GRIDCOR also carries out a cluster analysis of the similarities between constructs and between elements, as well as focusing the data afterwards (both procedures have been mentioned already). This type of analysis is based on the calculation of the euclidean distances between elements and then between constructs, as well as a clustering algorithm that gives the corresponding element and construct trees. The graphical tree arrangement enables us to see the similarities and ramifications of the elements in Daniel's grid (see Figure 5). It is clear that the two closest elements are IDEAL and PREVIOUS THERAPIST that, with the addition of the SPOUSE, form the "ideally good" cluster. This cluster is somehow associated with the main tree's branch which has several ramifications. On the one hand, MFRIEND and BROTHER are grouped with FATHER; and, on the other hand, SISTER and FFRIEND are linked to MOTHER and OTHERS[6]. Finally, the "undesirable" cluster is formed by the elements of SELF and NON-GRATA on one pole and SELF-BEFORE and GRANDMA on the other. Obviously, this is just another way in which the analysis of Daniel's grid reveals his poor self esteem, as well as the fact that some kind of self-conflict was present before the onset of the panic attacks.
We have already mentioned the problem faced by cluster analysis when handling constructs because of their bi-polarity. This is solved by the GRIDCOR programme by inverting the poles whose scores go in an opposite direction to that of the other constructs. In this way, the associations are established with the same-side pole. The two closest constructs according to Daniel's construct tree (Figure 6) are "nervous-relaxed" and "worried-happy," forming a cluster virtually independent from the rest of the constructs. We can also find some other associations in this tree, such us the link between the constructs "committed-no bothers" and "sexually healthy-perverse."
Summarising, cluster analysis can help us to visually paraphrase the distance matrix. Within the GRIDCOR programme this analysis also serves the purpose of focusing the grid. The focused output of data does not appear on the screen but in the output file that the programme automatically generates for printing purposes. The next page (Figure 7) shows the original outlay of the grid (as it has been entered) followed by the rearranged data matrix resulting from the focusing procedure.
Table 4 shows the matrix of distances for the elements followed by the one for the constructs, and by the element x construct matrix of the subspace of five axes as provided by the GRIDCOR programme. The distances from the centre of gravity ("orig.") that correspond to the multispace created by CA are shown on the first line of the matrix, slightly separated from the other lines. The distances between elements (or between constructs) are then shown immediately afterwards (the shorter the distance the greater the similarity and viceversa).
The GRIDCOR programme also calculates the product-moment correlations between elements and between constructs (Table 5). We have already discussed the advantages of distances over correlations. However, correlations do have some advantages over distances, such as a well-defined fluctuation range (from -1 to +1). The conjoint presentation of distances and correlations seems to be the most prudent solution at this point.
Because they contain immense quantities of information, these matrixes allow us to answer specific, clinically relevant questions. The following are a few possible sample questions on aspects that have not yet been covered:
Although he does not appear to be very close to either, we can say that he tends sees himself as a bit more similar to his Mother[7].
Finally, an additional advantage of the GRIDCOR programme is the introduction of supplementary constructs or elements. Unlike the constructs or elements included in the original grid, the supplementary elements or constructs are not used in the CA calculation. Because they are included later, they can be shown on the graph without affecting the calculation of the axes co-ordinates. Basically, the supplementary constructs and elements can be projected onto the grid space depending on the specific objectives of the investigator.
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