Spatial and Temporal Changes in Soil Organic Carbon Assessment using an Integrated Geostatistical and Compositional Data Analysis Approach

The Irish and UK governments, along with other countries, have made a commitment to limit the concentrations of greenhouse gases in the atmosphere by reducing emissions from the burning of fossil fuels. This can be achieved (in part) through increasing the sequestration of CO2 from the atmosphere including monitoring the amount stored in vegetation and soils. A large proportion of soil carbon is held within peat due to the relatively high carbon density of peat and organic-rich soils. This is particularly important for a country such as Ireland, where some 16% of the land surface is covered by peat. For Northern Ireland, it has been estimated that the total amount of carbon stored in vegetation is 4.4Mt compared to 386Mt stored within peat and soils. As a result it has become increasingly important to measure and monitor changes in stores of carbon in soils. The conservation and restoration of peat covered areas, although ongoing for many years, has become increasingly important. This is summed up in current EU policy outlined by the European Commission (2012) which seeks to assess the relative contributions of the different inputs and outputs of organic carbon and organic matter to and from soil. Results are presented from the EU-funded Tellus Border Soil Carbon Project (2011 to 2013) which aimed to improve current estimates of carbon in soil and peat across Northern Ireland and the bordering counties of the Republic of Ireland.
Historical reports and previous surveys provide baseline data. To monitor change in peat depth and soil organic carbon, these historical data are integrated with more recently acquired airborne geophysical (radiometric) data and ground-based geochemical data generated by two surveys, the Tellus Project (2004-2007: covering Northern Ireland) and the EU-funded Tellus Border project (2011-2013) covering the six bordering counties of the Republic of Ireland, Donegal, Sligo, Leitrim, Cavan, Monaghan and Louth. The concept being applied is that saturated organic-rich soil and peat attenuate gamma-radiation from underlying soils and rocks. This research uses the degree of spatial correlation (coregionalization) between peat depth, soil organic carbon (SOC) and the attenuation of the radiometric signal to update a limited sampling regime of ground-based measurements with remotely acquired data. To comply with the compositional nature of the SOC data (perturbations of loss on ignition [LOI] data), a compositional data analysis approach is investigated. Contemporaneous ground-based measurements allow corroboration for the updated mapped outputs. This provides a methodology that can be used to improve estimates of soil carbon with minimal impact to sensitive habitats (like peat bogs), but with maximum output of data and knowledge.

Compositional Data Analysis in Forensic Geoscience

Statistics are regularly used to make some form of comparison between trace evidence or deploy the exclusionary principle (Morgan and Bull, 2007) in forensic investigations. Trace evidence are routinely the results of particle size, chemical or modal analyses and as such constitute compositional data. The issue is that compositional data including percentages, parts per million etc. only carry relative information. This may be problematic where a comparison of percentages and other constraint/closed data is deemed a statistically valid and appropriate way to present trace evidence in a court of law. Notwithstanding an awareness of the existence of the constant sum problem since the seminal works of Pearson (1896) and Chayes (1960) and the introduction of the application of log-ratio techniques (Aitchison, 1986; Pawlowsky-Glahn and Egozcue, 2001; Pawlowsky-Glahn and Buccianti, 2011; Tolosana-Delgado and van den Boogaart, 2013) the problem that a constant sum destroys the potential independence of variances and covariances required for correlation regression analysis and empirical multivariate methods (principal component analysis, cluster analysis, discriminant analysis, canonical correlation) is all too often not acknowledged in the statistical treatment of trace evidence. Yet the need for a robust treatment of forensic trace evidence analyses is obvious. This research examines the issues and potential pitfalls for forensic investigators if the constant sum constraint is ignored in the analysis and presentation of forensic trace evidence. Forensic case studies involving particle size and mineral analyses as trace evidence are used to demonstrate the use of a compositional data approach using a centred log-ratio (clr) transformation and multivariate statistical analyses.

Lecture Notes on Compositional Data Analysis

These notes have been prepared as support to a short course on compositional data analysis. Their aim is to transmit the basic concepts and skills for simple applications, thus setting the premises for more advanced projects

Compositional data analysis: where we are and where should we be heading?

We take stock of the present position of compositional data analysis, of what has been achieved in the last 20 years, and then make suggestions as to what may be sensible avenues of future research. We take an uncompromisingly applied mathematical view, that the challenge of solving practical problems should motivate our theoretical research; and that any new theory should be thoroughly investigated to see if it may provide answers to previously abandoned practical considerations. Indeed a main theme of this lecture will be to demonstrate this applied mathematical approach by a number of challenging examples

Possible solution of some essential zero problems in compositional data analysis

One of the tantalising remaining problems in compositional data analysis lies in how to deal with data sets in which there are components which are essential zeros. By an essential zero we mean a component which is truly zero, not something recorded as zero simply because the experimental design or the measuring instrument has not been sufficiently sensitive to detect a trace of the part. Such essential zeros occur in many compositional situations, such as household budget patterns, time budgets, palaeontological zonation studies, ecological abundance studies. Devices such as nonzero replacement and amalgamation are almost invariably ad hoc and unsuccessful in such situations. From consideration of such examples it seems sensible to build up a model in two stages, the first determining where the zeros will occur and the second how the unit available is distributed among the non-zero parts. In this paper we suggest two such models, an independent binomial conditional logistic normal model and a hierarchical dependent binomial conditional logistic normal model. The compositional data in such modelling consist of an incidence matrix and a conditional compositional matrix. Interesting statistical problems arise, such as the question of estimability of parameters, the nature of the computational process for the estimation of both the incidence and compositional parameters caused by the complexity of the subcompositional structure, the formation of meaningful hypotheses, and the devising of suitable testing methodology within a lattice of such essential zero-compositional hypotheses. The methodology is illustrated by application to both simulated and real compositional data

Some last thoughts on compositional data analysis

One of the disadvantages of old age is that there is more past than future: this, however, may be turned into an advantage if the wealth of experience and, hopefully, wisdom gained in the past can be reflected upon and throw some light on possible future trends. To an extent, then, this talk is necessarily personal, certainly nostalgic, but also self critical and inquisitive about our understanding of the discipline of statistics. A number of almost philosophical themes will run through the talk: search for appropriate modelling in relation to the real problem envisaged, emphasis on sensible balances between simplicity and complexity, the relative roles of theory and practice, the nature of communication of inferential ideas to the statistical layman, the inter-related roles of teaching, consultation and research. A list of keywords might be: identification of sample space and its mathematical structure, choices between transform and stay, the role of parametric modelling, the role of a sample space metric, the underused hypothesis lattice, the nature of compositional change, particularly in relation to the modelling of processes. While the main theme will be relevance to compositional data analysis we shall point to substantial implications for general multivariate analysis arising from experience of the development of compositional data analysis…

A tale of two logits, compositional data analysis and zero observations

The application of compositional data analysis through log ratio trans- formations corresponds to a multinomial logit model for the shares themselves. This model is characterized by the property of Independence of Irrelevant Alter- natives (IIA). IIA states that the odds ratio in this case the ratio of shares is invariant to the addition or deletion of outcomes to the problem. It is exactly this invariance of the ratio that underlies the commonly used zero replacement procedure in compositional data analysis. In this paper we investigate using the nested logit model that does not embody IIA and an associated zero replacement procedure and compare its performance with that of the more usual approach of using the multinomial logit model. Our comparisons exploit a data set that com- bines voting data by electoral division with corresponding census data for each division for the 2001 Federal election in Australia

Compositional data analysis with R

Examples of compositional data. The simplex, a suitable sample space for compositional data and Aitchison's geometry. R, a free language and environment for statistical computing and graphics

CoDaPack. An Excel and Visual Basic based software of compositional data analysis. Current version and discussion form upcoming versions

In the eighties, John Aitchison (1986) developed a new methodological approach for the statistical analysis of compositional data. This new methodology was implemented in Basic routines grouped under the name CODA and later NEWCODA inMatlab (Aitchison, 1997). After that, several other authors have published extensions to this methodology: Marín-Fernández and others (2000), Barceló-Vidal and others (2001), Pawlowsky-Glahn and Egozcue (2001, 2002) and Egozcue and others (2003). (...)

An R Library for Compositional Data Analysis in Archaeometry

Compositional data naturally arises from the scientific analysis of the chemical composition of archaeological material such as ceramic and glass artefacts. Data of this type can be explored using a variety of techniques, from standard multivariate methods such as principal components analysis and cluster analysis, to methods based upon the use of log-ratios. The general aim is to identify groups of chemically similar artefacts that could potentially be used to answer questions of provenance. This paper will demonstrate work in progress on the development of a documented library of methods, implemented using the statistical package R, for the analysis of compositional data. R is an open source package that makes available very powerful statistical facilities at no cost. We aim to show how, with the aid of statistical software such as R, traditional exploratory multivariate analysis can easily be used alongside, or in combination with, specialist techniques of compositional data analysis. The library has been developed from a core of basic R functionality, together with purpose-written routines arising from our own research (for example that reported at CoDaWork'03). In addition, we have included other appropriate publicly available techniques and libraries that have been implemented in R by other authors. Available functions range from standard multivariate techniques through to various approaches to log-ratio analysis and zero replacement. We also discuss and demonstrate a small selection of relatively new techniques that have hitherto been little-used in archaeometric applications involving compositional data. The application of the library to the analysis of data arising in archaeometry will be demonstrated; results from different analyses will be compared; and the utility of the various methods discussed

A compositional data analysis package for R providing multiple approaches

”compositions” is a new R-package for the analysis of compositional and positive data. It contains four classes corresponding to the four different types of compositional and positive geometry (including the Aitchison geometry). It provides means for computation, plotting and high-level multivariate statistical analysis in all four geometries. These geometries are treated in an fully analogous way, based on the principle of working in coordinates, and the object-oriented programming paradigm of R. In this way, called functions automatically select the most appropriate type of analysis as a function of the geometry. The graphical capabilities include ternary diagrams and tetrahedrons, various compositional plots (boxplots, barplots, piecharts) and extensive graphical tools for principal components. Afterwards, ortion and proportion lines, straight lines and ellipses in all geometries can be added to plots. The package is accompanied by a hands-on-introduction, documentation for every function, demos of the graphical capabilities and plenty of usage examples. It allows direct and parallel computation in all four vector spaces and provides the beginner with a copy-and-paste style of data analysis, while letting advanced users keep the functionality and customizability they demand of R, as well as all necessary tools to add own analysis routines. A complete example is included in the appendix

Compositional data analysis in archaeometry

We shall call an n × p data matrix fully-compositional if the rows sum to a constant, and sub-compositional if the variables are a subset of a fully-compositional data set1. Such data occur widely in archaeometry, where it is common to determine the chemical composition of ceramic, glass, metal or other artefacts using techniques such as neutron activation analysis (NAA), inductively coupled plasma spectroscopy (ICPS), X-ray fluorescence analysis (XRF) etc. Interest often centres on whether there are distinct chemical groups within the data and whether, for example, these can be associated with different origins or manufacturing technologies

Compositional data analysis of archaeological glass: problems and possible solutions

Presentation in CODAWORK'03, session 4: Applications to archeometry

Exploration of geological variability and possible processes through the use of compositional data analysis: an example using scottish metamorphosed

Developments in the statistical analysis of compositional data over the last two decades have made possible a much deeper exploration of the nature of variability, and the possible processes associated with compositional data sets from many disciplines. In this paper we concentrate on geochemical data sets. First we explain how hypotheses of compositional variability may be formulated within the natural sample space, the unit simplex, including useful hypotheses of subcompositional discrimination and specific perturbational change. Then we develop through standard methodology, such as generalised likelihood ratio tests, statistical tools to allow the systematic investigation of a complete lattice of such hypotheses. Some of these tests are simple adaptations of existing multivariate tests but others require special construction. We comment on the use of graphical methods in compositional data analysis and on the ordination of specimens. The recent development of the concept of compositional processes is then explained together with the necessary tools for a staying- in-the-simplex approach, namely compositional singular value decompositions. All these statistical techniques are illustrated for a substantial compositional data set, consisting of 209 major-oxide and rare-element compositions of metamorphosed limestones from the Northeast and Central Highlands of Scotland. Finally we point out a number of unresolved problems in the statistical analysis of compositional processes