Construct system complexity can be defined as the

Construct system complexity can be defined as the capacity to use one’s construct system in a multidimensional way.

Bieri’s (1966) original definition of cognitive complexity was "the capacity to construe social behavior in a multidimensional way" (Bieri et al., 1966, p. 185).

Distinctive advantages of the Structural Quadrants Method for the assessment of construct system complexity via Grid data: • It is theoretically coherent in terms of Kelly's definition of a construct. • It is based directly on standard grid data. • The mathematical calculation of differentiation and integration indexes are based on the same logic but, nevertheless, both dimensions are orthogonal. • The method can be used to calculate a numerical index of differentiation and integration while also displaying a significant amount of qualitative information about construct system structure.

Kelly (1955/1991, p. 43) stated that "in its minimum context a construct is a way in which at least two elements are similar and contrast with a third".

• Differentiation and integration should be considered as two characteristics of the construct system when it is applied to a given set of elements. • Differentiation can be defined as the extent to what the construct system allows the person to focus on differences among elements rather than similarities among them. • Integration can be defined as the extent to what the construct system allows the person to focus on similarities among elements rather than differences among them.

• Quadrant I (Simple System): A construct system is simple to the extent that it does not allow the person either to differentiate or to integrate among a given set of elements, i.e., it is defined by a low level of differentiation and integration. • Quadrant II (Monolithic System): A construct system is monolithic to the extent that it allows the person to integrate a given set of elements rather than to differentiate among them, i.e., it is defined by a higher level of integration than differentiation. • Quadrant III (Fragmented System): A construct system is fragmented to the extent that it allows the person to differentiate among a given set of elements rather than to integrate them, i.e., it is defined by a higher level of differentiation than integration. • Quadrant IV (Complex System): A construct system is complex to the extent that it allows the person to simultaneously differentiate among a given set of elements and to integrate them, i.e., it is defined by a high level of differentiation and integration. We do not consider it possible to assess either the number of independent construct dimensions or, more importantly, the system's internal organization independently of the set of elements to which the system is being applied.

GENTLE FRIENDLY PLEASANT

A 1 2 1

B 1 2 1

C 1 2 1

D 1 2 2

NOT GENTLE UNFRIENDLY UNPLEASANT

GENTLE FRIENDLY PLEASANT

A 1 2 1

B 5 4 5

C 3 3 3

D 1 5 1

NOT GENTLE UNFRIENDLY UNPLEASANT

Differentiation Measures • Bieri's (1955) Cognitive Complexity index: Bieri's cognitive complexity score is computed as the number of perfect matches in ratings of elements on each pair of constructs, divided by the maximum possible score that could be obtained from a grid of that size. Fewer matches are interpreted as greater differentiation and, thus, greater complexity. • Functionally Independent Construction (FIC) (Landfield, 1971): The FIC score is a measure of the number of independent clusters of constructs used in the grid. It is based on the measure of the degree of dissimilarity in a subject's allocation of grid elements on different constructs, or their application of constructs to different elements. Higher FIC scores indicate that the person is using his or her constructs in an independent fashion and are thus interpreted as a measure of the degree of differentiation of the construct system. • Percentage of variance accounted for by the first factor (PVAFF) (Okeefe & Sypher, 1981): This index is computed by submitting the original grid to a principal component analysis. It is assumed that the larger the first factor, the more unidimensional the underlying structure of the grid. Thus, greater PVAFF scores are interpreted as lower differentiation and lower complexity.

Integration measures • Intensity (Fransella & Bannister, 1977): Intensity scores reflect the total degree of irterrelatedness among constructs of the grid. Intensity is calculated by summing the absolute values of the Pearson correlation between ratings performed on all possible pairs of constructs and then multiplying by 100. • Ordination (Landfield & Cannell, 1988): The ordination measure is calculated by multiplying the number of levels of extremity used in ratings with a particular construct, or of a particular element, by the difference between the highest and lowest ratings. The average ordination scores for constructs and for elements are then summed.

STEP I: From Repertory Grids to Similarity Matrixes let G be a standard repertory grid composed by n constructs and m elements; let ci be construct i in G; let ej be element j in G; let gij be the scoring of ej in ci in G; then, the scoring similarity between every element ej in G and every other element can be calculated construct by construct by the formula: sijk = r - |gij - gik| where sijk is the scoring similarity index between ej and ek in ci, and r is the scoring range of G, i.e., the total difference between the maximum and minimum scores in the Likert scale used in G. Note that if the scoring in ci is the same for ei and ek then sijk is maximum and equal to r. On the other hand, if the scoring of ej in ci is very different from the scoring of ek (i.e., if gij is at one end of the Likert scale, and gik at the opposite end) then sijk is minimum and equal to 0.

STEP II: Factor Analysis of Similarity Matrixes Each similarity matrix is now submitted to factor analysis. We extract two factors for each similarity matrix sj, and compute factor loadings for each construct ci. Factor loadings for every ci indicate the level of similarity between the scorings of ej and the rest of elements in G considered as a whole. Positive factor loadings indicate that the scoring of ej in ci is similar to the scoring of all the other elements in ci. In this case, the use of ci when rating ej is very similar to its use when rating all the other elements in G. Negative factor loadings indicate that the scoring of ej in ci is dissimilar to the scoring of all the other elements in ci.

Step III: Assessment of Differentiation Constructs and Integration Constructs Those constructs that yield the highest positive factor loading in Step II are used to integrate element ej with the rest of the elements in G. Those constructs that yield the highest negative factor loading in Step II are used to differentiate element ej from the rest of elements in G. The SQM considers a construct an integration construct when cl1 x pvaff + cl2 x pvasf > .3 x pvaff + .3 x pvasf being: cl1 = construct loading in the first factor; pvaff = percentage of variance accounted for by the first factor; cl2 = construct loading in the second factor; and pvasf = percentage of variance accounted for by the second factor. On the other hand, the SQM considers a construct a differentiation construct when |cl1 x pvaff + cl2 x pvasf| >.3 x pvaff + .3 x pvasf

STEP IV: Qualitative Analysis of Differentiation and Integration Differentiation/Integration Summary Table for the Student’s Grid

Differentiation Element

Weight

Constructs

Freud

-334.41 -390.12

Developmental vs. Behavioral (2) a Behavioral vs. Developmental (4)

Rogers

-349.07 -325.54 -390

Psychoanalytic vs. Non Psychoanalytic (4) Psychoanalytic vs. Constructivist (4) Psychoanalytic vs. Personality (4)

Piaget

-739.70 -319.34 -380.65

Psychoanalytic vs. Non Psychoanalytic (5) Psychoanalytic vs. Constructivist (4) Psychoanalytic vs. Personality (4)

Vygotsky -702.93 -313.61

Psychoanalytic vs. Non Psychoanalytic (5) Psychoanalytic vs. Personality (3)

Skinner

-474.44

Psychoanalytic vs. Non Psychoanalytic (5)

Pavlov

-463.26

Psychoanalytic vs. Non Psychoanalytic (5)

Adler b Jung b

STEP IV: Qualitative Analysis of Differentiation and Integration Differentiation/Integration Summary Table for the Student’s Grid Integration Element

Weight

Constructs

Freud

292.33

Psychoanalytic vs. Non Psychoanalytic (1)

Adler498.42 Psychoanalytic vs. Non Psychoanalytic (1) 341.84 Behavioral vs.Psychoanalytic (5) Jung

481.55 304.40

Psychoanalytic vs. Non Psychoanalytic (1) Behavioral vs.Psychoanalytic (5)

Rogers

317.47 294.37

Developmental vs. Behavioral (3) Behavioral vs. Developmental (4)

Piaget

423.62 339.47 401.55

Developmental vs. Behavioral (2) Behavioral vs. Psycholinguistics (4) Behavioral vs. Developmental (4)

Vygotsky 415.59 327.88 411.63

Developmental vs. Behavioral (2) Behavioral vs. Psycholinguistics (5) Behavioral vs. Developmental (4)

Skinner

367.84

Behavioral vs. Psycholinguistics (1)

Pavlov

396.02 281.58

Behavioral vs. Psycholinguistics (1) Behavioral vs. Development (1)

Note: a Rating of element Freud on construct Developmental vs. Behevioral in the original grid b Elements not differentiated in any construct

STEP V: Differentiation Index (a) Elements with no differentiation constructs associated. These elements are not specifically differentiated from the rest in G. (b) Elements whose differentiation constructs are different from the ones associated with any other element. These elements are genuinely differentiated from the rest in G. (c) Elements whose differentiation constructs are the same as the ones associated to other elements, as well as their rating in G. This is a case of no differentiation between these two elements, for the reasons discussed above. Taking this into account, a differentiation index can be calculated by the following formula: number of differentiated elements / m x number of differentiation constructs / n

STEP VI: Integration Index (a) Elements with no integration constructs associated. These elements are not specifically integrated with the rest in G. (b) Elements with integration constructs associated. These elements are specifically integrated with the rest by these constructs. Taking this into account, an integration index can be calculated by the following formula: number of integrated elements / m x number of integration constructs / n

STEP VII: Complexity Analysis • if the differentiation index for G < .5 and the integration index for G < .5 then G is a simple grid; • if the differentiation index for G > .5 and the integration index for G < .5 then G is a fragmented grid; • if the differentiation index for G < .5 and the integration index for G > .5 then G is a monolithic grid; • if the differentiation index for G > .5 and the integration index for G > .5 then G is a complex grid.