248 Structures of Personality Traits
by the questionnaire model (e.g., 30). The procedure would
consist of a target rotation of these principal components to-
ward the subscale in question. Thus, using the collateral
information contained in related items would generally in-
crease the subscale’s internal consistency, even though the
contribution of “bloated-specific” variance to it would be
diluted, which in itself would be a desirable side effect.
The previous script, however, amounts to proving that the
performance of a hierarchically conceived questionnaire can
be boosted by placing a network model under its hood. Fol-
lowing the script would sooner or later lead to adopting the
generalized circumplex approach, which implies a view of
personality structure as a tissue rather than a hierarchy. At the
superordinate scale level, one would hit upon a large number
of interesting AB5C facets, which are linear combinations of
the firstmprincipal components; at the subscale level, a great
amount of redundancy would be found, leading to a drastic
reduction of the conceptual rank of the data matrix. The
future of personality structure is hyperspheric.
Pruning the AB5C Model
The hypersphere of personality is riddled with gaps. Upon
presenting the AB5C model, Hofstee et al. (1992) already
noticed that its circumplexes were not evenly filled: The 1
o’clock versus 7 o’clock and 2 versus 8 segments attracted far
more trait terms than did the 4 versus 10 and 5 versus 11 seg-
ments. The former segments contain consonant mixtures of
either two positives factor poles (e.g., III, sociable) or two
negative poles (e.g., III, unsociable), whereas the latter
contain discords combining a positive and a negative pole
(e.g., III, submissive, vs. III, dominant). The scarcity
of discords reappears in Hendriks’s (1997, p. 45) results: Of
the off-diagonal items, only 23% combine a positive and a
negative factor pole, whereas the number of consonant and
discordant cells is equal. Furthermore, discords tend to have
the smaller projections in the 5-space, as may be verified from
the cited studies. These results reflect the classical (e.g.,
Cruse, 1965) finding that neutral trait terms are scarce. The
lexical axiom would imply that people find the corresponding
behaviors relatively unimportant.
The rationale for introducing blends, in circumplex mod-
els in general and in the AB5C model in particular, is commu-
nicative. In the case of discords, the communicative benefits
are unlikely to materialize. Rigid, for example, has a projec-
tion of .29 on the IIIIIvector in the AB5C model (Hofstee
et al., 1992, p. 157); unkind and orderly have projections of
.52 on IIand .67 on III, respectively. Thus, the projection
of the weighted sum of unkind and orderly on the IIIII
vector would be about twice as high as the projection of rigid
itself. “John is primarily unkind and secondarily orderly” may
thus be expected to communicate better than “John is rigid.”
Therefore, the discordant hyperquadrants may be deleted
from the AB5C model. It would thereby become semicircum-
plex: Of each circumplex, only the first and third quadrants
would be retained. Clinicians, who tend to be sensitive to am-
bivalences of personality, might deplore that loss. However,
the removal might well clarify intraprofessional communica-
tion, not to speak of communication with lay clients.
Extending this analysis would lead to a proposal for a
somewhat different rotational positioning of the 5-D axes in
order to maximize the coverage of consonant variables. In
their present definition, some factors (notably, II and III) are
associated more closely with desirability than are others
(notably, I and IV). Thus, the vector in the I by II
quadrant upon which the projections of the Desirability val-
ues of the traits would be maximal is closer to the II axis than
to the I axis. This asymmetry is illustrated by the fact that an
undesirable trait like unrestrained (at 2:30 on the clock) has a
distance of only 30 deg from that bisectrix (which is at 1:30),
whereas agreeable (at about 11:20) is more than 60 deg re-
moved from it. A counterclockwise rotation of the two factors
would recognize unrestrained as a discord and agreeable as a
consonant trait, which seems appropriate.
Applying this operation to all axes jointly amounts to a ro-
tation to desirable manifold, mirrored by undesirable mani-
fold. The resulting abridged Big Five semicircumplex
(AB5SC) model is thus contained by the 10 faces of the
hyperquadrant centered around the desirability axis and their
10 opposites. Each face is divided into three segments of
30 deg, placing the model vectors at clock positions of 12:30
versus 6:30, 1:30 versus 7:30, and 2:30 versus 8:30. (A more
elegant representation involving a 45-deg counterclockwise
rotation is presented later.) As no vectors recur in other semi-
circumplexes, there are now 30 bipolar model vectors.
In the following section the AB5SC model returns as a
member of a family of models. That family comes about by a
somewhat different rationale. The number five is no longer
fixed; the emphasis shifts from 5-D models to accounts of
trait structure that incorporate a number of principles that
contribute to an efficient description of personality. Also, the
factors as such disappear into the background, which is
where they should have been from the start.A FAMILY MODEL OF TRAIT STRUCTUREWhat remained of hierarchical structure is the fact that each
subsequent principal component explains less variance and is
subordinate to its predecessors in that respect. The head of