Contribuciones al análisis multivariante no lineal

Resumo

We have developed an optimal quantification method, based on the minimization of the sum of the quadratic interdistances between the quantified categories of the variables. This method guarantees that the more frequently associated categories have the more similar quantifications. Given that this method of quantification is not based on dimensionality reduction, it generates a single set of quantifications. These are the main advantages of this method called CUANTIFICA over the Gifi-system of non-linear multivariate analysis. In addition to the classical scaling levels (Numerical, Ordinal, Nominal), CUANTIFICA support Floating Numerical and Floating Ordinal scaling levels, which are suited to handle categories of the type �Don�t know/No answer�. These scaling levels assign a free quantification the floating category, keeping a numerical or ordinal scaling level for the remaining categories of the variable. In addition to the theory, we have developed some computational algorithms and a graphical interface to generate quantifications. As and additional contribution, we developed a methodology to generate the biplot display of a matrix with missing data. We start with a matrix of pairwise correlations, which is built by using all the available information for each pair of variables. The eigendecomposition of this correlation matrix allows getting the column markers for the incomplete matrix. After that, we achieve the file markers by using regressions with zero weighting for the missing values. We have developed the computational algorithms and the graphical interfaces both for calculating the vector markers and for drawing the graphical displays. Given that this display generalizes the one that preserves the column metric, we have called it Generalized Column Metric Preserving Biplot or GCMP-Biplot. Finally, we show the performance of the developed techniques by analyzing an ischemic cardiopathy patient population.