Personality in proportion

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 L-XY = 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 F-1 and 2 very small ones, F-2 and F-3. The sizes L-FE = SigmaF(2)/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.