Compositional analysis of bivariate discrete probabilities

A joint distribution of two discrete random variables with finite support can be displayed as a two way table of probabilities adding to one. Assume that this table has n rows and m columns and all probabilities are non-null. This kind of table can be seen as an element in the simplex of n · m parts. In this context, the marginals are identified as compositional amalgams, conditionals (rows or columns) as subcompositions. Also, simplicial perturbation appears as Bayes theorem. However, the Euclidean elements of the Aitchison geometry of the simplex can also be translated into the table of probabilities: subspaces, orthogonal projections, distances. Two important questions are addressed: a) given a table of probabilities, which is the nearest independent table to the initial one? b) which is the largest orthogonal projection of a row onto a column? or, equivalently, which is the information in a row explained by a column, thus explaining the interaction? To answer these questions three orthogonal decompositions are presented: (1) by columns and a row-wise geometric marginal, (2) by rows and a columnwise geometric marginal, (3) by independent two-way tables and fully dependent tables representing row-column interaction. An important result is that the nearest independent table is the product of the two (row and column)-wise geometric marginal tables. A corollary is that, in an independent table, the geometric marginals conform with the traditional (arithmetic) marginals. These decompositions can be compared with standard log-linear models. Key words: balance, compositional data, simplex, Aitchison geometry, composition, orthonormal basis, arithmetic and geometric marginals, amalgam, dependence measure, contingency table

Interpretation of wind components as compositional variables

The classical statistical study of the wind speed in the atmospheric surface layer is made generally from the analysis of the three habitual components that perform the wind data, that is, the component W-E, the component S-N and the vertical component, considering these components independent. When the goal of the study of these data is the Aeolian energy, so is when wind is studied from an energetic point of view and the squares of wind components can be considered as compositional variables. To do so, each component has to be divided by the module of the corresponding vector. In this work the theoretical analysis of the components of the wind as compositional data is presented and also the conclusions that can be obtained from the point of view of the practical applications as well as those that can be derived from the application of this technique in different conditions of weather

Discrete and continuous compositions

This paper examines a dataset which is modeled well by the Poisson-Log Normal process and by this process mixed with Log Normal data, which are both turned into compositions. This generates compositional data that has zeros without any need for conditional models or assuming that there is missing or censored data that needs adjustment. It also enables us to model dependence on covariates and within the composition

Revisió de la recerca educativa sobre les variables explicatives del rendiment acadèmic:Apunts per a l'ús del criteri de "modificabilitat pedagògica" de les variables.

La conceptualització del concepte de rendiment acadèmic ha variat al llarg de la història des de definicions que es basaven en un únic criteri fins a les més actuals concepcions multidimensionals. Aquestes darreres apareixen com a resultat del desenvolupament d'aquest concepte, paral.lel a l'evolució històrica d'un fenomen més ampli: el fracàs escolar