the sediment and that the grain size plays a key role. Therefore in some cases such as in the coastal environment submitted to input of fine particles coming from land via estuary, the sediment is not the major factor explaining the spatial distribution of benthic species, assemblages and communities. In fact, sediment samples may not be representative of real life conditions of benthic organisms which are exposed to natural environment and three-dimensional structure of habitat and heterogeneity of sediments with several grain size classes. Based on data acquired in September 2008 and 2009 from the benthic sampling surveys in the eastern part of the Bay of Seine which is characterized by the dominance of heterometric sediment, the main aim of this paper is to study for the first time the existing link between the spatial distribution of the benthic species and assemblages and selected environmental variables such as sedimentary, hydrodynamic and morphometric data, to explain the real part of each abiotic factors in the spatio-temporal structuration of the benthic assemblages in this area at the mouth of the Seine estuary. Redundancy Analyses had permitted to distinguish six assemblages in relation to heterometry of the sediment;current speed, bathymetry and salinity. generalized linear models permitted to explain between 30 and 89% of the variance within the chosen environmental factors. The species with a large distribution at the eastern part of the Bay of Seine were those showing the lowest percentage of explained variance while the species which were located in few stations were those showing the highest percentage of explained variance. (C) 2017 Elsevier Ltd. All rights reserved.

关键词： Spatial structures Bay of seine English channel Macrofauna environmental relationships Redundancy analyses generalized linear models

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Attributing changes in the distribution of species abundance to weather variables using the example of British breeding birds

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METHODS IN ECOLOGY AND EVOLUTION 2017年第12期8卷 1690-1702页

作者： Oedekoven, Cornelia S. Elston, David A. Harrison, Philip J. Brewer, Mark J. Buckland, Stephen T. Johnston, Alison Foster, Simon Pearce-Higgins, James W. Univ St Andrews Ctr Res Ecol & Environm Modelling St Andrews Fife Scotland Biomath & Stat Scotland Aberdeen Scotland British Trust Ornithol Thetford Norfolk England Scottish Nat Heritage Great Glen HouseLeachkin Rd Inverness Scotland

1. Modelling spatio-temporal changes in species abundance and attributing those changes to potential drivers such as climate, is an important but difficult problem. The standard approach for incorporating climatic variables into such models is to include each weather variable as a single covariate, whose effect is expressed through a low-order polynomial or smoother in an additive model. This, however, confounds the spatial and temporal effects of the covariates. 2. We developed a novel approach to distinguish between three types of change in any particular weather covariate. We decomposed the weather covariate into three new covariates by separating out temporal variation in weather (averaging over space), spatial variation in weather (averaging over years) and a space-time anomaly term (residual variation). These three covariates were each fitted separately in the models. We illustrate the approach using generalized additive models applied to count data for a selection of species from the UK's Breeding Bird Survey, 1994-2013. The weather covariates considered were the mean temperatures during the preceding winter and temperatures and rainfall during the preceding breeding season. We compare models that include these covariates directly with models including decomposed components of the same covariates, considering both linear and smooth relationships. 3. The lowest QAIC values were always associated with a decomposed weather covariate model. Different relationships between counts and the three new covariates provided strong evidence that the effects of changes in covariate values depended on whether changes took place in space, in time, or in the space-time anomaly. These results promote caution in predicting species distribution and abundance in future climate, based on relationships that are largely determined by environmental variation over space. 4. Our methods estimate the effect of temporal changes in weather, while accounting for spatial effects of long-ter

关键词： climate change decomposition of spatial temporal and anomaly effects generalized additive models generalized linear models spatio-temporal modelling species abundance UKCP09 climate projections

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A comparative study of models for the different covariance structure analysis of repeated measurement data

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International Journal of Biomathematics 2017年第1期10卷 115-125页

作者： Yazhou Wu Ling Zhang Liang Zhou Xiaoyu Liu Ling Liu Yanqi Zhang Dong Yi Department of Health StatisticsThird Military Medical University Chongqing 400038 P. R. China

In repeated measurement data, the variables are not independent, and a certain auto- correlation typically exists between different levels of repeated measurement factors. The random error is composed of at least two parts, i.e. the individual random effect and the intra-individual multi-repeated measurement effect. Traditional statistical analysis methods （such as the t-test and the one-way analysis of variance） are not applicable. The linear mixed model has been widely applied for the analysis and design of repeated measurement data. This paper focuses on medical examples and describes the selection of a covariance structure for the linear mixed model of repeated measurement in the modeling of different variance-eovariance structures. By selecting different covariance structures, we can perform the parameter estimation and statistical test for the fixed effect of repeated measurement data, the parameters of random effects, and the covari- ance matrix. The results are analyzed and compared to provide a reference for applying the linear mixed model of repeated measurement to medical research.

关键词： Repeated measurement data generalized linear models mixed model covari-ance structure.

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Tree species richness in tropical montane forests of Chiapas: estimates from herbaria data and floristic surveys

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REVISTA MEXICANA DE BIODIVERSIDAD 2017年第4期88卷 832-844页

作者： Campos-Sanchez, Elizabeth Gonzalez-Espinosa, Mario Ramirez-Marcial, Neptali Navarrete-Gutierrez, Alejandro Angel Perez-Farrera, Miguel El Colegio Frontera Sur Dept Conservac Biodiversidad Carretera Panamer & Periferico Sur S-N San Cristobal Casas 29290 Chiapas Mexico El Colegio Frontera Sur Lab Informat Geog & Estadist Carretera Panamer & Periferico Sur S-N San Cristobal Casas 29290 Chiapas Mexico Univ Ciencias & Artes Chiapas Fac Ciencias Biol HEM Libramiento Norte Poniente 1150 Tuxtla Gutierrez 29039 Chiapas Mexico

Estimates of tree species richness (S) have usually been approached with systematic surveys. More recently, with the increasing on-line availability of digital herbaria data, alternative S estimates are possible. How comparable are these two estimates? We fitted generalized linear models (GLM) to obtain estimates of S with both data types from three different mountain regions in Chiapas (>1,500 elevation) for which substantial numbers of both herbarium vouchers and survey plots are available. A total number of 792 tree species were detected with both types of data. Clench's model estimated 862 and 425 tree species with herbarium and survey data, respectively. The selected GLM models rendered S estimates that were positively correlated in two out of the three studied regions (not in the most species-rich region). Systematic surveys provide a snap-shot of species equitability among real samples of forest communities, and therefore, represent a useful set of data to approach the understanding of tree diversity structure. On the other hand, herbarium vouchers allow estimates of how many rare or restricted species may still be absent in the survey-based inventory. It seems convenient to make complementary use of both types of data in order to estimate S in poorly known tropical forests. (C) 2017 Universidad Nacional Autonoma de Mexico, Instituto de Biologia.

关键词： Montane forests Tropical forests Tree diversity Herbarium vouchers Forest surveys generalized linear models

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On the maximization of likelihoods belonging to the exponential family using a Levenberg-Marquardt approach

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JOURNAL OF STATISTICAL COMPUTATION AND SIMULATION 2017年第5期87卷 895-907页

作者： Giordana, M. Vaggi, F. Wehrens, R. IASMA Res & Innovat Ctr Grp Biostat & Data Management Via Edmund Mach 1 San Michele All Adige Italy IASMA Res & Innovat Ctr Grp Integrat Genom Res San Michele All Adige Italy

The Levenberg-Marquardt algorithm is a flexible iterative procedure used to solve non-linear least-squares problems. In this work, we study how a class of possible adaptations of this procedure can be used to solve maximum-likelihood problems when the underlying distributions are in the exponential family. We formally demonstrate a local convergence property and discuss a possible implementation of the penalization involved in this class of algorithms. Applications to real and simulated compositional data show the stability and efficiency of this approach.

关键词： Aitchison distribution compositional data Dirichlet distribution generalized linear models natural link optimization

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Robust bootstrap procedures for the chain-ladder method

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SCANDINAVIAN ACTUARIAL JOURNAL 2017年第10期000卷 870-897页

作者： Peremans, Kris Segaert, Pieter Van Aelst, Stefan Verdonck, Tim Katholieke Univ Leuven Dept Math Leuven Belgium

Insurers are faced with the challenge of estimating the future reserves needed to handle historic and outstanding claims that are not fully settled. A well-known and widely used technique is the chain-ladder method, which is a deterministic algorithm. To include a stochastic component one may apply generalized linear models to the run-off triangles based on past claims data. Analytical expressions for the standard deviation of the resulting reserve estimates are typically difficult to derive. A popular alternative approach to obtain inference is to use the bootstrap technique. However, the standard procedures are very sensitive to the possible presence of outliers. These atypical observations, deviating from the pattern of the majority of the data, may both inflate or deflate traditional reserve estimates and corresponding inference such as their standard errors. Even when paired with a robust chain-ladder method, classical bootstrap inference may break down. Therefore, we discuss and implement several robust bootstrap procedures in the claims reserving framework and we investigate and compare their performance on both simulated and real data. We also illustrate their use for obtaining the distribution of one year risk measures.

关键词： Claims reserving generalized linear models outliers inference Solvency II

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The effect of fire history in shaping diversity patterns of flower-visiting insects in post-fire Mediterranean pine forests

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BIODIVERSITY AND CONSERVATION 2017年第1期26卷 115-131页

作者： Lazarina, Maria Sgardelis, Stefanos P. Tscheulin, Thomas Devalez, Jelle Mizerakis, Vangelis Kallimanis, Athanasios S. Papakonstantinou, Spyridon Kyriazis, Thanassis Petanidou, Theodora Univ Aegean Dept Geog Lab Biogeog & Ecol Mitilini 81100 Greece Aristotle Univ Thessaloniki Sch Biol Dept Ecol Thessaloniki 54124 Greece Dodecanese Forest Directorate G Mavrou 2 Rhodes 85132 Greece

Fire affects diversity and structure of flower-visitor communities. We explored the effect of fire history on the diversity patterns and structure of the flower-visitor guilds (bees, beetles, flies, sawflies, and wasps), across a post-fire regeneration sequence of pine forests in Rhodes Island, Greece. Fire history was defined by fire frequency and post-fire age of sites. We did not find significant differences in species richness and abundance per guild between fire-history regimes except for the abundance of flies, sawflies and the entire flower-visitor community. Fire strongly affected the community structure of bees, beetles, and sawflies. Some of the most abundant and common species responded significantly to fire in terms of abundance;yet, we observed no significant variation in the abundance of the common species of bees, the most prominent pollinator group, implying that provision of pollination services may not be considerably affected by fire. Long-unburnt sites displayed higher heterogeneity in species composition compared to recently-burnt sites (either burnt once or twice). This pattern deviated significantly from null expectations when analyzing the abundance-based metric of beta-diversity and was obscure in the case of the presence/absence-based metric, indicating that fire affected mainly the spatial distribution of individuals, i.e. the main change is not due to species turnover but to changes in relative abundance. Furthermore, the species composition in recently-burnt sites (burnt once in 2008) were more similar than in twice-burnt sites (including areas burnt once between 1984 and 1992, and in 2008), indicating that fire frequency affected post-fire heterogeneity of species composition.

关键词： Bees Beetles Flies generalized linear models beta-diversity Null modelling

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Parasitism and grooming behavior of a natural white-tailed deer population in Alabama

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ETHOLOGY ECOLOGY & EVOLUTION 2017年第3期29卷 292-303页

作者： Heine, Kyle B. DeVries, Philip J. Penz, Carla M. Univ New Orleans Dept Biol Sci 2000 Lakeshore Dr New Orleans LA 70148 USA

We assessed responses in grooming behavior to ectoparasite densities in naturally occurring white-tailed deer (Odocoileus virginianus) in southwest Alabama, and tested predictions of the stimulus-driven and programmed grooming models with respect to intraspecific body size and vigilance. Stimulus-driven grooming predicts greater tick densities would lead to an increase in grooming, whereas the programmed model predicts a higher rate of grooming would decrease tick densities. Within the programmed model, smaller individuals are predicted to groom more and host fewer ticks, and, due to increased vigilance, breeding males will groom less than females and bachelor males, and thus host more ticks during the rut. We used generalized linear models to determine males had a higher average tick density than females and exhibited complete separation of tick parasitism between non-rutting and rutting periods. Our results support the stimulus-driven grooming model as both fawns and yearlings had significantly higher deer ked and combined deer ked/tick densities than adults. We used Mann-Whitney U tests to conclude fawns oral groomed at a significantly higher rate than adults, even in the absence of allogrooming. Programmed and stimulus-driven grooming were not mutually exclusive, but rather ectoparasite and host dependent. Although individuals observed grooming were analyzed separately from harvested individuals, we infer that heavy deer ked densities may lead to higher grooming rates. We suggest white-tailed deer grooming for ticks should be considered within an evolutionary framework, and grooming for deer keds should be viewed as a proximate response to agitation. This is the first study to show that deer keds may have a greater influence in overall grooming behavior of deer than do ticks. We recommend that future studies should consider other ectoparasites along with ticks to understand their effects on grooming behavior in dimorphic terrestrial mammals.

关键词： Alabama ectoparasites generalized linear models grooming Hippoboscidae Ixodidae white-tailed deer

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