PVAFF

Description
Percentage of Variance Accounted for by the First Factor (PVAFF) is used as a measure of cognitive complexity. The idea was introduced in an unpublished PhD thesis by Jones (1954, cit. Bonarius, 1965). To calculate it, the first factor is extracted from the construct correlation matrix by principal component analysis. The PVAFF reflects the amount of variation that is accounted for by a single latent linear component. If a single component is able to explain a lot of variation in the grid, the cognitive complexity is said to be low and the construct system is attributed the term 'simple' (Bell, 2003). It is argued, that as a consequence of a simple constructs system, less differentiation in anticipated events can be generated (cf. Adams-Webber, 1970).

R-Code
> indexPvaff(bell2010)

Percentage of Variance Accounted for by the First Factor

PVAFF: 60.02 %

To use the value for further processing, the console output can be surpressed. Note that the value returned is the proportion not the percentage.

> p <- indexPvaff(bell2010, out=0) > p  Comp.1 0.6002283

Literature

 * Adams-Webber, J. R. (1970). An analysis of the discriminant validity of several repertory grid indices. British Journal of Psychology, 61(1), 83-90.
 * Bell, R. C. (2003). An evaluation of indices used to represent construct structure. In G. Chiari & M. L. Nuzzo (Eds.), Psychological Constructivism and the Social World (pp. 297-305). Milan: FrancoAngeli.
 * Bonarius, J. C. J. (1965). Research in the personal construct theory of George A. Kelly: role construct repertory test and basic theory. In B. A. Maher (Ed.), Progress in experimental personality research (Vol. 2). New York: Academic Press.
 * James, R. E. (1954). Identification in terms of personal constructs (Unpublished doctoral thesis). Ohio State University, Columbus, OH.