Generalized hierarchical multivariate CAR models for areal data

In the fields of medicine and public health, a common application of areal data models is the study of geographical patterns of disease. When we have several measurements recorded at each spatial location (for example, information on p>/= 2 diseases from the same population groups or regions), we need to consider multivariate areal data models in order to handle the dependence among the multivariate components as well as the spatial dependence between sites. In this article, we propose a flexible new class of generalized multivariate conditionally autoregressive (GMCAR) models for areal data, and show how it enriches the MCAR class. Our approach differs from earlier ones in that it directly specifies the joint distribution for a multivariate Markov random field (MRF) through the specification of simpler conditional and marginal models. This in turn leads to a significant reduction in the computational burden in hierarchical spatial random effect modeling, where posterior summaries are computed using Markov chain Monte Carlo (MCMC). We compare our approach with existing MCAR models in the literature via simulation, using average mean square error (AMSE) and a convenient hierarchical model selection criterion, the deviance information criterion (DIC; Spiegelhalter et al., 2002, Journal of the Royal Statistical Society, Series B64, 583-639). Finally, we offer a real-data application of our proposed GMCAR approach that models lung and esophagus cancer death rates during 1991-1998 in Minnesota counties.     

Linear and nonlinear mixed-effects models for censored HIV viral loads using normal/independent distributions

HIV RNA viral load measures are often subjected to some upper and lower detection limits depending on the quantification assays. Hence, the responses are either left or right censored. Linear (and nonlinear) mixed-effects models (with modifications to accommodate censoring) are routinely used to analyze this type of data and are based on normality assumptions for the random terms. However, those analyses might not provide robust inference when the normality assumptions are questionable. In this article, we develop a Bayesian framework for censored linear (and nonlinear) models replacing the Gaussian assumptions for the random terms with normal/independent (NI) distributions. The NI is an attractive class of symmetric heavy-tailed densities that includes the normal, Student's-t, slash, and the contaminated normal distributions as special cases. The marginal likelihood is tractable (using approximations for nonlinear models) and can be used to develop Bayesian case-deletion influence diagnostics based on the Kullback-Leibler divergence. The newly developed procedures are illustrated with two HIV AIDS studies on viral loads that were initially analyzed using normal (censored) mixed-effects models, as well as simulations.     

Adjusting nonresponse bias at subdomain levels using multiple response phases

When a sampling unit doesn't respond to a survey it is termed unit nonresponse. Unit nonresponse may have a dramatic affect on estimation results of interest. Using only those who responded to the survey to calculate the estimate may bias the estimate, known as nonresponse bias. Many approaches have been created in order to account for nonresponse. One such approach is to resample those nonrespondents in a second response "phase" (or more). We build a Bayesian hierarchical model that uses information from multiple response "phases" to estimate the phase specific response rates from I subdomains. This information is simultaneously used to estimate the success rates in those I subdomains. Conditional success rates are then estimated for the first phase respondents, second phase respondents, and nonrespondents (the third response phase). A relationship between these three sets of conditional success rates is incorporated into the model. This is done through a spatially dependent structure. The 1998 Missouri Turkey Hunting Survey is used to illustrate this methodology. The success rate estimates from nonrespondents have a significant impact on the overall success rate.     

Hierarchical Bayesian modeling in dichotomous processes in the presence of nonresponse

Sampling units that do not answer a survey may dramatically affect the estimation results of interest. The response may even be conditional on the outcome of interest in the survey. If estimates are found using only those who responded, the estimate may be biased, known as nonresponse bias. We are interested in finding estimates of success rates from a survey. We begin by looking at two current Bayesian approaches to treating nonresponse in a hierarchical model. However, these approaches do not consider possible spatial correlations between domains for either success rate or response rate. We build a Bayesian hierarchical spatial model to explicitly estimate the success rate, response rate given success, and response rate given failure. The success rates in the domains of the survey are allowed to be spatially correlated. We also allow spatial dependence between domains in both response rate given success and response rate given failure. Spatial dependence is induced by a common latent spatial structure between the two conditional response rates. We use the 1998 Missouri Turkey Hunting Survey to illustrate this methodology. We find significant spatial correlation in the success rates and incorporating nonrespondents has an impact on the success rate estimates.     

Modelling habitat associations with fingernail clam (Family: Sphaeriidae) counts at multiple spatial scales using hierarchical count models

1. Macroinvertebrate count data often exhibit nested or hierarchical structure. Examples include multiple measurements along each of a set of streams, and multiple synoptic measurements from each of a set of ponds. With data exhibiting hierarchical structure, outcomes at both sampling (e.g. within stream) and aggregated (e.g. stream) scales are often of interest. Unfortunately, methods for modelling hierarchical count data have received little attention in the ecological literature. 2. We demonstrate the use of hierarchical count models using fingernail clam (Family: Sphaeriidae) count data and habitat predictors derived from sampling and aggregated spatial scales. The sampling scale corresponded to that of a standard Ponar grab (0.052 m²) and the aggregated scale to impounded and backwater regions within 38–197 km reaches of the Upper Mississippi River. Impounded and backwater regions were resampled annually for 10 years. Consequently, measurements on clams were nested within years. Counts were treated as negative binomial random variates, and means from each resampling event as random departures from the impounded and backwater region grand means. 3. Clam models were improved by the addition of covariates that varied at both the sampling and regional scales. Substrate composition varied at the sampling scale and was associated with model improvements, and reductions (for a given mean) in variance at the sampling scale. Inorganic suspended solids (ISS) levels, measured in the summer preceding sampling, also yielded model improvements and were associated with reductions in variances at the regional rather than sampling scales. ISS levels were negatively associated with mean clam counts. 4. Hierarchical models allow hierarchically structured data to be modelled without ignoring information specific to levels of the hierarchy. In addition, information at each hierarchical level may be modelled as functions of covariates that themselves vary by and within levels. As a result, hierarchical models provide researchers and resource managers with a method for modelling hierarchical data that explicitly recognises both the sampling design and the information contained in the corresponding data.     

中国谷子潜在地理分布的多模型比较

谷子是中国干旱和半干旱区主要的粮食作物之一.它耐旱、耐瘠薄、抗逆性强、适应性广,是未来应对干旱形势的重要战略储备作物.本文基于谷子的157个地理分布点数据,利用中国谷子产量与环境指标的相关性分析,选出10个气候指标、7个土壤指标和3个地形指标,采用MaxEnt、EMFA、RF和GAM共4个物种分布模型,分析中国谷子的潜在适宜性分布.结果表明: 4种模型均可成功模拟谷子的潜在地理分布,其中,MaxEnt模型的模拟效果最好.选用的环境指标中,水热条件对谷子生长最敏感.模型结果结合ArcGIS空间分析模块的结果表明,中国谷子的潜在适宜生长区(最适宜区和适宜区)总面积为55.68×10⁴ km²,远远大于当前谷子的实际种植面积,主要集中在东北地区的东北平原、长白山以南与牡丹江流域,华北地区的淮河以北,华中地区汉江以东与大别山以北,西北地区的黄土高原、鄂尔多斯高原南部、祁连山脉东部、天山山脉东部与阿尔泰山脉,西南地区的重庆以北和贵州西部局地区域.     

A study of the effects of truncation in bivariate normal distribution

The moments of bivariate normal distribution, which is truncated with respect to both the random variables, are obtained by using the orthogonal expansion of the distribution and the properties of HERMITE polynomials. In particular the correlation coefficient of the truncated distribution is derived in terms of the actual correlation coefficient. In order to study the effect of truncation tables have been prepared of this correlation coefficient for certain given values of the actual correlation coefficient and for a few selected values of the points of truncation. A listing of the computer program for this purpose is also given.     

Influence of priors in Bayesian estimation of genetic parameters for multivariate threshold models using Gibbs sampling

Simulated data were used to investigate the influence of the choice of priors on estimation of genetic parameters in multivariate threshold models using Gibbs sampling. We simulated additive values, residuals and fixed effects for one continuous trait and liabilities of four binary traits, and QTL effects for one of the liabilities. Within each of four replicates six different datasets were generated which resembled different practical scenarios in horses with respect to number and distribution of animals with trait records and availability of QTL information. (Co)Variance components were estimated using a Bayesian threshold animal model via Gibbs sampling. The Gibbs sampler was implemented with both a flat and a proper prior for the genetic covariance matrix. Convergence problems were encountered in > 50% of flat prior analyses, with indications of potential or near posterior impropriety between about round 10 000 and 100 000. Terminations due to non-positive definite genetic covariance matrix occurred in flat prior analyses of the smallest datasets. Use of a proper prior resulted in improved mixing and convergence of the Gibbs chain. In order to avoid (near) impropriety of posteriors and extremely poorly mixing Gibbs chains, a proper prior should be used for the genetic covariance matrix when implementing the Gibbs sampler.     

Evaluation of the spatial distribution of Anoplophora glabripennis (Motschulsky) (Coleoptera: Cerambycidae) in South Korea combining climate and host plant distribution

Anoplophora glabripennis (Motschulsky) (Coleoptera: Cerambycidae), a global forest pest, has a potential to damage forests in South Korea, requiring an effective tool for evaluating its potential distribution. This study aimed to evaluate the spatial distribution of A. glabripennis in South Korea by simultaneously considering climate and host plants. Climatic suitability was firstly evaluated using a CLIMEX model; then, it was combined with the areal distribution of host plants using a simple mathematical formulation. We finally projected the spatial distribution of A. glabripennis onto the map of administrative districts to identify hazardous areas to watch. As a result, the developed model predicted that over 40% of areas in South Korea could be exposed to A. glabripennis damage, and most of them were located in mountainous areas with abundant host plants. In addition, climatic suitability was higher in coastal areas, which was different than a previous record of A. glabripennis occurrence, while the prediction by a comprehensive model was consistent with the record. In conclusion, the model including both climate and host plant occurrence was more reliable than the model which only included climate, and could provide useful data for determining areas for monitoring and control.     

Bayesian prediction of breeding values for multivariate binary and continuous traits in simulated horse populations using threshold-linear models with Gibbs sampling

Simulated data were used to determine the properties of multivariate prediction of breeding values for categorical and continuous traits using phenotypic, molecular genetic and pedigree information by mixed linear-threshold animal models via Gibbs sampling. Simulation parameters were chosen such that the data resembled situations encountered in Warmblood horse populations. Genetic evaluation was performed in the context of the radiographic findings in the equine limbs. The simulated pedigree comprised seven generations and 40 000 animals per generation. The simulated data included additive genetic values, residuals and fixed effects for one continuous trait and liabilities of four binary traits. For one of the binary traits, quantitative trait locus (QTL) effects and genetic markers were simulated, with three different scenarios with respect to recombination rate (r) between genetic markers and QTL and polymorphism information content (PIC) of genetic markers being studied: r = 0.00 and PIC = 0.90 (r0p9), r = 0.01 and PIC = 0.90 (r1p9), and r = 0.00 and PIC = 0.70 (r0p7). For each scenario, 10 replicates were sampled from the simulated horse population, and six different data sets were generated per replicate. Data sets differed in number and distribution of animals with trait records and the availability of genetic marker information. Breeding values were predicted via Gibbs sampling using a Bayesian mixed linear-threshold animal model with residual covariances fixed to zero and a proper prior for the genetic covariance matrix. Relative breeding values were used to investigate expected response to multi- and single-trait selection. In the sires with 10 or more offspring with trait information, correlations between true and predicted breeding values ranged between 0.89 and 0.94 for the continuous traits and between 0.39 and 0.77 for the binary traits. Proportions of successful identification of sires of average, favourable and unfavourable genetic value were 81% to 86% for the continuous trait and 57% to 74% for the binary traits in these sires. Expected decrease of prevalence of the QTL trait was 3% to 12% after multi-trait selection for all binary traits and 9% to 17% after single-trait selection for the QTL trait. The combined use of phenotype and genotype data was superior to the use of phenotype data alone. It was concluded that information on phenotypes and highly informative genetic markers should be used for prediction of breeding values in mixed linear-threshold animal models via Gibbs sampling to achieve maximum reduction in prevalences of binary traits.     

Analysis of regional species distribution models based on radio-telemetry datasets from multiple small-scale studies

The identification of core habitat areas and resulting prediction maps are vital tools for land managers. Often, agencies have large datasets from multiple studies over time that could be combined for a more informed and complete picture of a species. Colorado Parks and Wildlife has a large database for greater sage-grouse (Centrocercus urophasianus) including 11 radio-telemetry studies completed over 12 years (1997–2008) across northwestern Colorado. We divided the 49,470-km² study area into 1-km² grids with the number of sage-grouse locations in each grid cell that contained at least 1 location counted as the response variable. We used a generalized linear mixed model (GLMM) using land cover variables as fixed effects and individual birds and populations as random effects to predict greater sage-grouse location counts during breeding, summer, and winter seasons. The mixed effects model enabled us to model correlations that may exist in grouped data (e.g., correlations among individuals and populations). We found only individual groupings accounted for variation in the summer and breeding seasons, but not the winter season. The breeding and summer seasonal models predicted sage-grouse presence in the currently delineated populations for Colorado, but we found little evidence supporting a winter season model. According to our models, about 50% of the study area in Colorado is considered highly or moderately suitable habitat in both the breeding and summer seasons. As oil and gas development and other landscape changes occur in this portion of Colorado, knowledge of where management actions can be accomplished or possible restoration can occur becomes more critical. These seasonal models provide data-driven, distribution maps that managers and biologists can use for identification and exploration when investigating greater sage-grouse issues across the Colorado range. Using historic data for future decisions on species management while accounting for issues found from combining datasets allows land managers the flexibility to use all information available. © 2013 The Wildlife Society.     

Performance evaluation of cetacean species distribution models developed using generalized additive models and boosted regression trees

Species distribution models (SDMs) are important management tools for highly mobile marine species because they provide spatially and temporally explicit information on animal distribution. Two prevalent modeling frameworks used to develop SDMs for marine species are generalized additive models (GAMs) and boosted regression trees (BRTs), but comparative studies have rarely been conducted; most rely on presence‐only data; and few have explored how features such as species distribution characteristics affect model performance. Since the majority of marine species BRTs have been used to predict habitat suitability, we first compared BRTs to GAMs that used presence/absence as the response variable. We then compared results from these habitat suitability models to GAMs that predict species density (animals per km²) because density models built with a subset of the data used here have previously received extensive validation. We compared both the explanatory power (i.e., model goodness of fit) and predictive power (i.e., performance on a novel dataset) of the GAMs and BRTs for a taxonomically diverse suite of cetacean species using a robust set of systematic survey data (1991–2014) within the California Current Ecosystem. Both BRTs and GAMs were successful at describing overall distribution patterns throughout the study area for the majority of species considered, but when predicting on novel data, the density GAMs exhibited substantially greater predictive power than both the presence/absence GAMs and BRTs, likely due to both the different response variables and fitting algorithms. Our results provide an improved understanding of some of the strengths and limitations of models developed using these two methods. These results can be used by modelers developing SDMs and resource managers tasked with the spatial management of marine species to determine the best modeling technique for their question of interest.     

利用分布有/无数据预测物种空间分布的研究方法综述

详细的物种地理分布信息是生态学研究和制定保护策略的基础。相比较于直接估测种群数量,获取物种分布的有/无数据更为实用。因此,利用分布有/无数据并结合环境变量建立模型预测物种空间分布的方法在近年来得到了长足发展,并被广泛应用。利用分布有/无数据预测物种分布,关键的步骤包括：1)构建总体概念模型,2)收集物种分布有/无数据,并准备环境变量图层;3)选择合适的统计模型和算法,以及4)对模型进行评估。概念模型提出研究假设,并确定数据收集及模型方法。收集物种分布数据有系统调查及非系统调查方法。筛选并准备与物种分布相关的环境变量,利用GIS工具处理,使之成为符合模型条件的具有合适的空间尺度的数字化图层。利用环境变量和物种分布有/无的数据,选择合适的方法及软件建立模型,并对模型进行检验和评估。我们总结了用于构建物种分布模型的不同算法和软件。本文将针对以上各个环节,阐述利用物种分布有/无数据进行研究所需要的技术细节,以期望为读者提供借鉴。     

Predictive cross-validation for the choice of linear mixed-effects models with application to data from the Swiss HIV Cohort Study

Model choice in linear mixed-effects models for longitudinal data is a challenging task. Apart from the selection of covariates, also the choice of the random effects and the residual correlation structure should be possible. Application of classical model choice criteria such as Akaike information criterion (AIC) or Bayesian information criterion is not obvious, and many versions do exist. In this article, a predictive cross-validation approach to model choice is proposed based on the logarithmic and the continuous ranked probability score. In contrast to full cross-validation, the model has to be fitted only once, which enables fast computations, even for large data sets. Relationships to the recently proposed conditional AIC are discussed. The methodology is applied to search for the best model to predict the course of CD4+ counts using data obtained from the Swiss HIV Cohort Study.