Paper #1082

Título:

Dynamic graphics of parametrically linked multivariate methods used in compositional data analysis

Autor:

Michael Greenacre

Fecha:

Abril 2008

Resumen:

Many multivariate methods that are apparently distinct can be linked by introducing one or more parameters in their definition. Methods that can be linked in this way are correspondence analysis, unweighted or weighted logratio analysis (the latter also known as "spectral mapping"), nonsymmetric correspondence analysis, principal component analysis (with and without logarithmic transformation of the data) and multidimensional scaling. In this presentation I will show how several of these methods, which are frequently used in compositional data analysis, may be linked through parametrizations such as power transformations, linear transformations and convex linear combinations. Since the methods of interest here all lead to visual maps of data, a "movie" can be made where where the linking parameter is allowed to vary in small steps: the results are recalculated "frame by frame" and one can see the smooth change from one method to another. Several of these "movies" will be shown, giving a deeper insight into the similarities and differences between these methods.

Palabras clave:

Compositional data, contingency tables, correspondence analysis, logratio transformation, singular value decomposition, spectral map, weighting

Códigos JEL:

C19, C88

Área de investigación:

Estadística, Econometría y Métodos Cuantitativos

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