The reliability of correspondence analysis for the representation of multiple proximity matrices.

摘要

A scaling method which applies ordinary correspondence analysis (CA) to stacked individual similarity matrices was recently suggested to replace traditional solutions, such as non-metric multidimensional scaling (MDS) and individual differences scaling (INDSCAL) for representing multiple proximity matrices. The method is much more efficient because it performs a single analysis on all individual matrices simultaneously and the resulting coordinates for each individual matrix are in the same orientation so that they can be plotted directly for comparison on the same Euclidean space without rotation.;The goal of this study is to investigate the reliability of the stacking method under various conditions. It was first demonstrated that the stacking method produces slightly closer fit to some empirical color data than non-metric MDS and INDSCAL. Some computer simulations with various conditions were further used to test: (1) how well the stacking method recovers Euclidean distances with correlations between the original shapes at different levels; (2) when the stacking method produces the greatest context effects. A modified CA was also introduced and compared with the ordinary CA in the computer simulations.;The results from those computer simulations showed that stacking method with both ordinary CA and modified CA represents sets of points in Euclidean space pretty well. Even when the method is applied to sets of points whose average correlation among their original shapes is almost zero, the average correlation between the recovered shapes and the original is at least as high as 0.74. Modified CA obtained higher correlations than ordinary CA on average and also the results from modified CA had less variation.;When testing context effects, the results from simulations show that the biggest context effect from the stacking method---either on individuals or on group mean correlations---appeared when the target group is scaled with the context group with the same (or very similar) mean within group correlation and the mean between group correlation is very low. The simulations also showed that the modified CA performed very poorly when it was applied to simulated empirical proximity data, especially non-homogeneous groups.