The structural characteristics of the construct system, as well as the weight of a particular construct, have been the focus of a number of grid measures. The ones which have been selected for inclusion in the GRIDCOR programme are presented hereafter.
Ever since Bieri (1955), a former student of Kelly, coined the term cognitive complexity as indicative of the cognitive structure of personality, interest in the structural characteristics of the cognitive system has been on the rise. Bieri et al. (1966, p. 185) defined cognitive complexity as:
"... the capacity to construe social behaviour in a multidimensional way. A more cognitively complex person has available a more differentiated system of dimensions for perceiving others' behaviour than does a less cognitively complex individual."
As illustrated by Huici (1981), Bieri relates cognitive complexity to the dimensions of the construct system, that is, the number of independently available dimensions that enable the handling of information related to social stimuli or evaluations of conduct (p. 203). From this perspective, a cognitively complex person can construe events from different points of view and not just from a good/bad, black/white perspective which would be characteristic of a cognitively simple person.
Bieri (1955) applied his concept of cognitive complexity to the grid using dichotomous scores based on the two by two comparison between rows (constructs). In grids with interval scores derived from 10 constructs and 10 elements, Bieri et al. (1966) suggest following the same rationale. The idea is to carry out a simple two-by-two comparison of all the constructs and then count all the scores that coincide for each given element. With the intention of standardizing the Bieri index, the GRIDCOR programme divides this count by the possible number of comparisons [number of elements x number of constructs x (number of constructs-1) x 1/2]. You can find this measure in the summary of cognitive measures (option 6 of the cognitive measures sub-menu). The Bieri1 index is calculated from a matrix of original data and the Bieri2 index from a matrix of reconstructed data (after having focused the data). Although the Bieri1 index is normally used in the literature, we consider the Bieri2 index to be the most appropiate, as it accounts for the constructs that score the data in a different direction.
Another index that Bonarius (1965) considers in his review as an indicator of cognitive complexity is the percentage of variance accounted for by the first factor (PVAFF) (or axis in the case of CA). This percentage (which in the GRIDCOR programme is shown in the eigenvalues table) indicates the importance of the main dimension of meaning. If this dimension accounts for a high percentage of variance, this indicates a degree of one-dimensionality in the subject's construing of his/her interpersonal world given that the other factors, or axes, have less weight. On the other hand, if the first axis accounts for only a small percentage of variance, there is room for other dimensions to play relevant roles in the way the subject construes.
In their studies on schizophrenic thought disorder, Bannister and his colleagues (e.g., 1960, 1962, 1965b; Bannister & Fransella, 1966; see Adams-Webber, 1979 for a review) adopted Kelly's concept of a "tight" construct leading to fixed predictions, as opposed to a "loose" construct which gives rise to varying predictions. Bannister suggested that tight thought processes allow for a limited view of things, whereas excessively loose thought processes do not allow for associations (and, therefore, predictions) to be made. As a result, the system loses its predictive capacity. Several research studies confirmed the hypothesis that an excessively loose or disintegrated system is characteristic of thought disordered schizophrenics who are unable to tighten their thought enough to produce specific, organized plans of action. The structural measure used by Bannister was that of Intensity. This measure is calculated by the GRIDCOR programme from the sum of the squared values of the correlations of each construct with the rest of the constructs, averaged by the total number of constructs minus one. This process is repeated with each element, and the overall Intensity is calculated by averaging the intensity scores of constructs and elements. These overall measures are shown in the summary of cognitive measures (Table 7) in addition to appearing in the detailed list of intensity scores (Table 9).
It is our belief that the Intensity score has a different meaning when taken as a general measure than when taken as a measure of the intensity of a particular construct in relation to other constructs. In the latter, the construct's Intensity cannot be taken as an indication of how superordinate it is, or of its hierarchical relevance (as some authors have done). Rather, it should be seen as an indicator of how central or important the construct is in that grid, given that it is this construct which has the strongest correlation with the other constructs. In comparison, the least intense construct is the least connected to other constructs and is, therefore, the most peripheral in the overall system. In the constructs of Daniel, having sex drive (or not) does not seem to have a central weight in his system given the low Intensity score of this construct. In this case, however, we cannot easily find a construct or element, that diverges far from the group. If such a construct or element were found, it could suggest cues for psychological intepretation.
Intensity has been interpreted as a measure of the degree to which a cognitive structure is integrated, (the greater the intensity, the greater the integration, and viceversa). It is similar to Bieri's Index of Cognitive Complexity to a great extent, since it derives its information from the degree of association between constructs (Adams-Webber, 1979). Both indices measure the functional similarity between constructs, i.e., the extent to which various constructs define the same thing, or the extent to which the subject's construing shows signs of multidimensionality and complexity.
This has sparked much debate within the scientific community, as low Intensity scores might indicate poor integration, looseness or cognitive complexity. Bannister discovered that schizophrenic patients could be distinguished from other psychiatric patients by their lower scores on the Intensity Index. Paradoxically, however, this made them more similar to normal subjects. The best way to discriminate between normal subjects and schizophrenics (Bannister & Fransella, 1966) was including a Consistency score. This fact revealed that normal subjects applied their judgments in later retests consistently in contrast with the almost random variability of the schizophrenic subjects.
Empirical studies on the interrelations between these three measures (Bieri, PVAFF and Intensity) further complicate matters. In a recent study of 82 Catalan and American subjects (Feixas, Lspez, Navarro, Tudela & Neimeyer, 1992), the Bieri index correlated with the Intensity Index (r=0.71, p>.001), although the strength of this association is not so apparent in previous studies (Honess, 1976). However, the PVAFF results only very modestly correlated with the Intensity Index (r=0.25, n.s.) and appear unrelated to the Bieri Index (r=-.02) not only in our study, but also in a previous research review (O'Keefe & Sypher, 1981). The inconsistency of these results leads us to doubt as to whether these three indices measure the same construct, or whether they appreciate different aspects of cognitive complexity.
Adams-Webber (1979), upon reviewing the studies on cognitive complexity using both the repertory grid and Crockett's (1965) Role Categorisation Questionnaire (based on the number of constructs used in a free-format task), suggested that cognitive complexity is not a single unitary concept but involves both differentiation and integration. Differentiation is understood as the number of functionally independent dimensions available to the subject during the process of interpersonal construction. However, the number of independent dimensions that the system has does not determine its complexity. These dimensions must also be integrated among themselves to an extent. PCT states that this integration is hierarchical and is derived from the superordinate constructs that give the system unity and coherence as a whole, facilitating the functions of the various subsystems at a higher level of abstraction. In effect, as supported by Bannister's findings, a high level of construct differentiation does not indicate complexity in the absence of a structure integrating these constructs. Rather, it can result in chaos and confusion. It is worth mentioning, however, that there is no single approved method for elucidating the hierarchical structure of a grid's constructs. Rather, all the structural indices are based on measures of association.
Following Adams-Webber's (1979) suggestion, which has been generally accepted by the personal construct community, we have outlined four possible theoretical profiles based on the extreme examples of differentiation and integration that constitute cognitive complexity (Table 10).
Having outlined these theoretical profiles, it is worth considering the same precautions as with the profiles relating to how the self is construed. These profiles only achieve some descriptive potential when the correlations are high, and it should be remembered that these clinical hypotheses require further investigation. This research would involve finding the best indices or ways of measuring the degree of integration and differentiation.
Based on the distinction between differentiation and integration, Landfield (1977) proposed an index, named "ordination," that he suggested may measure the hierarchical integration of the system. However, we (Feixas, 1988) consider it to be a measure of the subtlety and flexibility with which a construct is used and, therefore, prefer the more descriptive title of "discriminative power" for the GRIDCOR program. This measure can be calculated using the formula shown in Table 11.
For example, to calculate the discriminative power score for the element SELF in Daniel's focused grid (ratings: 7, 7, 7, 1, 1, 4, 3, 4, 7, 5) we must take the number of different ratings (i=5) and multiply this by the range, i.e., the difference between the higher (W=7) and lower (w=1) rating. The resulting number must then be divided by the total number of ratings. When calculating this score for an element, j equals the number of constructs; in this example, j=10. The results of each individual construct or element can then be averaged for all constructs (Tt constructs), elements (Tt elements), and an overall measure of discriminative power can also be calculated (see Table 12 for the results extracted from Daniel's grid). These overall measures can also be seen in the summary of cognitive measures (Table 7).
Some personal construct authors link the use of extreme scores to the meaningfulness of the construct or element involved (see Bonarius, 1977, for a review). However, the total proportion of extreme scores can be considered indicative of cognitive rigidity and polarised construing. Various empirical studies suggest that a high degree of polarisation is linked to neurotic problems (Winter, 1992) as well as to the severity of depressive symptomatology. Although polarisation is not the only characteristic of depressive disorders (it can also be found in schizophrenic patients), it does seem to be a cognitive element of depression (see Neimeyer & Feixas, 1992; Neimeyer, 1985). Therefore, Bonarius (1977) suggests, with empirical support, that the extremity of ratings is a joint function of the meaningfulness of the constructs, the meaningfulness of the elements, and a "judge" variable reflecting psychopathology.
The GRIDCOR programme gives the percentage of extremity ratings ("1" and "7" in the example given; Table 13) provided by the subject for constructs and elements, as well as a general average or total degree of polarisation. In the case of Daniel, there is one construct that stands out in its polarisation: the "responsible-irresponsible" construct. This construct shows over 50% (53.85%) extreme ratings which is above the average for his grid (30.77%). This suggests that it is a very meaningful construct for Daniel because it allows him to rate most of the elements with an extreme score (1 or 7). The fact that it is also one of the constructs with the greatest discriminative power enables us to consider it, albeit tentatively, a superordinate construct. As far as the elements are concerned, the SELF, IDEAL, and PREVIOUS THERAPIST elements stand out as the most meaningful.
Based on the concept of psychological conflict (or valence) derived from the cognitive balance or equilibrium theory in Heider's (1946) triads, Sheehan (1981) suggested a procedure for the assessment of the degree of conflict within the grid. This involves the analysis of each triad of constructs to see if there is balance or imbalance. A conflict involves an unbalanced triad, that is, when three constructs are negatively correlated, or when two are positively correlated and the third is negatively correlated.
To illustrate the idea of conflict, consider the case of Jane (there are no indicators of conflict in Daniel's case). Conflict analysisof her grid yielded the unbalanced triad shown in Figure 8.
This conflict can be expressed as follows: people who are "up in the air" are neither "balanced" nor "pessimistic." However, balanced people are not pessimistic either. Taking the opposite poles into account, this could be interpreted as: to be balanced and aware of problems involves not being optimistic, although being optimistic is simultaneously related to being balanced! This logical inconsistency may indicate a point of conflict for Jane which may interfere with decision- making and would, therefore, be a good area to explore in therapy. However, some authors link a high conflict score to cognitive complexity rather than to psychological disorder (Winter, 1983). This measure is calculated in the GRIDCOR program by computing the number of conflicts divided by the number of possible triads of constructs.
A measure that goes in the opposite direction of meaningfulness is the uncertainty score (see summary of cognitive measures) which describes the proportion of elements that the subject has been unable to place on either pole of the construct. The GRIDCOR programme calculates this via the percentage of middle-point ratings of the data matrix (rating "4" in our example). A very high percentage of poorly defined ratings indicates an operational difficulty within the construct system, related to the inability to give the elements significance. Landfield (1977) has associated such inability to construe important people within one's existing constructs with elevated suicide risk. Certainly, if one cannot attach some meaning to his or her close friends and relatives, it is dubious that he or she be able to give some meaning to his or her life. On the other hand, it is obvious that a high Indefinition score might also reflect problems in the grid design (such us elements falling out of the range of convenience of the constructs) or lack of co-operation on the part of the client.
Of certain research interest, albeit with no tradition in the grid literature, are the extremity bias and the rating range measures (also in the summary of cognitive measures, Table 7). The first index measures the deviation of the subject's ratings from the expected score, and the second measures their degree of variance. It remains to be seen whether these measures will end up being more appropriate than the extremity score and the discriminative power measure, respectively. To the moment they are just being investigated by the authors.