Generalized common spatial factor model

There are often two types of correlations in multivariate spatial data: correlations between variables measured at the same locations, and correlations of each variable across the locations. We hypothesize that these two types of correlations are caused by a common spatially correlated underlying factor. Under this hypothesis, we propose a generalized common spatial factor model. The parameters are estimated using the Bayesian method and a Markov chain Monte Carlo computing technique. Our main goals are to determine which observed variables share a common underlying spatial factor and also to predict the common spatial factor. The model is applied to county-level cancer mortality data in Minnesota to find whether there exists a common spatial factor underlying the cancer mortality throughout the state.     

Effects of Land Use on Lake Nutrients: The Importance of Scale,Hydrologic Connectivity,and Region

Catchment land uses, particularly agriculture and urban uses, have long been recognized as major drivers of nutrient concentrations in surface waters. However, few simple models have been developed that relate the amount of catchment land use to downstream freshwater nutrients. Nor are existing models applicable to large numbers of freshwaters across broad spatial extents such as regions or continents. This research aims to increase model performance by exploring three factors that affect the relationship between land use and downstream nutrients in freshwater: the spatial extent for measuring land use, hydrologic connectivity, and the regional differences in both the amount of nutrients and effects of land use on them. We quantified the effects of these three factors that relate land use to lake total phosphorus (TP) and total nitrogen (TN) in 346 north temperate lakes in 7 regions in Michigan, USA. We used a linear mixed modeling framework to examine the importance of spatial extent, lake hydrologic class, and region on models with individual lake nutrients as the response variable, and individual land use types as the predictor variables. Our modeling approach was chosen to avoid problems of multi-collinearity among predictor variables and a lack of independence of lakes within regions, both of which are common problems in broad-scale analyses of freshwaters. We found that all three factors influence land use-lake nutrient relationships. The strongest evidence was for the effect of lake hydrologic connectivity, followed by region, and finally, the spatial extent of land use measurements. Incorporating these three factors into relatively simple models of land use effects on lake nutrients should help to improve predictions and understanding of land use-lake nutrient interactions at broad scales.     

Assessing spatial covariance among time series of abundance

For species of conservation concern, an essential part of the recovery planning process is identifying discrete population units and their location with respect to one another. A common feature among geographically proximate populations is that the number of organisms tends to covary through time as a consequence of similar responses to exogenous influences. In turn, high covariation among populations can threaten the persistence of the larger metapopulation. Historically, explorations of the covariance in population size of species with many (>10) time series have been computationally difficult. Here, we illustrate how dynamic factor analysis (DFA) can be used to characterize diversity among time series of population abundances and the degree to which all populations can be represented by a few common signals. Our application focuses on anadromous Chinook salmon (Oncorhynchus tshawytscha), a species listed under the US Endangered Species Act, that is impacted by a variety of natural and anthropogenic factors. Specifically, we fit DFA models to 24 time series of population abundance and used model selection to identify the minimum number of latent variables that explained the most temporal variation after accounting for the effects of environmental covariates. We found support for grouping the time series according to 5 common latent variables. The top model included two covariates: the Pacific Decadal Oscillation in spring and summer. The assignment of populations to the latent variables matched the currently established population structure at a broad spatial scale. At a finer scale, there was more population grouping complexity. Some relatively distant populations were grouped together, and some relatively close populations – considered to be more aligned with each other – were more associated with populations further away. These coarse‐ and fine‐grained examinations of spatial structure are important because they reveal different structural patterns not evident in other analyses.     

中国陆地生态系统通量观测站点空间代表性

涡度相关技术是测定大气与陆地生态系统之间CO₂交换、水分和能量通量最直接的方法,可用于研究土壤、植被与大气间的CO₂交换及其调控机制。收集了11个影响净碳交换量的主要变量信息,包括气象因素、土壤因素和地形因素的非生物因子、实际植被状态以及植被生产力,采用多元地理变量空间聚类分析方法,绘制出不同聚类数（25、50、75、85、100、150和200类）的通量生态区。结合中国现有通量观测站点的空间分布格局,与新生成的通量生态区和已有的自然地理区划进行对比分析,发现由于中国地形复杂,生态系统类型多样,现有85个涡度相关通量观测站点仅能刻画部分中国生态系统类型的净碳交换量时空特征,通量生态区划分为100-150类比较合适。考虑到涡度相关通量观测运行成本,通量站点可增加至150个,从而使得优化后的通量观测网络能够代表中国主要类型的生态系统,并且有利于通量观测数据与遥感资料的有效结合,提高碳水通量观测从站点扩展到区域尺度的精度,从而更好地检验过程机理模型的模拟结果。     

Estimating linear causality in the presence of latent variables

Learning causality from data is known as the causal discovery problem, and it is an important and relatively new field. In many applications, there often exist latent variables, if such latent variables are completely ignored, which can lead to the estimation results seriously biased. In this paper, a method of combining exploratory factor analysis and path analysis (EFA-PA) is proposed to infer the causality in the presence of latent variables. Our method expands latent variables as well as their linear causal relationships with observed variables, which enhances the accuracy of causal models. Such model can be thought of as the simplest possible causal models for continuous data. The EFA-PA is very similar to that of structural equation model, but the theoretical model established by the structural equation model needs to be modified in the process of data fitting until the ideal model is established.The model gained by EFA-PA not only avoids subjectivity but also reduces estimation complexity. It is found that the EFA-PA estimation model is superior to the other models. EFA-PA can provides a basis for the correct estimation of the causal relationship between the observed variables in the presence of latent variables. The experiment shows that EFA-PA is better than the structural equation model.     

Joint model selection of marginal mean regression and correlation structure for longitudinal data with missing outcome and covariates

This work develops a joint model selection criterion for simultaneously selecting the marginal mean regression and the correlation/covariance structure in longitudinal data analysis where both the outcome and the covariate variables may be subject to general intermittent patterns of missingness under the missing at random mechanism. The new proposal, termed “joint longitudinal information criterion” (JLIC), is based on the expected quadratic error for assessing model adequacy, and the second‐order weighted generalized estimating equation (WGEE) estimation for mean and covariance models. Simulation results reveal that JLIC outperforms existing methods performing model selection for the mean regression and the correlation structure in a two stage and hence separate manner. We apply the proposal to a longitudinal study to identify factors associated with life satisfaction in the elderly of Taiwan.     

Double‐wavelet transform for multisubject task‐induced functional magnetic resonance imaging data

The goal of this article is to model multisubject task‐induced functional magnetic resonance imaging (fMRI) response among predefined regions of interest (ROIs) of the human brain. Conventional approaches to fMRI analysis only take into account temporal correlations, but do not rigorously model the underlying spatial correlation due to the complexity of estimating and inverting the high dimensional spatio‐temporal covariance matrix. Other spatio‐temporal model approaches estimate the covariance matrix with the assumption of stationary time series, which is not always feasible. To address these limitations, we propose a double‐wavelet approach for modeling the spatio‐temporal brain process. Working with wavelet coefficients simplifies temporal and spatial covariance structure because under regularity conditions, wavelet coefficients are approximately uncorrelated. Different wavelet functions were used to capture different correlation structures in the spatio‐temporal model. The main advantages of the wavelet approach are that it is scalable and that it deals with nonstationarity in brain signals. Simulation studies showed that our method could reduce false‐positive and false‐negative rates by taking into account spatial and temporal correlations simultaneously. We also applied our method to fMRI data to study activation in prespecified ROIs in the prefontal cortex. Data analysis showed that the result using the double‐wavelet approach was more consistent than the conventional approach when sample size decreased.     

Spatial regression techniques for inter‐population data: studying the relationships between morphological and environmental variation

Understanding the importance of environmental dimensions behind the morphological variation among populations has long been a central goal of evolutionary biology. The main objective of this study was to review the spatial regression techniques employed to test the association between morphological and environmental variables. In addition, we show empirically how spatial regression techniques can be used to test the association of cranial form variation among worldwide human populations with a set of ecological variables, taking into account the spatial autocorrelation in data. We suggest that spatial autocorrelation must be studied to explore the spatial structure underlying morphological variation and incorporated in regression models to provide more accurate statistical estimates of the relationships between morphological and ecological variables. Finally, we discuss the statistical properties of these techniques and the underlying reasons for using the spatial approach in population studies.     

Global patterns and predictors of tropical reef fish species richness

In the marine realm, the tropics host an extraordinary diversity of taxa but the drivers underlying the global distribution of marine organisms are still under scrutiny and we still lack an accurate global predictive model. Using a spatial database for 6336 tropical reef fishes, we attempted to predict species richness according to geometric, biogeographical and environmental explanatory variables. In particular, we aimed to evaluate and disentangle the predictive performances of temperature, habitat area, connectivity, mid‐domain effect and biogeographical region on reef fish species richness. We used boosted regression trees, a flexible machine‐learning technique, to build our predictive model and structural equation modeling to test for potential ‘mediation effects’ among predictors. Our model proved to be accurate, explaining 80% of the total deviance in fish richness using a cross‐validated procedure. Coral reef area and biogeographical region were the primary predictors of reef fish species richness, followed by coast length, connectivity, mid‐domain effect and sea surface temperature, with interactions between the region and other predictors. Important indirect effects of water temperature on reef fish richness, mediated by coral reef area, were also identified. The relationship between environmental predictors and species richness varied markedly among biogeographical regions. Our analysis revealed that a few easily accessible variables can accurately predict reef fish species richness. They also highlight concerns regarding ongoing environmental declines, with region‐specific responses to variation in environmental conditions predicting a variable response to anthropogenic impacts.     

结构方程模型及其在生态学中的应用

基于多变量统计方法同时研究自然系统内多个因子之间的相互关系, 是阐释复杂的自然系统的一个重要手段。相比传统的多变量统计法, 结构方程模型基于研究者的先验知识预先设定系统内因子间的依赖关系, 不仅能够判别各因子之间的关系强度(路径系数), 还能对整体模型进行拟合和判断, 从而能更全面地了解自然系统。由于结构方程模型只在近年才被应用到生态学的数据分析中, 因此该文试图对其作一简略介绍, 包括结构方程模型的定义和变量类型, 结合事例研究展现结构方程模型分析的一般步骤、在生态学中的应用以及相关软件的介绍等。望能为相关研究人员提供直观的认识, 加强结构方程模型在生态学数据分析中的应用。     

Using simultaneous equation modeling for defining complex phenotypes

Background

Interactions between multiple biological phenotypes are difficult to model. Simultaneous equation modelling (SEM), as used in econometric modelling, may prove an effective tool for this problem. Generalized linear models were used to derive the structural equations defining the interactions between cholesterol, glucose, triglycerides and high-density lipoprotein cholesterol (HDL-C). These structural equations were then applied, using SEM, to Cohort 2 data (replicates 1–100) to estimate the phenotypic structure underlying the simulation. The goal was to determine if this empiric method of deriving structural equations for use in SEM was able to recover the simulation model better than generalized linear models.

Results

First, the underlying structural equations were estimated using generalized linear model techniques, which found strong a relationship between glucose, triglycerides and HDL-C. Using these structural equations, I used SEM to evaluate these relationships jointly. I found that a combination of the empiric structural equations and the SEM method was better at recovering the underlying simulated relationship between biologic measures than generalized linear modelling.

Conclusion

The empiric SEM procedure presented here estimated different relationships between dependent variables than generalized linear modelling. The SEM procedure using empirically developed structural equations was able to recover the underlying simulation relationship partially and thus holds promise as a technique for complex phenotype analysis. Robust methods for determining the structural equations must be developed for application of SEM to population data.

     

Ontogenetic study of the supraorbital region in modern humans: a longitudinal test of the spatial model

The structural significance of the hominid supraorbital torus and its morphological variation have always been a controversial topic in physical anthropology. Understanding the function of browridge variation in living and fossil human populations is relevant to questions of human evolution. This study utilizes radiograph images to evaluate the spatial model in modern humans during ontogeny. This structural model attributes variation in the supraorbital region to the positional relationship between the neurocranium and the orbits. The relationship between measurements of the antero-posterior supraorbital length and the factors specified in the spatial model were assessed by correlation and partial correlation analyses. Growth rates were also examined to study ontogenetic trajectories and infer aspects of developmental relationships between critical variables. Results agree with previous research supporting the existence of spatial influences between the neural and orbital-upper facial regions on browridge length during ontogeny.     

Bayesian lasso for semiparametric structural equation models

There has been great interest in developing nonlinear structural equation models and associated statistical inference procedures, including estimation and model selection methods. In this paper a general semiparametric structural equation model (SSEM) is developed in which the structural equation is composed of nonparametric functions of exogenous latent variables and fixed covariates on a set of latent endogenous variables. A basis representation is used to approximate these nonparametric functions in the structural equation and the Bayesian Lasso method coupled with a Markov Chain Monte Carlo (MCMC) algorithm is used for simultaneous estimation and model selection. The proposed method is illustrated using a simulation study and data from the Affective Dynamics and Individual Differences (ADID) study. Results demonstrate that our method can accurately estimate the unknown parameters and correctly identify the true underlying model.     

The Relationship between Economic Status,Knowledge on Dengue,Risk Perceptions and Practices

The reemergence of dengue as an important public health problem reflects the difficulties in sustaining vertically organized, effective, control programs and the need for community-based strategies for Aedes aegypti control that result in behavioral change. We aimed to disentangle the relationships between underlying determinants of dengue related practices. We conducted a cross-sectional study in 780 households in La Lisa, Havana, Cuba. A questionnaire and an observation guide were administrated to collect information on variables related to economic status, knowledge on dengue, risk perception and practices associated with Aedes aegypti breading sites. To test a conceptual model that hypothesized direct relationships among all these constructs, we first used Exploratory Factor Analysis with Principal Component Analysis to establish the relationship between observed variables and the underlying latent variables. Subsequently, we tested whether the observed data supported the conceptual model through Confirmatory Factor Analysis. Exploratory Factor Analysis indicated that the items measured could be reduced into five factors with an eigenvalue >1.0: Knowledge on dengue, Intradomiciliar risk practices, Peridomiciliar risk practices, Risk perception and Economic status. The proportion of the total variance in the data explained by these five factors was 74.3%. The Confirmatory Factor Analysis model differed from our hypothesized conceptual model. Only Knowledge on dengue had a significant, direct, positive, effect on Practices. There was also a direct association of Economic status with Knowledge on dengue, but not with Risk perception and Practices. Clarifying the relationship between direct and indirect determinants of dengue related practices contributes to a better understanding of the potential effect of Information Education and Communication on practices and on the reduction of Aedes aegypti breeding sites and provides inputs for designing a community based strategy for dengue control.     

Matching data sets from two different spatial samples

Abstract. Methods for coupling two data sets (species composition and environmental variables for example) are well known and often used in ecology. All these methods require that variables of the two data sets have been recorded at the same sample stations. But if the two data sets arise from different sample schemes, sample locations can be different. In this case, scientists usually transform one data set to conform with the other one that is chosen as a reference. This inevitably leads to some loss of information. We propose a new ordination method, named spatial‐RLQ analysis, for coupling two data sets with different spatial sample techniques. Spatial‐RLQ analysis is an extension of co‐inertia analysis and is based on neighbourhood graph theory and classical RLQ analysis. This analysis finds linear combinations of variables of the two data sets which maximize the spatial cross‐covariance. This provides a co‐ordination of the two data sets according to their spatial relationships. A vegetation study concerning the forest of Chizé (western France) is presented to illustrate the method.     

Multivariate geostatistical methods for analysis of relationships between ecological indicators and environmental factors at multiple spatial scales

As all biodiversity-related variables, ecological indicators are influenced by environmental factors working at different spatial scales. However, assessing the relationship between environmental factors and ecological indicators is limited to a set of spatial scales determined a priori. This a priori assumption can hide important relationships, especially for ecological indicators with a complex spatial structure that can be driven, for example, by the influence of multiple pollutants with different dispersion ranges or by the influence of local and regional factors such as land-cover and climate. To relate ecological indicators and environmental factors without assuming a priori spatial scales of analysis, we used a Linear Model of Coregionalization. This method has been used in literature to analyze the joint distribution of biodiversity variables. Here we show that it can be used to gain insight into spatial patterns of relationships between ecological indicators and underlying environmental factors. We applied this method to a region of south-west Europe, relating data from land-cover, altitude and climate with an ecological indicator, the abundance of fruticose lichen species, known to be very sensitive to multiple environmental factors. Based on variogram analysis we identified distinct spatial scales of relationships between the ecological indicator and environmental factors. For each spatial scale we described relationships using Principal Component Analysis applied to the coregionalization matrices. This way we could assess how strong the relationship between each environmental factor and ecological indicator at each spatial scale was: at medium scales (c. 15 km) open spaces areas (a proxy for particle emissions) were more important; at larger scales (c. 45 km) open spaces, artificial areas (a proxy for gaseous pollutants) and also climate were preponderant. Thus, multivariate geostatistics provided a tool to improve knowledge on relationships between ecological indicators and environmental factors at multiple spatial scales without setting a priori spatial scales of analysis.     

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.     

Spatial variation in bird species abundances: Environmental constraints across southern Neotropical regions

Climate and habitat type are frequently related with the abundance of individual species and have been hypothesized to be primary drivers of the spatial variation in species abundances at the regional scale. Our aim is to evaluate the relative roles of those environmental factors in determining spatial variation in bird species abundance. We surveyed birds and habitat-cover variables and compiled climatic data along a 1700-km latitudinal gradient in the southern Neotropics. To identify the primary environmental variable explaining spatial changes in species abundances we performed simple regressions; a goodness of fit test identified the environmental factor that most frequently acted as the primary predictor. Mantel tests and partial regressions were performed to account for the spatial structure of abundance and environmental factors and collinearity between them. Of the 88 species included, 70% responded primarily to habitat cover and the remaining to climate. Forest cover and annual thermal amplitude were the main habitat-cover and climatic variables, respectively, explaining spatial variation in bird abundances. Our results indicated that the considered environmental factors accounted for latitudinal changes in species abundances; however, habitat cover and climate together explained a higher proportion of the variation than each factor independently of each other. There was a primacy of habitat-cover type over climate to predict spatial changes in bird species abundances across the neotropical biogeographic regions studied, but the underlying causes are likely related with the interaction of both factors.