240 Structures of Personality Traits
I document the relativeness of the opposition between the
person-centered and variable-centered paradigms (see also
Millon, 1990) but try to do justice to a real difference in their
ranges of application.
Persons in Principal Component Analysis
Unlike factor analysis proper, in which factor scores are
hardly more than an afterthought, PCA offers a fairly sym-
metric treatment of individuals and variables. One could ro-
tate a matrix of scores on principal components to simple
structure and characterize individuals by the person factor on
which they had their highest score. In an even closer approx-
imation to the person-centered approach, factors and load-
ings may be rescaled such that individuals receive loadings
and variables receive factor scores. That is not precisely the
same thing as performing Q-factor analysis, as the scores still
become standardized per variable instead of per individual as
in Q-analysis; but the two operations would be mathemati-
cally identical in the case of raw-score PCA. If the argument
in favor of raw-score PCA is accepted, the difference
between variable-centered and person-centered analysis re-
duces to a set of scaling constants and rotation criteria being
applied to one matrix rather than another, which is hard to get
excited about.
Variables and Types
An orthodox typological solution may be viewed as a binary
matrix of persons by types with one 1 per row, representing
the type to which that person is assigned, and 0 scores in the
remaining cells. At the other extreme, each person could be
given a score for each type on a continuous scale, represent-
ing the extent to which that person corresponds with that
type, thereby treating the types as continuous variables. The
orthodox solution could be reconstructed from that matrix by
selecting the highest score per row and dichotomizing ac-
cordingly. Intermediate, liberalized typological solutions
(Millon, 1990) could also be derived, most notably through
matrix-wise dichotomization of the continuous scores. In the
liberalized solution, some persons would appear to be as-
signed to more than one type, whereas some others would fail
to meet the threshold for any type at all. The types would no
longer be orthogonal in the way they are forced to be accord-
ing to the orthodox solution; so one could correlate the types,
factor analyze them, and the like.
To those who would find this methodological play with
types improper, there is a perfectly serious answer. In the ideal
case, a diagnosis is performed by an infinite number of inde-
pendent experts. Experts do not agree perfectly in all cases.
Thus the sum or average of even their orthodox typological
solutions would give precisely the kind of matrix of continu-
ous scores introduced in the earlier argument. In a scientific
(in the sense of intersubjective) conception of types, the con-
tinuous matrix is the primitive case, not the binary matrix. The
primitive case arises not because types (or even personality
variables in general) are necessarily continuous as such, but
because of the tacit third dimension of the matrix.Q-Sorts and Likert ScalesInvestigators working in the person-centered paradigm prefer
ipsative scores, as they would represent intra-individual
rather than interindividual comparisons. Varieties of ipsative
scoring are row standardization, which fixes the means and
standard deviations, and forced distribution, whereby all
moments are fixed. Q-sorts automatically result in forced-
distribution scores (unless the number of items in the “most
applicable” to “least applicable” categories is not fixed, in
which case, however, the method is indistinguishable from
using a Likert scale).
Like orthodox typologies, ipsative scores may be con-
structed from continuous “interactive” scores, in this case by
standardizing over variables or by forcing a distribution on
them. One might object that Q-sorts are different in principle
from Likert-scale scores, but that remains to be seen. In the
first place, judges need not respond the way we instruct them
to. If I am asked, by way of intra-individual comparison,
whether I am (or John is) more reliable than friendly, I may
well respond against the background of people in general; it
could even be argued that the question is meaningless with-
out that background. Conversely, when confronted with a
standard personality questionnaire, intra-individual consider-
ations might well enter into my response process. It is thus ar-
guable that all responding is interactive. In the second place,
Q-sorts are usedto compare people, therefore, interindividu-
ally: If John is said to be of Type A whereas Mary is not, the
intra-individual level is automatically surpassed.
Theeffectof ipsatization is to remove interindividual dif-
ferences in elevation and spread (and skewness, kurtosis, and
so on) of the responses. The operation thus implies a view
of personality in which such individual differences have
no place. Surprisingly, that view appears to be shared by
some unadulterated trait researchers, most notably Goldberg
(1992a) and Saucier (1992; see, however, Saucier, 2002a).
Their rationale, however, has nothing to do with an emphasis
on intra-individual differences. Rather, they use ipsatization
of Likert-scale data to remove differences in scale usage, in
other words, response sets. Whatever the rationale is, the
implication needs to be examined in detail.