We assess the performance of a new clustering method for Hierarchical Factor Classification of variables, which is based on the evaluation of the least differences among representative variables of groups, as defined by a set of two-dimensional Principal Components Analysis. As an additional feature the method gives at each step a principal plane where both grouped variables and units, as seen only by these variables, can be projected. We compare the method results with both single and complete linkage clustering, applied to simulated data with known correlation structure and we evaluate the results with a coherence measure based on the entropy between the expected partitions and those found by the methods. We found that the Hierarchical Factor Classification method performed as good as, and in some cases better than, both single and complete linkage clustering in detecting the known group structures in simulated data, with the advantage that the groups of variables and the units can be viewed on principal planes where usual interpretations apply.
In order to enhance interpretation of two-way contingency tables (cross-classifications) derived from two hierarchical classifications, new indices are suggested to evaluate the relative contribution of nodes in either hierarchy to the nodes or to a partition of groups derived from the other hierarchy. Using these tools, cut-levels in both hierarchies can be found to define optimal partitions, and groups from both partitions can be associated in order to identify their mutual relationships. The method is illustrated with an actual example from vegetation ecology.
Two simulated coenoclines and a real data set were differently recoded with respect to the Braun-Blanquet coding (including presence/absence) and analysed through the most common multidimensional scaling methods. This way, we aim at contributing to the debate concerning the nature of the Braun-Blanquet coding and the consequent multidimensional scaling methods to be used. Procrustes, Pearson, and Spearman correlation matrices were computed to compare the resulting sets of coordinates and synthesized through their Principal Component Analyses (PCA). In general, both Procrustes and Pearson correlations showed high coherence of the obtained results, whereas Spearman correlation values were much lower. This proves that the main sources of variation are similarly identified by most of used methods/transformations, whereas less agreement results on the continuous variations along the detected gradients. The conclusion is that Correspondence Analysis on presence/absence data seems the most appropriate method to use. Indeed, presence/absence data are not affected by species cover estimation error and Simple Correspondence Analysis performs really well with this coding. As alternative, Multiple Correlation Analysis provides interesting information on the species distribution while showing a pattern of relevés very similar to that issued by PCA.
In the analysis of multidimensional ecological data, it is often relevant to identify groups of variables since these groups may reflect similar ecological processes. The usual approach, the application of well-known clustering procedures using an appropriate similarity measure among the variables, may be criticized, but specific methods for clustering variables are neither investigated in detail nor used broadly. Here we introduce a new clustering method, the Hierarchical Factor Classification of variables, which is based on the evaluation of the least differences among representative variables of groups, as revealed by a two-dimensional Principal Components Analysis. As an additional feature, the method gives at each step a principal plane where both the grouped variables and the units, considered only according to these variables, can be projected. This method can be adapted to count data, so that it may be used for classifying both rows and columns of a contingency data table, by using the chi-square metric. In an example, we apply both methods to vegetation and soil data from the Campos in Southern Brazil.