No abstract

This paper considers descriptive methods of comparing components from different studies, based on correlations between columns of component scores matrices, on congruence coefficients between columns of pattern, structure or component scores coefficient matrices, or on coefficients of invariance. Contrary to common belief, it is shown that coefficients of invariance are unrelated to correlations between component scores. On the other hand, having a perfect coefficient of invariance is shown to be equivalent to having a perfect congruence between corresponding columns of the component scores coefficient matrices. A similar but weaker relationship between the latter congruence and congruence between columns of pattern matrices is demonstrated.

No abstract

reliability, coefficient alpha, components, factors, rotation, greatest lower bound to reliability,

Trait structures resulting from personality assessments on Likert scales are affected by the additive and multiplicative transformations implied in interval scaling and correlational analysis. The effect comes into view on selecting a plausible alternative scale. To this end, we propose a bipolar bounded scale ranging from -1 to +1 representing an underlying process in which the assessor would review and discount positive and negative behavioral instances of a trait. As an appropriate index of likeness between variables X and Y, we propose LXY = SigmaXY/N, the average of the raw scores cross products. Using this index, we carried out a raw scores principal component analysis on data consisting of 133 participants who had each been rated by 5 assessors including self on 914 items. Contrary to the Big-Five structure that was found in these data on standard analysis, the results showed a relatively large first principal component F1 and 2 very small ones, F2 and F3. The sizes LFF=SigmaF2/N, the averages of the squared component scores, were modest to small. It thus appears that the scale, bipolar proportional versus standard, has a profound impact on the size and structure of personality assessments. The dissimilarity remains on analyzing self-ratings rather than averaged (over the 5 assessors) ratings.