Biplots of compositional data

The singular value decomposition and its interpretation as a linear biplot has proved to be a powerful tool for analysing many forms of multivariate data. Here we adapt biplot methodology to the speciffic case of compositional data consisting of positive vectors each of which is constrained to have unit sum. These relative variation biplots have properties relating to special features of compositional data: the study of ratios, subcompositions and models of compositional relationships. The methodology is demonstrated on a data set consisting of six-part colour compositions in 22 abstract paintings, showing how the singular value decomposition can achieve an accurate biplot of the colour ratios and how possible models interrelating the colours can be diagnosed.Logratio transformation, principal component analysis, relative variation biplot, singular value decomposition, subcomposition

La distància de l'eixample

Inspirándonos en el diseño del Ensanche de Barcelona de Ildefonso Cerdá, definimos una nueva distancia estadística, denominada la distancia del ensanche. Se estudian algunas propiedades de esta función de distancia y se proponen algunas posibles aplicaciones

The impact of muscle relaxation techniques on the quality of life of cancer patients, as measured by the FACT-G questionnaire

Introduction Patients with cancer frequently suffer from emotional distress, characterized by psychological symptoms such as anxiety or depression. The presence of psychological symptoms combined with the complex nature of oncology processes can negatively impact patients' quality of life. We aimed to determine the impact of a relaxation protocol on improving quality of life in a sample of oncological patients treated in the Spanish National Public Health System. Materials and methods We conducted a multicenter interventional study without a control group. In total, 272 patients with different oncologic pathologies and showing symptoms of anxiety were recruited from 10 Spanish public hospitals. The intervention comprised abbreviated progressive muscle relaxation training, according to Bernstein and Borkovec. This was followed by weekly telephone calls to each patient over a 1-month period. We collected sociodemographic variables related to the disease process, including information about mental health and the intervention. Patients' quality of life was assessed using the Functional Assessment of Cancer Therapy-General (FACT-G) questionnaire. Bivariate and univariate analyses were performed, along with an analysis of multiple correspondences to identify subgroups of patients with similar variations on the FACT-G. Results Patients showed statistically significant improvements on the FACT-G overall score (W = 16806; p<0.001), with an initial mean score of 55.33±10.42 and a final mean score of 64.49±7.70. We also found significant improvements for all subscales: emotional wellbeing (W = 13118; p<0.001), functional wellbeing (W = 16155.5; p<0.001), physical wellbeing (W = 8885.5; p<0.001), and social and family context (W = ?1840; p = 0.037). Conclusions Patients with cancer who learned and practiced abbreviated progressive muscle relaxation experienced improvement in their perceived quality of life as measured by the FACT-G. Our findings support a previous assumption that complementary techniques (including relaxation techniques) are effective in improving the quality of life of patients with cancer

Novetats de software

Peer Reviewe

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 methodsGeologische Vereinigung; Institut d’Estadística de Catalunya; International Association for Mathematical Geology; Càtedra Lluís Santaló d’Aplicacions de la Matemàtica; Generalitat de Catalunya, Departament d’Innovació, Universitats i Recerca; Ministerio de Educación y Ciencia; Ingenio 2010

La distància de l'eixample

Inspirándonos en el diseño del Ensanche de Barcelona de Ildefonso Cerdá, definimos una nueva distancia estadística, denominada la distancia del ensanche. Se estudian algunas propiedades de esta función de distancia y se proponen algunas posibles aplicaciones

Measuring Subcompositional Incoherence

Subcompositional coherence is a fundamental property of Aitchison’s approach to compositional data analysis, and is the principal justification for using ratios of components. For dimension reduction of a matrix of compositional data, either an unweighted (Aitchison & Greenacre 2002) or weighted (Greenacre & Lewi 2009; Greenacre 2010a: chapter 7) form of log-ratio analysis can be used, and these are both subcompositionally coherent. Many alternative methods that might be applied to compositional data are subcompositionally incoherent, but some can be judged to be less incoherent than others. In other words, either for a particular data set, or in general, a method might actually be quite subcompositionally “robust” in that its results for a subcomposition are quite close to its results for the same components as part of a full composition. So we propose that lack of subcompositional coherence, that is subcompositional incoherence, can be measured in an attempt to evaluate whether any given technique is close enough, for all practical purposes, to being subcompositionally coherent. This opens up the field to alternative methods, which might be better suited to cope with problems such as data zeros and outliers, while being only slightly incoheren