Is there a general factor
of personality?
Probably not.
Presented as part of a symposium on the Structure of Personality
49th Annual Meeting of the Society of Multivariate Experimental
Psychology
Shalishan, Oregon, October 8-11, 2009
William Revelle and Joshua Wilt
Northwestern University
The claim
I. “A recent hypothesis is that a General Factor of
Personality occupies the apex of the hierarchical
structure of personality in the same way that g, the
general factor of mental ability, occupies the apex
in the organization of cognitive ability.” Rushton
and Irwing, 2009. p 571
II. Hofstee (2001): the p factor of personality: “the
Primordial One”
Recent Claims
2007
2008
Even more claims
2008
2009
Papers given at ISSID 2009
And even more
2009
Based upon implausible
(impossible) solutions
claim that GFP accounts for 25% of “first order factors”
23% based on multilevel structure
Rushton and Irwing, 2009
Is the General Factor of
Personality really general?
I. Ways of estimating a general factor
II. Comparisons with g of ability
III.General factors from uncorrelated factors
IV.Why there could be a general factor (but
probably isn’t)
Viewing g: using R graphics
V2
V3
V4
V5
V6
V6
V5
V4
V3
V2
V1
g + two groups
V1
all equal
V1
V2
V3
V4
V5
V6
V1
V2
V4
V5
V6
V5
V6
V2
V3
V4
V5
V6
V6
V5
V4
V3
V2
V1
Two groups
V1
g + two groups
V3
V1
V2
V3
V4
V5
V6
V1
V2
V3
V4
Estimating a general factor
I. Magnitude of first factor -- NO
II. Loadings of lower order factors on a higher order
factor -- NO
III. McDonald’s omega hierarchical -- YES
A.Exploratory procedure - using omega function in the
psych package in R
ωh
B. ICLUST to estimate β the worst split half reliability
C. Confirmatory procedure - using the sem package
Estimating a general
factor: the MPQ
I. Graphical description
II. Exploratory Factoring using minres
III.Omega solutions
IV.ICLUST
AB
TR
HA
CO
AG
AL
SR
SC
AC
SP
WB
Correlation plot of MPQ
Wellbeing
Achievement
Alienation
Control
Traditionalism
MinRes with oblimin
Oblimin transformation of MPQ
Stress_Reaction
Alienation
Aggression
Social_Closeness
0.7
0.6
0.5
-0.3
MR1
0.2
Social_Potency
Wellbeing
Achievement
0.6
0.6
0.5
0.5
MR2
0
Absorption
Control
Traditionalism
Harmavoidance
0.1
0.6
0.4
0.3
MR3
Exploratory solution
Hierarchical (multilevel) Structure
ωh = .53
But clearly due to F1
Stress_Reaction
Alienation
Aggression
Social_ClosenessSocial_PotencyWellbeingAchievement-
0.7
0.6
0.5
0.3
0.5
0.6
0.6
0.5
-0.5
0.4
Control-
0.6
-0.4
0.3
Harmavoidance-
1
F2
0.2
0.1
Absorption
Traditionalism
F1
F3
g
Omega with Schmid Leiman Transformation
ωh = .53
Stress_Reaction
But clearly due to F1
Alienation
Aggression
g
0.7
0.6
0.5
0.6
0.3
0.2
0.1
0
0
0
0.1
F1*
WellbeingSocial_ClosenessAbsorption
0.5
Achievement-
0.5
0.5
0.6
Social_Potency-
0.4
Harmavoidance-
0.3
0.3
0.6
Traditionalism
Control-
F2*
F3*
Hierarchical (multilevel) Structure
ωh = .17
Aggression
Stress_Reaction
Alienation
Absorption
ControlHarmavoidance-
0.6
0.5
0.5
0.5
0.3
0.4
F1
0.4
g
-0.4
-0.3
TraditionalismWellbeingSocial_PotencyAchievementSocial_Closeness-
0.4
0.8
0.5
0.4
0.3
F2
Omega with Schmid Leiman Transformation
ωh = .17
Aggression
Stress_Reaction
Alienation
g
0.3
0.4
0.3
0.1
0.1
0
0
0.4
0.1
0.1
0.2
Absorption
ControlHarmavoidanceTraditionalismWellbeingSocial_PotencyAchievementSocial_Closeness-
0.5
0.5
0.5
0.4
0.2
0.2
0.4
F1*
0.3
0.3
0.2
0.7
0.5
0.3
0.2
F2*
ICLUST of MPQ
Absorption
Harmavoidance
-0.52
Control
0.48
Aggression
0.61
0.61
Alienation
Wellbeing
0.69 C1
! = 0.65
-0.69! = 0.65
Social_Potency
C4
! = 0.54
! = 0.54
0.75
0.85
C2
! = 0.45
0.54 ! = 0.45
0.54
β = .10
C7
! = 0.48
! = 0.41
0.13
C10
! = 0.55
! = 0.1
C6
! = 0.68
! = 0.6
0.13
0.32
-0.59
Social_Closeness
Achievement
0
C5 -0.81
! = 0.35
! = 0.35
0.48
Traditionalism
Stress_Reaction
C3
! = 0.43
! = 0.43
0.52
General factor
based upon worst
split half
-0.32
C8
! = 0.67
! = 0.48
0.11C9
! = 0.62
! = 0.25
Comparing GFP to g
I. Classic cognitive data sets
A.Thurstone 9 variables
B. Holzinger 14 variables (example of bifactor)
II. Purported GFP results
A.MPQ
B. Digman’s data sets
Letter.Group
Letter.Series
First.Letters
Vocabulary
Correlation plot of 9 cognitive variables from Thurstone
! = .79
Sentences
Sent.Completion
Suffixes
Pedigrees
T77
T18
T36a
T34
T29
T6
T2
T1
Correlation plot of 14 cognitive variables from Holzinger
! = .71
T1
T2 T3.4 T6
T28
T32
T35
T13
T25b
E
Correlation plot of Digman meta analysis
! = .35
ES
Socialization
A
C
O
Growth
E
O
Plasticity
C
A
Stability
ES
AB
TR
HA
CO
AG
AL
SR
SC
AC
SP
WB
Correlation plot of MPQ
Wellbeing
Achievement
Alienation
Control
Traditionalism
V 11
V1
V6
V 11
V7
Sentences Letter.Group
V 11
O
Holzinger
! = .71
E
ES
D
T29
T18
V6
V 11
MPQ
! = .31
MMPI
! = .31
Mf
T1
V1
Digman
! = .35
V7 V13
T77 T28
V4
Thurstone
! = .79
V6
ES
V1
S8: two groups
! = .0
V 12 V 4
Bechtold
! = .67
V17 V7
V4
V9
V4
V1
C
Jensen
! = .69
V1
S7: g + two groups
! = .29
V4
Open Empathy
Comrey
! = .29
Ex
V6
V1
V 12 V 4
S6: g + two groups
! = .57
V4
MT
V1
V2
V1
V 12 V 4
V 12 V 4
S5: all equal
! = .70
V4
V6
V2
V1
S4: two groups
! = .0
Emot_Stability
V4
S3: g + two groups
! = .25
V6
V2
S2: g + two groups
! = .49
V6
V2
V6
V1
V9
Interocular
Trauma
test
S1: all equal
! = .72
Sc Pd Pa Mf
Activity
Trust
Creating g when it is
not there
I. g implies a positive manifold
II. reverse scoring items can lead to the
appearance of g
III.Consider the case of a circumplex with and
without reverse keying half of the items
V 24
V 21
V 18
V 15
V 12
V9
V7
V5
V3
V1
Correlation plot of 24 circumplex variables
! = .03
V1
V3
V5
V7
V9
V 11
V 14
V 17
V 20
V 23
0.6
24 circumplex variables
3
2
1
24
23
0.4
4
5
0.2
6
21
0.0
7
20
8
-0.2
1918
-0.4
9
17
10
11
16
12
-0.6
MR2
22
14
13
-0.6
-0.4
-0.2
0.0
MR1
15
0.2
0.4
0.6
reverse scoring 12 items leads to a 'general' factor
! = .85
0.6
13
14
2
0.5
15
3
1
12
23
16 4
0.4
11
5
10
22
0.3
17
6
21
9
0.2
0.1
MR2
24
18
19
7
8
20
-0.6
-0.4
-0.2
0.0
MR1
0.2
0.4
0.6
Is there a general factor
of personality?
Is there a general factor
of personality?
Probably not
Is there a general factor
of personality?
Probably not
How important is the General Factor of Personality? A General Critique
William Revelle and Joshua Wilt
Northwestern University
http://personality-project.org/revelle/syllabi/454/gfp.pdf (to be submitted)
Why there could be a
general factor
I. Goldberg, Peabody, Saucier talk about
general evaluation
II. Rushton: Evolutionary selection