Mathematical competence for information visualization by correspondence analysis methods

Report published in the Proceedings of the National Conference on "Education and Research in the Information Society", Plovdiv, May, 2016

Qualitative assessment of stock prices listed on the Sao Paulo stock exchange: An approach from the perspective of homogeneity analysis

The stock market suffers uncertain relations throughout the entire negotiation process, with different variables exerting direct and indirect influence on stock prices. This study focuses on the analysis of certain aspects that may influence these values offered by the capital market, based on the Brazil Index of the Sao Paulo Stock Exchange (Bovespa), which selects 100 stocks among the most traded on Bovespa in terms of number of trades and financial volume. The selected variables are characterized by the companies` activity area and the business volume in the month of data collection, i.e. April/2007. This article proposes an analysis that joins the accounting view of the stock price variables that can be influenced with the use of multivariate qualitative data analysis. Data were explored through Correspondence Analysis (Anacor) and Homogeneity Analysis (Homals). According to the research, the selected variables are associated with the values presented by the stocks, which become an internal control instrument and a decision-making tool when it comes to choosing investments.

Some reflections on acquisition, processing and analysis of statistical data in forest soils

Beyond the classical statistical approaches (determination of basic statistics, regression analysis, ANOVA, etc.) a new set of applications of different statistical techniques has increasingly gained relevance in the analysis, processing and interpretation of data concerning the characteristics of forest soils. This is possible to be seen in some of the recent publications in the context of Multivariate Statistics. These new methods require additional care that is not always included or refered in some approaches. In the particular case of geostatistical data applications it is necessary, besides to geo-reference all the data acquisition, to collect the samples in regular grids and in sufficient quantity so that the variograms can reflect the spatial distribution of soil properties in a representative manner. In the case of the great majority of Multivariate Statistics techniques (Principal Component Analysis, Correspondence Analysis, Cluster Analysis, etc.) despite the fact they do not require in most cases the assumption of normal distribution, they however need a proper and rigorous strategy for its utilization. In this work, some reflections about these methodologies and, in particular, about the main constraints that often occur during the information collecting process and about the various linking possibilities of these different techniques will be presented. At the end, illustrations of some particular cases of the applications of these statistical methods will also be presented.

Victimization in Childhood of Male Sex Offenders: Relationship between Violence Experienced and Subsequent Offenses through Discourse Analysis

This study aims at better understanding how the form of childhood violence experienced and the type of offense subsequently committed affect how sex offenders recall punishments and difficult events. Fifty-four male perpetrators convicted of sexual offenses against children (SOCs) or against adults (SOAs) were interviewed in France, Belgium, and Switzerland using the Lausanne Clinical Interview (Entretien Clinique de Lausanne or LCI). Almost three-quarters of the sex offenders reported having been victimized during childhood. The correspondence analysis identified several factors that differentiated them. Their appraisal of the distressing event, method of coping with and distancing themselves from it, and how they dealt with emotions varied markedly depending on whether they recognized having experienced various forms of violence during childhood and on what type of offense they subsequently committed. Victimization can be identified as much by the events experienced as by their effect on the sex offender's discourse. Identification of these discursive indicators may lead to an improved therapeutic approach for potentially traumatic childhood experiences.

Dynamic graphics of parametrically linked multivariate methods used in compositional data analysis

Many multivariate methods that are apparently distinct can be linked by introducing oneor more parameters in their definition. Methods that can be linked in this way arecorrespondence analysis, unweighted or weighted logratio analysis (the latter alsoknown as "spectral mapping"), nonsymmetric correspondence analysis, principalcomponent analysis (with and without logarithmic transformation of the data) andmultidimensional scaling. In this presentation I will show how several of thesemethods, which are frequently used in compositional data analysis, may be linkedthrough parametrizations such as power transformations, linear transformations andconvex linear combinations. Since the methods of interest here all lead to visual mapsof data, a "movie" can be made where where the linking parameter is allowed to vary insmall steps: the results are recalculated "frame by frame" and one can see the smoothchange from one method to another. Several of these "movies" will be shown, giving adeeper insight into the similarities and differences between these methods

Distributional equivalence and subcompositional coherence in the analysis of contingency tables, ratio-scale measurements and compositional data

We consider two fundamental properties in the analysis of two-way tables of positive data: the principle of distributional equivalence, one of the cornerstones of correspondence analysis of contingency tables, and the principle of subcompositional coherence, which forms the basis of compositional data analysis. For an analysis to be subcompositionally coherent, it suffices to analyse the ratios of the data values. The usual approach to dimension reduction in compositional data analysis is to perform principal component analysis on the logarithms of ratios, but this method does not obey the principle of distributional equivalence. We show that by introducing weights for the rows and columns, the method achieves this desirable property. This weighted log-ratio analysis is theoretically equivalent to spectral mapping , a multivariate method developed almost 30 years ago for displaying ratio-scale data from biological activity spectra. The close relationship between spectral mapping and correspondence analysis is also explained, as well as their connection with association modelling. The weighted log-ratio methodology is applied here to frequency data in linguistics and to chemical compositional data in archaeology.

Dynamic graphics of parametrically linked multivariate methods used in compositional data analysis

Many multivariate methods that are apparently distinct can be linked by introducing oneor more parameters in their definition. Methods that can be linked in this way arecorrespondence analysis, unweighted or weighted logratio analysis (the latter alsoknown as "spectral mapping"), nonsymmetric correspondence analysis, principalcomponent analysis (with and without logarithmic transformation of the data) andmultidimensional scaling. In this presentation I will show how several of thesemethods, which are frequently used in compositional data analysis, may be linkedthrough parametrizations such as power transformations, linear transformations andconvex linear combinations. Since the methods of interest here all lead to visual mapsof data, a "movie" can be made where where the linking parameter is allowed to vary insmall steps: the results are recalculated "frame by frame" and one can see the smoothchange from one method to another. Several of these "movies" will be shown, giving adeeper insight into the similarities and differences between these methods.

Analysis of matched matrices

We consider the joint visualization of two matrices which have common rowsand columns, for example multivariate data observed at two time pointsor split accord-ing to a dichotomous variable. Methods of interest includeprincipal components analysis for interval-scaled data, or correspondenceanalysis for frequency data or ratio-scaled variables on commensuratescales. A simple result in matrix algebra shows that by setting up thematrices in a particular block format, matrix sum and difference componentscan be visualized. The case when we have more than two matrices is alsodiscussed and the methodology is applied to data from the InternationalSocial Survey Program.

European research funding and regional technological capabilities: Network composition analysis

We use network and correspondence analysis to describe the compositionof the research networks in the European BRITE--EURAM program. Our mainfinding is that 27\% of the participants in this program fall into one oftwo sets of highly ``interconnected'' institutions --one centered aroundlarge firms (with smaller firms and research centers providing specializedservices), and the other around universities--. Moreover, these ``hubs''are composed largely of institutions coming from the technologically mostadvanced regions of Europe. This is suggestive of the difficulties of attainingEuropean ``cohesion'', as technically advanced institutions naturally linkwith partners of similar technological capabilities.

Where and how family members spend time at home? A quantitative analysis of the observational tracking on the everyday lives of Italian families

This paper examines a dataset that derives from an observational tracking, in order to analyze where and how middle-class working families spend time at home. We use an ethnographic approach to study the everyday lives of Italian dual-income middle-class families, with the aim to analyze quantitatively the use of home spaces and the types of activities of family members on weekday afternoons and evenings. The different analyses (multiple correspondence analysis, agglomerative hierarchical cluster, discriminant analysis) show how particular spaces and activities in these spaces are dominated by certain family members. We suggest a combination of qualitative and quantitative methodologies as useful tools to explore in detail the everyday lives of families, and to understand how family members use the domestic spaces. In particular, we consider relevant the use of quantitative analyses to examine ethnographic data, especially in connection with the methodological reflexivity among researchers

Multivariate analysis of pollen frequency of the native species Escallonia pulverulenta (Saxifragaceae) in Chilean honeys

The aim of this work was the identification of geographic zones suitable for the production of honeys in which pollen grains of Escallonia pulverulenta (Ruiz & Pav.) Pers. (Saxifragaceae) can be detected. The analysis of botanical origin of 240 honey samples produced between La Serena and Puerto Mont (the IV and X Administrative Regions of Chile), allowed the detection of pollen grains of E. pulverulenta in 46 Chilean honeys. The geographic distribution of the honeys studied is presented together with their affinities, through factor analysis and frequency tables. The study was based on the presence of E. pulverulenta pollen. Escallonia pulverulenta pollen percentages oscillated between 0.24% and 78.5%. Seventeen of the studied samples were designated as unifloral - i.e. samples showing more than 45% pollen of a determined plant species. Two of these corresponded to E. pulverulenta (corontillo, madroño or barraco) honeys. The remaining unifloral honeys correspond to 8 samples of Lotus uliginosus Schkuhr (birdsfoot trefoil), 2 samples of Aristotelia chilensis (Molina) Stuntz (maqui) and 1 sample of Escallonia rubra (Ruiz & Pav.) Pers. (siete camisas), Eucryphia cordifolia Cav. (ulmo or muemo), Weinmannia trichosperma Cav. (tineo), Rubus ulmifolius Schott (blackberry) and Brassica rapa L. (turnip). Honeys with different percentages of E. pulverulenta pollen - statistically analyzed through correspondence analysis - could be associated and assigned to one of three geographic types, defined on the basis of this analysis. The geographical type areas defined were the Northern Mediterranean Zone (samples from the IV Region), Central Mediterranean Zone (samples from the V to the VIII regions including two samples of unifloral Escallonia pulverulenta honey), and Southern Mediterranean Zone (samples from the IX Region).

Dynamic graphics of parametrically linked multivariate methods used in compositional data analysis

Many multivariate methods that are apparently distinct can be linked by introducing one or more parameters in their definition. Methods that can be linked in this way are correspondence analysis, unweighted or weighted logratio analysis (the latter also known as "spectral mapping"), nonsymmetric correspondence analysis, principal component analysis (with and without logarithmic transformation of the data) and multidimensional scaling. In this presentation I will show how several of these methods, which are frequently used in compositional data analysis, may be linked through parametrizations such as power transformations, linear transformations and convex linear combinations. Since the methods of interest here all lead to visual maps of data, a "movie" can be made where where the linking parameter is allowed to vary in small steps: the results are recalculated "frame by frame" and one can see the smooth change from one method to another. Several of these "movies" will be shown, giving a deeper insight into the similarities and differences between these methods