A Canonical Dual-STATIS Biplot for Repeated Cross-Sectional Data with Non-Matched Individuals: An Application to Proximity and Directional Voting in Spanish General Elections (2015–2019)

The original Canonical Dual-STATIS biplot incorporates an a priori group structure into the analysis of a sequence of data tables, but its formulation requires the same individuals to be observed on every occasion, which excludes repeated cross-sectional designs. This paper lifts that restriction and extends the method to tables with non-matched individuals. The group structure is then carried entirely by the variable space: for each table, the between-group and within-group covariance matrices are normalised by their Hilbert–Schmidt norms and combined into two separate compromises, each weighted by the leading eigenvector of its own inter-structure. Canonical directions follow from a symmetric formulation of the generalised eigenvalue problem defined by both compromises, and are displayed in a row-metric-preserving canonical GH biplot whose inter-centroid distances are Mahalanobis distances induced by the within-group compromise. Groups present on only some occasions enter as supplementary elements, and occasion-specific centroids are projected as trajectories. The method is illustrated with four Spanish pre-election surveys comparing the proximity and directional models of electoral evaluation. The joint reading of the global and canonical solutions reveals a Simpson’s paradox: directionality is positively associated with voting probability within every party, but the association reverses between parties, whereas proximity is the stronger discriminator between parties.