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

Aspectes metodològics i técnica d'analisi en l'estudi dels grups i les classes socials

En aquest article es presenta el procés metodològic, com també les tècniques d'anàlisi de dades, que s'ha utilitzat en l'anàisi dels grups socials mitjançant la informació d'una gran enquesta sobre hàbits i condicions de vida. L'anàlisi dels grups socials des d'una perspectiva globalitzadora i estructuradora de les condicions de vida, tenint en compte com aquests sorgeixen mitjançant I 'associació i la coherència entre múltiples característiques. Les tècniques d'anàlisi de dades que s'han utilitzat han estat l'anàlisi de correspondències múltiples i l'anàlisi de classificació.

La construcció de tipologies: progrés i analisi de les dades

Aquest article recull un mateix procés metodològic en el qual s'emmarquen diverses investigacions presentades en aquest volum de la revista, amb un mateix objectiu: la construcció de tipologies en diferents àmbits temàtics. L'article especifica el marc general del disseny, descriu el seu procés metodològic i d'anàlisi de dades que pot caracteritzar-se per: (1) La font de dades prové d'una gran enquesta sobre hàbits i condicions de vida de la població, l'Enquesta Metropolitana de Barcelona 1990. (2) El plantejament d'un objecte d'estudi concret dins d'una realitat multivariable. (3) La utilització de tecniques d'anàlisi multivariables, en concret,l'Anàlisi de Correspondències Múltiples i les Tècniques de Classificació Automàtica.

Padrão alimentar de mulheres obesas que subnotificam ou não a ingestão energética

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

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.

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.

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.