The Linear Approach to the Concept of Personality 239In sum, item scoring through weights obtained by raw-
scores PCA deserves more consideration than it has received
so far. The standard objection to treating scores on a Likert
scale as absolute is that strong assumptions would be im-
posed on the data. I am unable to see the validity of that
argument. So-called weak models may in fact be very strong:
To assume that the midpoint of a personality scale has no
meaning and, consequently, that respondents’ evaluations can
be reversed, is about as strong as hypothesizing, for example,
that a large proportion of the population cannot be trusted. At
the very least, the absolute conception of Likert-scale scores
is no more indefensible than the interval conception.
A Review of the Grounds for the Number Five
A way to obtain many principal components is to analyze ma-
trices with large numbers of variables, in this case single trait
descriptors. Earlier, limitations on computing capacity virtu-
ally prevented the number of trait variables from being much
larger than the 35 employed by Tupes and Christal (1961/
1992). With the expanding power of computers, however, it
became feasible to analyze the very large numbers of vari-
ables that were needed to justify claims of representativeness
if not exhaustiveness. However, the sorcerer’s apprentice
problem then becomes keeping the number of factors from
getting out of hand. With hundreds of variables, it will take
many factors to get down to the time-honored “eigenvalue 1”
threshold; for example, the 20th factor in Ostendorf’s (1990)
PCA of 430 traits still has an eigenvalue of 3.
Hofstee et al. (1998) proposed a more stringent criterion
based on the alpha reliability of principal components, which
is approximately 11/Ewith large numbers of variables, E
being the eigenvalue of that principal component. Setting the
minimum alpha at .75, an “eigenvalue 4” threshold results
(E= 1 gives=0).Using this criterion, Ostendorf (1990)
should still have set the dimensionality of the personality
sphere at about 14 rather than 5; with even larger numbers of
traits, the dimensionality would only increase. There can be
no doubt that the 5-D model discards linear composites of
traits that are of sufficient internal consistency, and would
add to the number of dimensions. It is of interest to note that
the most prominent 5-D questionnaire, Costa and McCrae’s
(1992) NEO-PI-R, in fact postulates 30 dimensions rather
than 5, as each of the 30 subscales is deemed to have specific
variance in their hierarchical model. (The five second-order
factors do not add to the dimensionality, as they are linear
combinations of six subscales at a time.)
An entirely valid pragmatic reason to restrict the number
of factors is parsimony. The first principal component is
the linear combination of traits that explains a maximum of
variance; the second maximizes the explained variance in the
residual, and so on. Consecutive factors thus follow the law
of diminishing returns. Next, the scree test acts on the amount
of drop in eigenvalue between consecutive factors; it thus
signals points of increasingly diminishing returns. Using the
scree test, Brokken (1978) retained 6 principal components in
a set of 1,203 trait adjectives; Ostendorf (1990) retained 5.
However, the scree test does not offer a unique solution;
Ostendorf, for example, could have opted for an 8-factor so-
lution on that basis. Neither PCA nor the scree test dictates
the number of five.
Does replicability of factors provide a cogent criterion
for the dimensionality of the space? That depends on how
the term is understood. If one and the same large trait list were
administered to large samples from the same population, the
number of replicable factors would in all likelihood exceed
five. At the other extreme, when independent, “emic” replica-
tions of the lexical approach in different languages are under-
taken, the number tends to be in the order of three (De Raad
et al., 1997; Saucier et al., 2000) rather than five, Ostendorf’s
replication being an exception. Saucier, Hampson, and
Goldberg list 18 points on which such studies might diverge
and recommend methodological standardization. A familiar
objection is that standardization leads to premature closure of
the issue: Not only would the outcome depend on arbitrary
choices, but moreover one could not tell anymore what makes
a difference and what does not. It would be preferable to use
these points for studies on whether and how the number varies
in function of differences in approach.
In sum, the number five takes on the character of a point
estimate in a Bayesian credibility function on an abscissa that
runs from 0 to some fairly large number, with the bulk of the
density stacked up between 3 and 7. As with other empirical
constants, the uncertainty does not so much result from ran-
dom error as from the interplay of diverging arguments and
specifications. In any case, the number should be taken with
a grain of salt.The Person-Centered or Typological ApproachA familiar critique of trait psychology is that it loses the
individual from sight (see, e.g., Block, 1995; Magnusson,
1992). A set of alternative operations is available under labels
such as type or person-centered approach; it comprises
Q-sorts in preference to Likert scales, longitudinal designs to
assess the dynamics of personality, and cluster analysis of
persons rather than PCA of variables. Recent empirical stud-
ies (e.g., Asendorpf & Van Aken, 1999; Robins, John, Caspi,
Moffit, & Stouthamer-Loeber, 1996) concentrate on the three
“Block” types: resilient, overcontrolled, and undercontrolled.