Asymmetric circular-linear multivariate regression models with applications to environmental data

We propose asymmetric angular-linear multivariate regression models, which were motivated by the need to predict some environmental characteristics based on some circular and linear predictors. A measure of fit is provided through the residual analysis. Some applications using data from solar energy radiation experiment and wind energy are given. Received: September 2003 / Revised: February 2005     

Modelling skewed data with many zeros: A simple approach combining ordinary and logistic regression

We discuss a method for analyzing data that are positively skewed and contain a substantial proportion of zeros. Such data commonly arise in ecological applications, when the focus is on the abundance of a species. The form of the distribution is then due to the patchy nature of the environment and/or the inherent heterogeneity of the species. The method can be used whenever we wish to model the data as a response variable in terms of one or more explanatory variables. The analysis consists of three stages. The first involves creating two sets of data from the original: one shows whether or not the species is present; the other indicates the logarithm of the abundance when it is present. These are referred to as the presence data and the log-abundance data, respectively. The second stage involves modelling the presence data using logistic regression, and separately modelling the log-abundance data using ordinary regression. Finally, the third stage involves combining the two models in order to estimate the expected abundance for a specific set of values of the explanatory variables. A common approach to analyzing this sort of data is to use a ln (y+c) transformation, where c is some constant (usually one). The method we use here avoids the need for an arbitrary choice of the value of c, and allows the modelling to be carried out in a natural and straightforward manner, using well-known regression techniques. The approach we put forward is not original, having been used in both conservation biology and fisheries. Our objectives in this paper are to (a) promote the application of this approach in a wide range of settings and (b) suggest that parametric bootstrapping be used to provide confidence limits for the estimate of expected abundance.     

Multivariate analysis of spatial patterns: a unified approach to local and global structures

We propose a new approach to the multivariate analysis of data sets with known sampling site spatial positions. A between-sites neighbouring relationship must be derived from site positions and this relationship is introduced into the multivariate analyses through neighbouring weights (number of neighbours at each site) and through the matrix of the neighbouring graph. Eigenvector analysis methods (e.g. principal component analysis, correspondence analysis) can then be used to detect total, local and global structures. The introduction of the D-centring (centring with respect to the neighbouring weights) allows us to write a total variance decomposition into local and global components, and to propose a unified view of several methods. After a brief review of the matrix approach to this problem, we present the results obtained on both simulated and real data sets, showing how spatial structure can be detected and analysed. Freely available computer programs to perform computations and graphical displays are proposed.     

Regression analysis of correlated circular data based on the multivariate von Mises distribution

Environmental and Ecological Statistics - A regression model for correlated circular data is proposed by assuming that samples of angular measurements are drawn from a multivariate von Mises...     

Compositional analysis of topsoil metals and its associations with cancer mortality using spatial misaligned data

The presence of toxic metals in soil per se, and in soil impacted by mining, industry, agriculture and urbanisation in particular, is a major concern for both human health and ecotoxicology. The dual aim of this study was: to ascertain whether topsoil composition could influence the spatial distribution of mortality due to different types of cancer and to identify possible errors committed by epidemiological studies which analyse soil composition data as a closed number system. We conducted an ecological cancer mortality study, covering 861,440 cancer deaths (27 cancer sites) in 7917 Spanish mainland towns, from 1999 to 2008. Topsoil levels of Al, As, Cd, Cr, Cu, Fe, Mn, Ni, Pb and Zn were determined by ICP-MS at 13,317 sampling points. We transformed the topsoil data in two ways, i.e. log transformation and centred logratio transformation. Principal factor analysis was performed to obtain independent latent factors for the transformed variables. To estimate the effect on mortality of topsoil factor loadings, we fitted Besag, York and Mollié models embedded in geostatistical-spatial models. This model included soil sample locations and town centroids (non-aligned data), fitted using the integrated nested Laplace approximation (INLA) as a tool for Bayesian inference and stochastic partial differential equations (SPDE). All results were adjusted for socio-demographic variables. The results indicated that soil composition could have an influence on the spatial distribution and mortality patterns of cancer. The analysis adjusted for socio-demographic variables showed excess male mortality due to digestive system tumours in areas with soils containing higher Cd, Pb, Zn, Mn and Cu concentrations, bladder cancer in areas with soils containing higher Cd concentrations, and brain cancer in areas with soils containing As. In both sexes, cancer of oesophagus was associated with soils containing a higher lead content, while lung cancer was associated with soils containing a higher copper content. Stress should be laid on the importance of taking into account the compositional nature of the data in this type of analysis.     

Modelling the spatial structure of forest stands by multivariate point processes with hierarchical interactions

A stochastic model is applied to describe the spatial structure of a forest stand. We aim at quantifying the strength of the competition process between the trees in terms of interaction within and between different size classes of trees using multivariate Gibbs point processes with hierarchical interactions introduced in [Högmander, H., Särkkä, A., 1999. Multitype spatial point patterns with hierarchical interactions. Biometrics 55, 1051–1058]. The new model overcomes the main limitation of the traditional use of the Gibbs models allowing to describe systems with non-symmetric interactions between different objects. When analyzing interactions between neighbouring trees it is natural to assume that the size of a tree determines its hierarchical level: the largest trees are not influenced by any other trees than the trees in the same size class, while trees in the other size classes are influenced by the other trees in the same class as well as by all larger trees. In this paper, we describe a wide range of Gibbs models with both hierarchical and non-hierarchical interactions as well as a simulation algorithm and a parameter estimation procedure for the hierarchical models. We apply the hierarchical interaction model to the analysis of forest data consisting of locations and diameters of tree stems.     

Design-based spatial interpolation with data driven selection of the smoothing parameter

Environmental and Ecological Statistics - In the inverse distance weighting interpolation the interpolated, value is a weighted mean of the sampled values, with weights decreasing with the...     

Using a non-homogeneous Poisson model with spatial anisotropy and change-points to study air pollution data

Environmental and Ecological Statistics - A non-homogeneous Poisson process is used to study the rate at which a pollutant’s concentration exceeds a given threshold of interest. An...     

Using spatial smoothing to model a functional regression estimator to points on a lattice with application to surface-level ozone in the Eastern United States

Environmental and Ecological Statistics - Spatial functional regression methods allow researchers to model spatially dependent functional random variables, often using a kriging-based interpolation...     

A geostatistical approach for mapping thematic classification accuracy and evaluating the impact of inaccurate spatial data on ecological model predictions

Spatial information in the form of geographical information system coverages and remotely sensed imagery is increasingly used in ecological modeling. Examples include maps of land cover type from which ecologically relevant properties, such as biomass or leaf area index, are derived. Spatial information, however, is not error-free: acquisition and processing errors, as well as the complexity of the physical processes involved, make remotely sensed data imperfect measurements of ecological attributes. It is therefore important to first assess the accuracy of the spatial information being used and then evaluate the impact of such inaccurate information on ecological model predictions. In this paper, the role of geostatistics for mapping thematic classification accuracy through integration of abundant image-derived (soft) and sparse higher accuracy (hard) class labels is presented. Such assessment leads to local indices of map quality, which can be used for guiding additional ground surveys. Stochastic simulation is proposed for generating multiple alternative realizations (maps) of the spatial distribution of the higher accuracy class labels over the study area. All simulated realizations are consistent with the available pieces of information (hard and soft labels) up to their validated level of accuracy. The simulated alternative class label representations can be used for assessing joint spatial accuracy, i.e., classification accuracy regarding entire spatial features read from the thematic map. Such realizations can also serve as input parameters to spatially explicit ecological models; the resulting distribution of ecological responses provides a model of uncertainty regarding the ecological model prediction. A case study illustrates the generation of alternative land cover maps for a Landsat Thematic Mapper (TM) subscene, and the subsequent construction of local map quality indices. Simulated land cover maps are then input into a biogeochemical model for assessing uncertainty regarding net primary production (NPP).     

A varying-coefficient regression approach to modeling the effects of wind speed on the dispersion of pollutants

Environmental and Ecological Statistics - The real-world monitoring system of air pollution ordinarily collects data about pollutant concentration levels at pollution sources and monitors stations...     

Tradeoffs between forestry resource and conservation values under alternate policy regimes: A spatial analysis of the western Canadian boreal plains

An important element of resource management and conservation is an understanding of the tradeoffs between marketed products, such as timber, and measures of environmental quality, such as biodiversity. In this paper, we develop an integrated economic-ecological spatial optimization model that we then apply to evaluate alternate forest policies on a 560,000 km² study region of managed boreal forest in Alberta and British Columbia, Canada. The integrated model incorporates dynamic forest sector harvesting, current levels of oil and gas sector development, coarse-filter or habitat-based old forest indicators, a set of empirical forest bird abundance models, and statistical models of the natural and current fire regimes. Using our integrated model, economic tradeoff curves, or production possibility frontiers, are developed to illustrate the cost of achieving coarse-filter targets by a set time (50 years) within a 100-year time horizon. We found levels of ecological indicators and economic returns from the timber industry could both be increased if spatial constraints imposed by the current policy environment were relaxed; other factors being equal, this implies current policy should be revised. We explore the production possibility frontier's relationship to the range of natural variation of old forest habitat, and show how this range can be used to guide choices of preferred locations along the frontier. We also show that coarse-filter constraints on the abundance of certain habitat elements are sufficient to satisfy some fine-filter objectives, expressed as the predicted abundances of various species of songbirds.     

Using regression models to evaluate the formation of trihalomethanes and haloacetonitriles via chlorination of source water with low SUVA values in the Yangtze River Delta region,China

The purpose of this study was to develop the multiple regression models to evaluate the formation of trihalomethanes (THMs) and haloacetonitriles (HANs) during chlorination of source water with low specific ultraviolet absorbance (SUVA) in Yangtze River Delta, China. The results showed that the regression models of THMs exhibited good accuracy and precision, and 86–97 % of the calculated values fell within ±25 % of the measured values. While the HANs models showed relatively weak evaluation ability, as only 75–83 % of the calculated values were within ±25 % of the measured values. The organic matter [dissolved organic carbon (DOC) or UV absorbance at 254 nm] and bromide exerted the most important influence on the formation of HANs. While for THMs, besides the organic matter and bromide, reaction time was also a key factor. Comparing the models for total THMs (T-THMs) in this study with others revealed that the regression models from the low SUVA waters may have low DOC coefficients, but high bromide coefficients as compared with those from the high SUVA waters.     

A general approach to the analysis of habitat selection

The investigation of animal habitat selection aims at the detection of selective usage of habitat types and the identification of covariates influencing their selection. The results not only allow for a better understanding of the habitat selection process but are also intended to help improve the conservation of animals. Usually, habitat selection by larger animals is assessed by radio-tracking or visual observation studies, where the chosen habitat is determined for some animals at a set of specific points in time. Hence the resulting data often have the following structure: a categorical variable indicating the habitat type selected by an animal at a specific point in time is repeatedly observed and will be explained by covariates. These may either describe properties of the habitat types currently available and/or properties of the animal. In this paper, we present a general approach to the analysis of such data in a categorical regression setup. The proposed model generalizes and improves upon several of the approaches previously discussed in the literature. In particular, it accounts for changing habitat availability due to the movement of animals within the observation area. It incorporates both habitat- and animal-specific covariates, and includes individual-specific random effects to account for correlations introduced by the repeated measurements on single animals. Furthermore, the assumption that the effects are linear can be dropped by including the effects in nonparametric manner based on a penalized spline approach. The methodology is implemented in a freely available software package. We demonstrate the general applicability and the potential of the proposed approach in two case studies: The analysis of a songbird community in South-America and a study on brown bears in Central Europe.     

Detection and delineation of critical areas using echelons and spatial scan statistics with synoptic cellular data

Geographical surveillance for hotspot detection and delineation has become an important area of investigation both in geospatial ecosystem health and in geospatial public health. In order to find critical areas based on synoptic cellular data, geospatial ecosystem health investigations apply recently discovered echelon tools. In order to find elevated rate areas based on synoptic cellular data, geospatial public health investigations apply recently discovered spatial scan statistic tools. The purpose of this paper is to conceptualize a joint role for these together in the spirit of a cross-disciplinary cross-fertilization to accomplish more effective and efficient geographical surveillance for hotspot detection and delineation, and early warning system.     

Quantitative approaches to the analysis of stable isotope food web data

Ecologists use stable isotopes (delta13C, delta15N) to better understand food webs and explore trophic interactions in ecosystems. Traditionally, delta13C vs. delta15N bi-plots have been used to describe food web structure for a single time period or ecosystem. Comparisons of food webs across time and space are increasing, but development of statistical approaches for testing hypotheses regarding food web change has lagged behind. Here we present statistical methodologies for quantitatively comparing stable isotope food web data. We demonstrate the utility of circular statistics and hypothesis tests for quantifying directional food web differences using two case studies: an arthropod salt marsh community across a habitat gradient and a freshwater fish community from Lake Tahoe, USA, over a 120-year time period. We calculated magnitude and mean angle of change (theta) for each species in food web space using mean delta13C and delta15N of each species as the x, y coordinates. In the coastal salt marsh, arthropod consumers exhibited a significant shift toward dependence on Spartina, progressing from a habitat invaded by Phragmites to a restored Spartina habitat. In Lake Tahoe, we found that all species from the freshwater fish community shifted in the same direction in food web space toward more pelagic-based production with the introduction of nonnative Mysis relicta and onset of cultural eutrophication. Using circular statistics to quantitatively analyze stable isotope food web data, we were able to gain significant insight into patterns and changes in food web structure that were not evident from qualitative comparisons. As more ecologists incorporate a food web perspective into ecosystem analysis, these statistical tools can provide a basis for quantifying directional food web differences from standard isotope data.     

Random denominators and the analysis of ratio data

Ratio data, observations in which one random value is divided by another random value, present unique analytical challenges. The best statistical technique varies depending on the unit on which the inference is based. We present three environmental case studies where ratios are used to compare two groups, and we provide three parametric models from which to simulate ratio data. The models describe situations in which (1) the numerator variance and mean are proportional to the denominator, (2) the numerator mean is proportional to the denominator but its variance is proportional to a quadratic function of the denominator and (3) the numerator and denominator are independent. We compared standard approaches for drawing inference about differences between two distributions of ratios: t-tests, t-tests with transformations, permutation tests, the Wilcoxon rank test, and ANCOVA-based tests. Comparisons between tests were based both on achieving the specified alpha-level and on statistical power. The tests performed comparably with a few notable exceptions. We developed simple guidelines for choosing a test based on the unit of inference and relationship between the numerator and denominator.     

Application of multivariate statistical analysis in the pollution and health risk of traffic-related heavy metals

This study aims to analyse the heavy metal pollutants in Jeddah, the second largest city in the Gulf Cooperation Council with a population exceeding 3.5 million, and many vehicles. Ninety-eight street dust samples were collected seasonally from the six major roads as well as the Jeddah Beach, and subsequently digested using modified Leeds Public Analyst method. The heavy metals (Fe, Zn, Mn, Cu, Cd, and Pb) were extracted from the ash using methyl isobutyl ketone as solvent extraction and eventually analysed by atomic absorption spectroscopy. Multivariate statistical techniques, principal component analysis (PCA), and hierarchical cluster analysis were applied to these data. Heavy metal concentrations were ranked according to the following descending order: Fe > Zn > Mn > Cu > Pb > Cd. In order to study the pollution and health risk from these heavy metals as well as estimating their effect on the environment, pollution indices, integrated pollution index, enrichment factor, daily dose average, hazard quotient, and hazard index were all analysed. The PCA showed high levels of Zn, Fe, and Cd in Al Kurnish road, while these elements were consistently detected on King Abdulaziz and Al Madina roads. The study indicates that high levels of Zn and Pb pollution were recorded for major roads in Jeddah. Six out of seven roads had high pollution indices. This study is the first step towards further investigations into current health problems in Jeddah, such as anaemia and asthma.