Compositional data analysis of vote shares in the 2001 Australian Federal election

First application of compositional data analysis techniques to Australian election data

The single principle of compositional data analysis, continuing fallacies, confusionsand misunderstandings and some suggested remedies

In any discipline, where uncertainty and variability are present, it is important to haveprinciples which are accepted as inviolate and which should therefore drive statisticalmodelling, statistical analysis of data and any inferences from such an analysis.Despite the fact that two such principles have existed over the last two decades andfrom these a sensible, meaningful methodology has been developed for the statisticalanalysis of compositional data, the application of inappropriate and/or meaninglessmethods persists in many areas of application. This paper identifies at least tencommon fallacies and confusions in compositional data analysis with illustrativeexamples and provides readers with necessary, and hopefully sufficient, arguments topersuade the culprits why and how they should amend their ways

A panel data analysis of FDI and informal labor markets

The objective of this paper is to examine whether informal labor markets affect the flows of Foreign Direct Investment (FDI), and also whether this effect is similar in developed and developing countries. With this aim, different public data sources, such as the World Bank (WB), and the United Nations Conference on Trade and Development (UNCTAD) are used, and panel econometric models are estimated for a sample of 65 countries over a 14 year period (1996-2009). In addition, this paper uses a dynamic model as an extension of the analysis to establish whether such an effect exists and what its indicators and significance may be.

Efficient Optimization Algorithms for Nonlinear Data Analysis

Identification of low-dimensional structures and main sources of variation from multivariate data are fundamental tasks in data analysis. Many methods aimed at these tasks involve solution of an optimization problem. Thus, the objective of this thesis is to develop computationally efficient and theoretically justified methods for solving such problems. Most of the thesis is based on a statistical model, where ridges of the density estimated from the data are considered as relevant features. Finding ridges, that are generalized maxima, necessitates development of advanced optimization methods. An efficient and convergent trust region Newton method for projecting a point onto a ridge of the underlying density is developed for this purpose. The method is utilized in a differential equation-based approach for tracing ridges and computing projection coordinates along them. The density estimation is done nonparametrically by using Gaussian kernels. This allows application of ridge-based methods with only mild assumptions on the underlying structure of the data. The statistical model and the ridge finding methods are adapted to two different applications. The first one is extraction of curvilinear structures from noisy data mixed with background clutter. The second one is a novel nonlinear generalization of principal component analysis (PCA) and its extension to time series data. The methods have a wide range of potential applications, where most of the earlier approaches are inadequate. Examples include identification of faults from seismic data and identification of filaments from cosmological data. Applicability of the nonlinear PCA to climate analysis and reconstruction of periodic patterns from noisy time series data are also demonstrated. Other contributions of the thesis include development of an efficient semidefinite optimization method for embedding graphs into the Euclidean space. The method produces structure-preserving embeddings that maximize interpoint distances. It is primarily developed for dimensionality reduction, but has also potential applications in graph theory and various areas of physics, chemistry and engineering. Asymptotic behaviour of ridges and maxima of Gaussian kernel densities is also investigated when the kernel bandwidth approaches infinity. The results are applied to the nonlinear PCA and to finding significant maxima of such densities, which is a typical problem in visual object tracking.

GLUT4 protein expression in obese and lean 12-month-old rats: insights from different types of data analysis

GLUT4 protein expression in white adipose tissue (WAT) and skeletal muscle (SM) was investigated in 2-month-old, 12-month-old spontaneously obese or 12-month-old calorie-restricted lean Wistar rats, by considering different parameters of analysis, such as tissue and body weight, and total protein yield of the tissue. In WAT, a ~70% decrease was observed in plasma membrane and microsomal GLUT4 protein, expressed as µg protein or g tissue, in both 12-month-old obese and 12-month-old lean rats compared to 2-month-old rats. However, when plasma membrane and microsomal GLUT4 tissue contents were expressed as g body weight, they were the same. In SM, GLUT4 protein content, expressed as µg protein, was similar in 2-month-old and 12-month-old obese rats, whereas it was reduced in 12-month-old obese rats, when expressed as g tissue or g body weight, which may play an important role in insulin resistance. Weight loss did not change the SM GLUT4 content. These results show that altered insulin sensitivity is accompanied by modulation of GLUT4 protein expression. However, the true role of WAT and SM GLUT4 contents in whole-body or tissue insulin sensitivity should be determined considering not only GLUT4 protein expression, but also the strong morphostructural changes in these tissues, which require different types of data analysis.

Sensory evaluation of "dulce de leche" with coffee and whey using different affective data analysis methods

This study sought to evaluate the acceptance of "dulce de leche" with coffee and whey. The results were analyzed through response surface, ANOVA, test of averages, histograms, and preference map correlating the global impression data with results of physical, physiochemical and sensory analysis. The response surface methodology, by itself, was not enough to find the best formulation. For ANOVA, test of averages, and preference map it was observed that the consumers' favorite "dulce de leche" were those of formulation 1 (10% whey and 1% coffee) and 2 (30% whey and 1% coffee), followed by formulation 9 (20% whey and 1.25% coffee). The acceptance of samples 1 and 2 was influenced by the higher acceptability in relation to the flavor and for presenting higher pH, L*, and b* values. It was observed that samples 1 and 2 presented higher purchase approval score and higher percentages of responses for the 'ideal' category in terms of sweetness and coffee flavor. It was found that consumers preferred the samples with low concentrations of coffee independent of the concentration of whey thus enabling the use of whey and coffee in the manufacture of dulce de leche, obtaining a new product.

Data analysis tools and methods for DNA microarray and high-throughput sequencing data

The recent rapid development of biotechnological approaches has enabled the production of large whole genome level biological data sets. In order to handle thesedata sets, reliable and efficient automated tools and methods for data processingand result interpretation are required. Bioinformatics, as the field of studying andprocessing biological data, tries to answer this need by combining methods and approaches across computer science, statistics, mathematics and engineering to studyand process biological data. The need is also increasing for tools that can be used by the biological researchers themselves who may not have a strong statistical or computational background, which requires creating tools and pipelines with intuitive user interfaces, robust analysis workflows and strong emphasis on result reportingand visualization. Within this thesis, several data analysis tools and methods have been developed for analyzing high-throughput biological data sets. These approaches, coveringseveral aspects of high-throughput data analysis, are specifically aimed for gene expression and genotyping data although in principle they are suitable for analyzing other data types as well. Coherent handling of the data across the various data analysis steps is highly important in order to ensure robust and reliable results. Thus,robust data analysis workflows are also described, putting the developed tools andmethods into a wider context. The choice of the correct analysis method may also depend on the properties of the specific data setandthereforeguidelinesforchoosing an optimal method are given. The data analysis tools, methods and workflows developed within this thesis have been applied to several research studies, of which two representative examplesare included in the thesis. The first study focuses on spermatogenesis in murinetestis and the second one examines cell lineage specification in mouse embryonicstem cells.

Spurring innovation through idea contests : data analysis and process improvements

This research concerns the Urban Living Idea Contest conducted by Creator Space™ of BASF SE during its 150th anniversary in 2015. The main objectives of the thesis are to provide a comprehensive analysis of the Urban Living Idea Contest (ULIC) and propose a number of improvement suggestions for future years. More than 4,000 data points were collected and analyzed to investigate the functionality of different elements of the contest. Furthermore, a set of improvement suggestions were proposed to BASF SE. Novelty of this thesis lies in the data collection and the original analysis of the contest, which identified its critical elements, as well as the areas that could be improved. The author of this research was a member of the organizing team and involved in the decision making process from the beginning until the end of the ULIC.

Conceptual knowledge discovery and data analysis

In this paper, we discuss Conceptual Knowledge Discovery in Databases (CKDD) in its connection with Data Analysis. Our approach is based on Formal Concept Analysis, a mathematical theory which has been developed and proven useful during the last 20 years. Formal Concept Analysis has led to a theory of conceptual information systems which has been applied by using the management system TOSCANA in a wide range of domains. In this paper, we use such an application in database marketing to demonstrate how methods and procedures of CKDD can be applied in Data Analysis. In particular, we show the interplay and integration of data mining and data analysis techniques based on Formal Concept Analysis. The main concern of this paper is to explain how the transition from data to knowledge can be supported by a TOSCANA system. To clarify the transition steps we discuss their correspondence to the five levels of knowledge representation established by R. Brachman and to the steps of empirically grounded theory building proposed by A. Strauss and J. Corbin.

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