A principal component method to analyse disconnected frequency tables by means of contextual information

• Autores: Belchin Adriyanov Kostov
• Directores de la Tesis: François Husson (dir. tes.), Mónica Bécue-Bertaut (dir. tes.)
• Lectura: En la Universitat Politècnica de Catalunya (UPC) ( España ) en 2015
• Idioma: inglés
• Tribunal Calificador de la Tesis: Montserrat Guillén Estany (presid.), Ignacio García Lautre (secret.), Fionn Murtagh (voc.)
• Materias:
  • Matemáticas
    • Estadística
      • Análisis multivariante
• Enlaces
  • Tesis en acceso abierto en: TDX
• Resumen

  • This thesis arises from the need to deal with open-ended questions answered in different languages in international surveys. For every language, the free answers are encoded in the form of a individuals x words lexical table. An important feature is that the lexical tables, from one language to the other, have neither the row-individuals nor the column-words in common. However, the global analysis and the comparison of the different samples require to place all the words, in any language, in the same space. As a solution, we propose to integrate the answers to the closed questions into the analysis, where the contextual variables the same for all the samples. This integration plays an essential role by permitting a global analysis. Thus, for every language, we have one lexical table and one categorical/quantitative table, a structure that we call "coupled tables". The global complex data structure is a sequence of "coupled tables". To analyse these data, we adopt a Correspondence Analysis-like approach. We propose a method which combines: Multiple Factor Analysis for Contingency Tables, in order to balance the influence of the sets of words in the global analysis and Correspondence Analysis on a Generalised Aggregated Lexical Table, which places all the words in the same space. The new method is called Multiple Factor Analysis on Generalised Aggregated Lexical Table. The results in an application show that the method provides outputs that are easy to interpret. They allow for studying the similarities/dissimilarities between the words including when they belong to different languages as far as they are associated in a similar/different way to the contextual variables. The methodology can be applied in other fields provided that the data are coded in a sequence of coupled tables.