Revisiting Guerry’s data: Introducing spatial constraints in multivariate analysis

<p>This thesis investigates three research problems which arise in multivariate data and censored regression. The first is the identification of outliers in multivariate data. The second is a dissimilarity measure for clustering purposes. The third is the diagnostics analysis for the Buckley-James method in censored regression. Outliers can be defined simply as an observation (or a subset of observations) that is isolated from the other observations in the data set. There are two main reasons that motivate people to find outliers; the first is the researcher's intention. The second is the effects of an outlier on analyses, i.e. the existence of outliers will affect means, variances and regression coefficients; they will also cause a bias or distortion of estimates; likewise, they will inflate the sums of squares and hence, false conclusions are likely to be created. Sometimes, the identification of outliers is the main objective of the analysis, and whether to remove the outliers or for them to be down-weighted prior to fitting a non-robust model. This thesis does not differentiate between the various justifications for outlier detection. The aim is to advise the analyst of observations that are considerably different from the majority. Note that the techniques for identification of outliers introduce in this thesis is applicable to a wide variety of settings. Those techniques are performed on large and small data sets. In this thesis, observations that are located far away from the remaining data are considered to be outliers. Additionally, it is noted that some techniques for the identification of outliers are available for finding clusters. There are two major challenges in clustering. The first is identifying clusters in high-dimensional data sets is a difficult task because of the curse of dimensionality. The second is a new dissimilarity measure is needed as some traditional distance functions cannot capture the pattern dissimilarity among the objects. This thesis deals with the latter challenge. This thesis introduces Influence Angle Cluster Approach (iaca) that may be used as a dissimilarity matrix and the author has managed to show that iaca successfully develops a cluster when it is used in partitioning clustering, even if the data set has mixed variables, i.e. interval and categorical variables. The iaca is developed based on the influence eigenstructure. The first two problems in this thesis deal with a complete data set. It is also interesting to study about the incomplete data set, i.e. censored data set. The term 'censored' is mostly used in biological science areas such as a survival analysis. Nowadays, researchers are interested in comparing the survival distribution of two samples. Even though this can be done by using the logrank test, this method cannot examine the effects of more than one variable at a time. This difficulty can easily be overcome by using the survival regression model. Examples of the survival regression model are the Cox model, Miller's model, the Buckely James model and the Koul- Susarla-Van Ryzin model. The Buckley James model's performance is comparable with the Cox model and the former performs best when compared both to the Miller model and the Koul-Susarla-Van Ryzin model. Previous comparison studies proved that the Buckley-James estimator is more stable and easier to explain to non-statisticians than the Cox model. Today, researchers are interested in using the Cox model instead of the Buckley-James model. This is because of the lack of function of Buckley-James model in the computer software and choices of diagnostics analysis. Currently, there are only a few diagnostics analyses for Buckley James model that exist. Therefore, this thesis proposes two new diagnostics analyses for the Buckley-James model. The first proposed diagnostics analysis is called renovated Cook's distance. This method produces comparable results with the previous findings. Nevertheless, this method cannot identify influential observations from the censored group. It can only detect influential observations from the uncensored group. This issue needs further investigation because of the possibility of censored points becoming influential cases in censored regression. Secondly, the local influence approach for the Buckley-James model is proposed. This thesis presents the local influence diagnostics of the Buckley-James model which consist of variance perturbation, response variable perturbation, censoring status perturbation, and independent variables perturbation. The proposed diagnostics improves and also challenge findings of the previous ones by taking into account both censored and uncensored data to have a possibility to become an influential observation.</p>

The processes by which plant spatial patterns are formed, and the effects of those patterns on plant community dynamics, remain important areas of research in plant ecology. Plant spatial pattern formation has been linked to many ecological processes that act to structure plant communities at different spatiotemporal scales. Past studies of pattern formation are common, but recent methodological advances in data collection and analysis have permitted researchers to conduct more advanced observational studies of pattern formation in space and time. While studies of the effects of plant spatial patterns were formally rare, they have increased in the last decade as new types of experiments and analysis have been developed to better understand the myriad effects of plant patterns on community dynamics. My dissertation research examined both the causes and consequences of plant spatial patterns in the context of natural and experimental Great Basin semi-arid plant communities. In both cases, I implemented novel methodologies for data collection, experimental design, and data analysis in an attempt to address current gaps in knowledge related to the processes by which plant spatial patterns are formed, as well as the effect of plant spatial patterns on community dynamics. The results inform both basic and applied plant ecology, and set the stage for further research on the causes and consequences of plant spatial patterns in semi-arid plant communities.

Parallel coordinate plots (PCPs) are commonly used in information visualization to provide insight into multi-variate data. These plots help to spot correlations between variables. PCPs have been successfully applied to unstructured datasets up to a few millions of points. In this paper, we present techniques to enhance the usability of PCPs for the exploration of large, multi-timepoint volumetric data sets, containing tens of millions of points per timestep. The main difficulties that arise when applying PCPs to large numbers of data points are visual clutter and slow performance, making interactive exploration infeasible. Moreover, the spatial context of the volumetric data is usually lost. We describe techniques for preprocessing using data quantization and compression, and for fast GPU-based rendering of PCPs using joint density distributions for each pair of consecutive variables, resulting in a smooth, continuous visualization. Also, fast brushing techniques are proposed for interactive data selection in multiple linked views, including a 3D spatial volume view. These techniques have been successfully applied to three large data sets: Hurricane Isabel (Vis'04 contest), the ionization front instability data set (Vis'08 design contest), and data from a large-eddy simulation of cumulus clouds. With these data, we show how PCPs can be extended to successfully visualize and interactively explore multi-timepoint volumetric datasets with an order of magnitude more data points.

Multivariate data analysis for Raman imaging of a model pharmaceutical tablet

Using airborne laser scanning to model potential abundance and assemblages of forest passerines

Modeling spatial and spatio-temporal continuous processes is an important and challenging problem in spatial statistics. Advanced Spatial Modeling with Stochastic Partial Differential Equations Using R and INLA describes in detail the stochastic partial differential equations (SPDE) approach for modeling continuous spatial processes with a Matern covariance, which has been implemented using the integrated nested Laplace approximation (INLA) in the R-INLA package. Key concepts about modeling spatial processes and the SPDE approach are explained with examples using simulated data and real applications. This book has been authored by leading experts in spatial statistics, including the main developers of the INLA and SPDE methodologies and the R-INLA package. It also includes a wide range of applications: * Spatial and spatio-temporal models for continuous outcomes * Analysis of spatial and spatio-temporal point patterns * Coregionalization spatial and spatio-temporal models * Measurement error spatial models * Modeling preferential sampling * Spatial and spatio-temporal models with physical barriers * Survival analysis with spatial effects * Dynamic space-time regression * Spatial and spatio-temporal models for extremes * Hurdle models with spatial effects * Penalized Complexity priors for spatial models All the examples in the book are fully reproducible. Further information about this book, as well as the R code and datasets used, is available from the book website at http://www.r-inla.org/spde-book. The tools described in this book will be useful to researchers in many fields such as biostatistics, spatial statistics, environmental sciences, epidemiology, ecology and others. Graduate and Ph.D. students will also find this book and associated files a valuable resource to learn INLA and the SPDE approach for spatial modeling.

The origins of modern spatial analysis lie in the development of quantitative geography and regional science in the late 1950s. The use of quantitative procedures and techniques to analyse patterns of points, lines, areas and surfaces depicted on analogue maps or defined by co-ordinates in two-or three-dimensional space characterise the initial stage. Later on, more emphasis was placed on the indigenous features of geographical space, on spatial choices and processes, and their implications for the spatio-temporal evolution of complex spatial systems. Spatial analysis, as it has become over the past four decades, is more than spatial statistics and data analysis, and goes far beyond data sampling, data manipulation, exploratory and confirmatory spatial data analysis, into areas of spatial modelling encompassing a large and diverse set of models in both the environmental and the social sciences. In the environmental sciences, they range from physical dispersion models (e.g. for suspended particulates), chemical reaction models (e.g. photochemical smog), and biological systems models (e.g. for ecosystems in water), through deterministic process and stochastic process models of regional environmental quality management, and integrated models for environment-energy-economic assessment. For many models, especially the physical dispersion models, chemical reaction models, and biological systems models, the geographical location of the site is not considered to be of overriding importance. The variation in model results over space can be achieved by obtaining different inputs to the area in question. Process models include deterministic versions which attempt to describe a particular sequence in terms of known physical laws, and stochastic model versions which aim to describe a particular process such as erosion, groundwater movement and absorption of pollutants in terms of probability theory. For such processes, there is an interaction between the spatial process and a substrate. This substrate provides a one-, two-or three-dimensional framework within which the process model can operate. The space in which the process is modelled is disaggregated into a set of finite elements which are usually assumed to be internally homogeneous. Two-dimensional models generally use as their data small pixels (see Fischer et al., 1996).

PurposeThe purpose of this paper is to describe how to measure workplace configuration, show its application in, and the results of, a field experiment aimed at improving collaborative knowledge work and identify and discuss larger problems involved with research on workplace configuration.Design/methodology/approachThe paper reviews recent thought on density, proximity and problems with evaluating configuration. It then describes a method of spatial network analysis used in a field experiment involving the reconfiguration of a workplace. This is followed with a discussion of recent research on knowledge work from economic geography.FindingsIt was found that, instead of increasing it, the reconfigured workplace decreased collaborative activity. The spatial network analysis shows how this occurred.Research limitations/implicationsThis method of spatial network analysis, when used carefully, is a robust technique for analyzing and comparing spatial configuration. Further research needs to address the links between spatial proximity and information and communications technologies as well as the relation of types of knowledge bases and associated forms of proximity that can stimulate collaboration.Practical implicationsWhile spatial network analysis methods are not do‐it‐yourself tools, corporate real estate managers should employ them, especially in larger‐scale projects, before committing to final workplace designs. They can also use them to identify and map best spatial patterns (like best practices) to identify strategic spatial patterns.Originality/valueThis appears to be the first rigorous application of spatial network methods in a field experiment involving a real workplace. The paper shows the method can clearly extract and discriminate spatial network patterns underlying configurations and relate them both quantitatively and graphically to employee evaluations of collaborative performance. It introduces concepts of comparative knowledge bases that need to be understood in determining the types of collaboration needed in a workplace.

Effects of including spatial information in clustering multivariate image data

Abstract:Understanding how species assemblages are structured in relation to environmental variation is a central issue in community ecology. However, factors that create regional variation in relative species abundances have been little studied due to the rarity of large-scale datasets. Here, we investigated a large dataset (30 180 0.5-ha plots spread over 1 600 000 ha) gathered from forest planning inventories in the semi-deciduous forest of the south western Central African Republic. We used Correspondence Analysis and Non-Symmetric Correspondence Analysis on Instrumental Variables to analyse variation in the abundance of 73 common tree species in relation to soil type, rainfall and proximity to villages. Together, environmental variables explained 10.3% of multi-species floristic variation among plots, and the regional spatial structure almost disappeared when the effects of these variables were removed. A Trend Surface Analysis using a third order polynomial function of the geographical coordinates of the plots explained 14.5% of the floristic variation and more than 75% of this variation was explained by environmental variables. Sandy soil was the most influential factor affecting floristic composition. Residual spatial variation not explained by the environmental variables probably reflects the natural and anthropogenic history of the vegetation.

Spatial and temporal variability of spontaneous grass cover and its influence on sediment losses in an extensive olive orchard catchment

Mangrove forests are highly productive and have large carbon sinks while also providing numerous goods and ecosystem services. However, effective management and conservation of the mangrove forests are often dependent on spatially explicit assessments of the resource. Given the remote and highly dispersed nature of mangroves, estimation of biomass and carbon in mangroves through routine field-based inventories represents a challenging task which is impractical for large-scale planning and assessment. Alternative approaches based on geospatial technologies are needed to support this estimation in large areas. However, spatial data processing and analysis approaches used in this estimation of mangrove biomass and carbon have not been adequately investigated. In this study, we present a spatially explicit analytical framework that integrate remotely sensed data and spatial analyses approaches to support the estimation of mangrove biomass and carbon stock and their spatial patterns in West Africa. Forest canopy height derived from SRTM and ICESat/GLAS data was used to estimate mangrove biomass and carbon in nine West African countries. We developed a geospatial software toolkit that implemented the proposed framework. The spatial analysis framework and software toolkit provide solid support for the estimation and relative comparisons of mangrove-related metrics. While the mean canopy height of mangroves in our study area is 10.2 m, the total biomass and carbon were estimated as 272.56 and 136.28 Tg. Nigeria has the highest total mangrove biomass and carbon in the nine countries, but Cameroon is the country with the largest mean biomass and carbon density. The resulting spatially explicit distributions of mangrove biomass and carbon hold great potential in guiding the strategic planning of large-scale field-based assessment of mangrove forests. This study demonstrates the utility of online geospatial data and spatial analysis as a feasible solution for estimating the distribution of mangrove biomass and carbon at larger or smaller scales.

Is power everything? What can we learn from large data sets

The spatial association pattern of insect and mite populations in a steel bin containing stored wheat, Triticum durum Desf., in central Greece, was studied using the Spatial Analysis by Distance IndicEs (SADIE). The monitoring was carried out for 7 mo by using grain trier samples and probe traps. The most abundant insect species were Cryptolestes ferrugineus (Stephens) (Coleoptera: Laemophloeidae) and Plodia interpunctella (Hübner) (Lepidoptera: Pyralidae). For mites, the most abundant species were the phytophagous Lepidoglyphus destructor (Schrank) (Acari: Glycyphagidae) and the predator Blattisocius tarsalis (Berlese) (Mesostigmata: Ascidae). Both for P. interpunctella and C. ferrugineus, trap catches were associated with numbers of individuals in the trier samples, but the overall association index calculated among trap and sample counts was significant only in the 33% of trap-sample pairs of values. Generally, P. interpunctella had the main patch areas in the central part of the bin, with few exceptions, during the entire monitoring period. Similar trends also were noted in the case of C. ferrugineus, which was clearly aggregated in the center of the grain mass. Spatial association maps indicated a stable positive association in the central part of the bin, but in most of the other sampling zones the association was negative. However, distribution of L. destructor, based on trier samples, indicated increased presence in peripheral zones of the grain sampling area. Moreover, B. tarsalis presented the most dispersed distribution among all four species. For each species, the association between two consecutive samplings was significant in the majority of cases, indicating a stable spatial pattern. Finally, B. tarsalis was spatially associated to a higher degree with the insects found rather than with L. desctructor. Moreover, there was no association of insect and mite presence with grain temperature and moisture content. The results of the current study suggest that the coexistence of insects and mites in bulked grain follows a complex pattern, with significant interactions, especially in the case of mite predators, which are spatially associated with insect species.

Chapter 5 - Spatiotemporal pattern and hotspot detection of malaria using spatial analysis and GIS in West Bengal: an approach to medical GIS