Log-ratios analysis to study the relative information on ordinal variables

Ordinal variables occur commonly in many disciplines and they are pervasive in the social sciences for measuring attitudes and opinions. An alternative to the scaling procedures, in order to analyze such kinds of data, is to consider only the relative information present in them, so they are considered for a compositional analysis. In accordance with the strategy based on a variety of log-ratio transformations, the singular value decomposition and its interpretation as biplots is applied to transformed data, with inferences translatable back into compositional statements.