ANALYSIS OF CONCENTRATION AND DETECTION OF UNDERLYING FACTORS IN STRUCTURED TABLES

If the rows and columns of a data table are rearranged in such a way that the non-zero values are concentrated in distinct blocks, the table is said to be structured. In such tables, two specific properties are often subject to interpretations: the sharpness of the block structure and the compositional variation among the blocks. A simple chi square analysis is satisfactory to test the overall sharpness of the block structure. The interpretation of compositional variation is more difficult, since the dimensionality of such variation will almost certainly exceed the dimensionality of the table. A solution can nevertheless be obtained based on a two-step analysis. In the first step, the canonical variates of compositional variation are identified. These are characteristics of the vegetation. In the second step, the environmental variables are identified which are highly correlated with the canonical variates. The example in the paper uses data from fossil flood plains. The data table is structured into 18 blocks of 6 species groups and 3 relevé groups. The chi square test indicates a sharp block structure. The structuring generated two canonical variates. The dominant of these two signifies the environmental influence of changing elevation on the flood plain. The second seems to be a response of the vegetation to disturbance. The algorithm which performs analysis of concentration is AOC. A program is available to enquirers free of charge. The programming language is BASIC. © 1979 Dr. W. Junk b.v.