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Variability Indicators in Structural Equation Models

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Variability Indicators in Structural Equation Models Michael Biderman University of Tennessee at Chattanooga www.utc.edu/Michael-Biderman – PowerPoint PPT presentation

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Title: Variability Indicators in Structural Equation Models


1
Variability Indicators in Structural Equation
Models
  • Michael Biderman
  • University of Tennessee at Chattanooga
  • www.utc.edu/Michael-Biderman

2
Background Modeling Faking of Personality Tests
  • For the past few years Ive investigated the
    utility of a structural equation model of faking
    of personality questionnaires, specifically the
    Big Five.
  • The model is a CFA containing
  • latent variables representing personality
    dimensions, and
  • one or more latent variables representing amount
    of response distortion, i.e., faking.

3
The Basic Faking Model
Applied to two-condition data
Applied to three-condition data
4
Beyond the Basic Model
The basic model represents changes in central
tendency associated with faking fairly well. Is
that all there is? Last year, during manual data
entry of Mike Clarks thesis data (Yes, UTC is a
full-service university) . . . I noticed that
some participants seemed to be targeting specific
responses, e.g., 6 6 6 6 6 6 Since such
targeting results in low variability this
suggested the possibility that variability of
responding might be an indicator of faking. The
following describes an attempt to model
variability.
5
Other studies of variability
Traitedness studies (Britt, 1993 Dwight, Wolf
Golden, 2002 Hershberger, Plomin, Pedersen,
1995). A person is highly traited on a dimension
if the variability of responses to items from the
dimension is small. Extreme response style
(Greenleaf, 1992). Stability of responses to the
same scale over time (Eid Diener, 1999 Kernis,
2005). No studies of variability of responses in
faking situations. None of variability and the
Big Five.
6
Three used datasets.
  • 1 Biderman Nguyen, 2004. N203
  • 2 Wrensen Biderman, 2005. N166
  • Two-condition data Honest and Fake Good
  • 50 item IPIP Big Five questionnaire given twice
  • 2-item parcels analyzed
  • Clark Biderman, 2006. N166
  • Three-conditions Honest, Incentive, Instructed
    faking
  • Three 30-item IPIP Questionnaires given.
  • Whole-scale scores analyzed.
  • Wonderlic Personnel Test (WPT) was given to all
    participants prior to the first condition.

7
Measuring Variability
To represent variability of responses within
dimensions, I computed the standard deviation of
responses within each Big Five dimension for each
participant for each condition I added the
standard deviations as observed variables to the
data to which the faking model had previous been
applied
8
Datasets 1 and 2 with Standard Deviations added
9
Dataset 3 with standard deviations added
SdE-H
E-H
SdA-H
A-H
SdC-H
C-H
SdS-H
S-H
SdO-H
O-H
SdE-D
SdA-D
SdC-D
SdS-D
SdO-D
SdE-I
SdA-I
SdC-I
SdS-I
SdO-I
10
Modeling Standard Deviations - 1 Faking leads
to elevated central tendency, often resulting in
ceiling effects. Ceiling effects lead to lower
variability. So the standard deviations were
connected to central tendency via regression
links. Specifically, standard deviations were
regressed onto parcel or scale scores.
11
Modeling Ceiling Effects in Datasets 1 and
2Standard deviations were regressed onto parcel
scores
12
Modeling Ceiling Effects in Dataset 3 Standard
Deviations regressed onto scale scores
13
Modeling Standard Deviations - 2 The
assumption/hope? was that there are individual
differences in variability of responding within
dimensions So a latent variable representing such
individual differences was added to the model.
14
Modeling variability in Dataset 1 2 Adding a
Variability latent variable
15
Modeling variability in Dataset 3 Adding a
Variability latent variable
16
Results
Did the regression links significantly improve
goodness of fit? Are there individual
differences in variability of responding that are
captured by the V latent variable?
17
Results of application of Variability model to
Dataset 1
Model ?2(1539)2501.249 plt.001 CFI.871
RMSEA.055
Both the regression links and the V latent
variable improved model fit.
18
Results of application of Variability model to
Dataset 2
Model ?2(1539)2666.874 plt.001 CFI.816
RMSEA.066
Again, both the regression links and the V latent
variable improve model fit.
19
Results of application of Variability model to
Dataset 3
Model ?2(352)532.552 plt.001 CFI.883
RMSEA.056
20
Tentative Conclusions regarding Variability Model
1) Ceiling effects seem to be successfully
modeled by the regressions of standard deviations
onto parcels or scale scores. 2) Individual
differences in variability of responding to items
within dimensions seem to be captured by the V
latent variable.
Some persons consistently exhibited little
variability in responding to items within
questionnaire scales. Others exhibit greater
variability in responding.
21
What about V and faking?
1) Loadings on V might be larger in faking
conditions magnifying individual differences in
variability because some people are targeting
while others are not.
Mean Standardized Loadings of Standard Deviation
indicators on V Dataset 1 Honest Incentive to
fake Instructed to fake Mean loading .406
.366 Dataset 2 Honest Incentive to
fake Instructed to fake Mean loading .411
.496 Dataset 3 Honest Incentive to
fake Instructed to fake Mean loading .468
.521 .413
Tentative Conclusion Loadings on V are
approximately equal in honest and faking
conditions.
22
What about V and faking?
2) V might be related to the faking latent
variables. Dataset 1 Correlation of V with
F .04 NS Dataset 2 Correlation of V with
F .02 NS Dataset 3 Correlation of V with
FP .16 NS Correlation of V with
FA .10 NS It appears from these preliminary
analyses that variability of responding is not
related to faking However, other scenarios and
models should be explored
23
What is V?
1) Perhaps V is related to personality
characteristics
It appears that V has discriminant validity with
respect to the Big Five.
24
What is V?
2) Perhaps V is related to cognitive ability
These results suggest that persons with higher CA
exhibit less variability of responding.
25
Uses of V
How about using it to extract cognitive ability
from the Big Five?
The structural model suggests that there is
information on cognitive ability embedded in
noncognitive personality tests.
26
Conclusions
  • 1) V appears to be an individual difference
    variable that cuts across personality dimensions.
  • V appears to be unrelated to faking
  • 3) V appears to be independent of the Big Five
    dimensions.
  • 4) V appears to be related to cognitive ability
    persons higher in cognitive ability have lower
    variability of responding

27
Implications
Dont throw away old datasets. You never know
what constructs may be hidden in them.
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