Testing inequality of lengths of three dimensions underlying the structure of individual variation in 6 sleep-wake abilities and 6 broad personality traits

The dimensionality of structures proposed to explain the interrelations among several individual traits can be overestimated due to applying factor-analytic methodology for uncovering factorial dimensions of such structures. Although the factors are forced into orthogonality by means of rotation, significant inter-correlations are always found among questionnaire scales constructed for assessment of these factors. The assumption of inequal lengths of the axes of such structures provides the possibility to map 6 dimensions yielded by factor analysis on the surface of three-dimensional shape. Mathematically, this shape is a triaxial ellipsoid (i.e. an ellipsoid with three inequal axes) named “rugby cake” for simplicity. Here, this assumption of inequality of the axes of this shape was tested using (1) data on correlation coefficients among 6 scales of the questionnaires designed to assess 6 broad personality traits and 6 sleep-wake abilities that were collected from 3676 participants of three surveys, and (2) 100 matrices of correlation among 6 HEXACO’s scales (Honesty-Humility-Emotionality-eXtraversion-Agreeableness-Conscientiousness-Openness to Experience) from the literature. Results supported the assumption of inequal lengths of three axes of “rugby cake” representation of individual variation in personality traits and sleep-wake abilities. This representation can be used for predicting factorial structure of yet-undeveloped questionnaires and missed questionnaire scales.