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Item analysis of the subscales in the Eight State Questionnaire (8SQ): Exploratory and confirmatory factor analyses

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The Eight State Questionnaire (8SQ) is a comprehensive self-report inventory which has been used in numerous studies of multidimensional mood states. The 8SQ has been useful in clinical situations for evaluating the efficacy of various therapeutic interventions, as well as in other contexts. The instrument takes about 20-25 minutes to administer, thereby enhancing its usefulness as a quick measure of transitory, constantly fluctuating mood states. Nevertheless, examination of the congeneric factor structure of the 8SQ subscales suggests that a number of the items are complex, contributing significantly to more than one subscale dimension. Both exploratory and confirmatory factor analyses have failed to provide substantial support for the existing subscale structure. Hence, further research should be directed toward refining the 8SQ item composition, by replacing items which contribute inadequately to the respective subscales, and/or those which are factorially complex. Such "progressive rectification" (Cattell's term) should result in a more psychometrically efficient instrument, which is characterized by greater factor purity and reduced intercorrelations, than is currently evident.
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1
Item analysis of the Subscales in the Eight State
Questionnaire (8SQ): Exploratory and Confirmatory Factor
Analyses
Gregory J. Boyle
University of Queensland
Correspondence should be addressed to: Gregory J. Boyle, PhD, Department of
Psychology, University of Queensland, St. Lucia, Q. 4072, Australia.
2
Abstract
The Eight State Questionnaire (8SQ) is a comprehensive self-report inventory
which has been used in numerous studies of multidimensional mood states. The
8SQ has been useful in clinical situations for evaluating the efficacy of various
therapeutic interventions, as well as in other contexts. The instrument takes about
20-25 minutes to administer, thereby enhancing its usefulness as a quick measure
of transitory, constantly fluctuating mood states. Nevertheless, examination of the
congeneric factor structure of the 8SQ subscales suggests that a number of the
items are complex, contributing significantly to more than one subscale
dimension. Both exploratory and confirmatory factor analyses have failed to
provide substantial support for the existing subscale structure. Hence, further
research should be directed toward refining the 8SQ item composition, by
replacing items which contribute inadequately to the respective subscales, and/or
those which are factorially complex. Such "progressive rectification" (Cattell's
term) should result in a more psychometrically efficient instrument, which is
characterized by greater factor purity and reduced intercorrelations, than is
currently evident.
3
Introduction
The Eight State Questionnaire (8SQ) (Curran & Cattell, 1976) is a multi-
dimensional, self-report instrument which is purported to measure eight
fundamental and clinically relevant emotions/mood states labeled Anxiety, Stress,
Depression, Regression, Fatigue, Guilt, Extraversion, and Arousal, respectively
(cf. Curran, 1968, 1974). An individual's behaviors depend not only on intra-
personal characteristics such as enduring personality traits, motivational dynamics,
as well as cognitive/intellectual attributes and abilities, but also on prevailing
levels of several emotional/mood states. Mood-state measurement has practical
importance in many research and applied psychological contexts, such as those
involved in trials on the effectiveness of new drugs, monitoring treatment efficacy
in clinical situations, assessing the influence of mood states on academic school
learning, investigating the moods of different categories of employees in industrial
and occupational settings, and so forth.
Multivariate assessment of mood states is mandated by virtue of the
observed complexity of human behavior. Restriction (prematurely) of
measurement to single mood-state dimensions such as anxiety or depression may
inadvertently fail to reveal important mood-state interactions and corresponding
interdependencies in specific situations. This issue has been addressed both by
Kline (1979) and by Boyle (1985b). The situationist debate provoked by Mischel
(1968) was directed at traits alone, and ignored the role of situationally sensitive
mood states, as well as the Cattellian concept of state liability factors (cf. Cattell,
1979/80).
4
Clearly, therapeutic interventions or experimental manipulations may
influence a wide range of mood states simultaneously. If measurement is confined
to only certain states, elevations or depressions in other states must necessarily
remain undetected. Conceivably, changes in unmeasured states may even bring
about alterations in those states actually measured. The only satisfactory way of
avoiding this difficulty is to utilize multidimensional state measurement. The 8SQ,
along with other multidimensional self-report instruments such as the Profile of
Mood States (POMS) (McNair, Lorr, & Droppleman, 1971/1981) and the
Differential Emotions Scale (DES-IV) (Izard, Doughtery, Bloxom, & Kotsch,
1974), was designed specifically to avoid the problems associated with the
psychometrically inadequate univariate measurement of emotional/mood states.
The usefulness of the 8SQ instrument has been investigated in several applied
psychological studies (e.g., Barton, Cattell, & Curran, 1973; Boyle, 1983b, 1984,
1986e, 1986f, 1987c; Boyle & Cattell, 1984; Gilliland, 1980), suggesting thereby
the situational sensitivity of the eight subscales comprising the questionnaire.
According to Curran and Cattell (1976, p. 4), "The eight emotional states
measured by the 8SQ have been shown, by factor analyzing change scores, to be
distinct but interrelated constructs ... The present forms are based on the results of
over ten separate factor-analytic studies ... numerous item analyses were
conducted in order to select maximally valid items. This research continues and
refinement of some of the test items would not be unexpected in the course of
time." Curran and Cattell (p. 4) further maintained that "coordinated factor
analyses have repeatedly shown that substantially more than two distinct states can
be found in questionnaire responses. The 8SQ has been designed to include the
best defined eight among them."
5
Several studies have examined the higher-order factor structure of the 8SQ
(Barton, 1978; Boyle, 1983c, 1985a, 1986a, 1986d, 1987a, 1987f; Dorans, 1977;
Stewart & Stewart, 1976). Also, the relationships between the 8SQ and other
psychological self-report inventories have been investigated (Boyle, 1986b, 1986c,
1987d, 1987e; Boyle, Stanley & Start, 1985). In general, up to four higher-order
8SQfactors have been identified, suggesting interpretations of State Neuroticism,
State Extraversion, Arousal-Fatigue, and Depression/Guilt. The quantitative
measurement overlap (redundancy) with other psychometric instruments has been
shown to be slight. Cattell and Kline (1977), as well as Kline (1979), have
concluded that the eight states measured in the 8SQ are reasonably reliable and
valid (cf. Curran, 1974).
In constructing the 8SQ, an equal number of "reversed" and "non-reversed"
items were included in each subscale in order to minimize the likelihood of
response sets. This practice has been questioned in previous research (Boyle,
1979, 1983a, 1989; Schmitt & Stults, 1985), wherein it was shown (in the state-
trait curiosity domain, for instance) that the reversed and non-reversed items were
loaded by essentially orthogonal factors, rather than by single combined factors as
predicted. In effect, the reverse-worded items measured something different, rather
than the actual construct under investigation. Reverse-worded items therefore are
potentially problematic.
The major reason for this study was to test the validity of the claimed
factor structure of the 8SQ instrument. Even though the 8SQ has been shown to be
useful in applied investigations, the fundamental question concerning the construct
validity of the subscale structure has not been addressed adequately. Despite
numerous studies by Cattell and his colleagues (cf. Cattell, 1973, 1979,
6
1981, 1983), separation of the eight mood-state dimensions has not yet been
verified by an independent investigation on large samples, different from those
initially utilized.
In view of these considerations, it seems germane to re-examine the item
composition of each 8SQ subscale, and to ascertain whether each subscale is
robust for a sample differing considerably from those employed in the initial
development of the instrument. Recent research with the POMS along similar lines
(Boyle, 1987b) revealed that the items, by and large, contributed to the subscales
as stipulated by the test authors. A similar demonstration for the 8SQ would
clearly add to the virtues of the instrument. The present paper reports such an
investigation into the item-structure characteristics of the 8SQ.
Method
Subjects and Procedure
The sample comprised a total of 1,111 Australian college students (926
females; 185 males) from several tertiary institutions located in the Melbourne
metropolitan area. The mean age of the sample was 22.23years (S.D. = 6.18
years). Participation in the study was voluntary, and subjects were free to either
participate or not participate. In fact, most subjects seemed quite willing to
respond to the 8SQ items, and virtually all completed the 96 items as requested.
Protocols with significant numbers of unanswered items were excluded from the
subsequent analyses. Most subjects were Australian-born and came from
essentially middle-class socioeconomic backgrounds. All subjects were fluent
readers of written English. The 8SQ was administered as part of the regular classes
in which the students normally participated. In order to facilitate the students'
7
motivation to respond to the 8SQ items, the instrument was administered in
cooperation with the usual instructor in each class. This task was readily accepted
by the students, who in most instances appeared to take the study seriously and to
respond to the 8SQ items conscientiously.
Data Analysis and Methodology
Item analyses for each subscale in the 8SQ were performed by subjecting
the 12 x 12 intercorrelation matrix in each instance to a principal-components
analysis, using the SPSSX (Edition 3) statistical package (SPSSX, 1988). For each
of the eight subscales, only the first unrotated component was extracted so that the
resulting loadings on the items represented the correlations between the individual
items and the component representing the subscale. Hence, it was possible to
determine the contribution of each item to its respective subscale. In accord with
accepted practice, only items with loadings greater than 0.30 were regarded as
contributing adequately to the various subscales.
The item loadings for each subscale having been determined, it was
appropriate to further investigate the relationship of the items in the 8SQ to the
various subscales by conducting exploratory item factor analyses of the
instrument. Given the large number of items involved (a total of 96 items), only
the best six items for each subscale (those items with the highest loadings) were
included in the subsequent factor analyses. An iterative, maximum-likelihood
procedure was employed, together with extraction of factors by the Scree test
(Hakstian, Rogers, & Cattell, 1982), and rotation to direct Oblimin simple
structure. In general, the factor-analytic methodology followed recommendations
of Cattell (1978), Gorsuch (1983), and Kline (1987). Both six-factor and seven-
8
factor solutions were derived in an attempt to verify the underlying dimensionality
of the 8SQ instrument, as described below.
Mood states are most often delineated using exploratory factor-analytic
procedures, wherein the observed variables (mood-state items) are linked to latent
constructs (subscales) as specified by the measurement model (see below).
According to Hinshaw (1987), the vast majority of studies reported in the
literature have employed orthogonal rotation methods (typically principal
components, or iterative principal factoring, with Varimax rotation). According to
Rowe and Rowe (1990), such approaches are problematic. Using exploratory
(unrestricted) methods of factor analysis results in arbitrary, data-driven factor
solutions which merely conflate theory. Orthogonal methods assume that the
factors are independent. However, there is considerable literature pertaining to
overlapping dimensions. Moreover, the Pearson product-moment correlation
coefficient is often computed from responses measured on dichotomous or Likert-
type ordinal scales. Yet, the underlying assumptions (normality of distribution and
homogeneity of variance) are usually ignored. By using product-moment estimates
for dichotomous or ordinal variables, instead of less-biased tetrachoric/polychoric
estimates, significant bias is introduced inadvertently into the subsequent analyses
(cf. Jöreskog & Sörbom, 1988). As Rowe and Rowe (1990) pointed out, failure to
recognize the measurement and distributional properties of response variables
amounts to "an undisciplined romp through a correlation matrix" (Hendrickson &
Jones, 1987, p. 105). Hence, claims about substantive knowledge often may be
prefaced largely on statistical artifact.
Accordingly, the corresponding matrix of polychoric correlation
coefficients was computed via PRELIS (Jöreskog & Sörbom, 1986), and
9
congeneric factor analyses via SIMPLIS (which uses a two-stage least squares
method of parameter estimation) - (Jöreskog & Sörbom, 1987), and LISREL
(using the maximum- likelihood estimation option)-(Jöreskog & Sörbom, 1989)
were undertaken for each 8SQ subscale with the aim of delineating more precisely
the importance of each of the items in the respective subscales. Finally, an overall
confirmatory factor analysis of the best 48 items for the 8SQ was carried out using
the LISREL statistical package.
Results and Discussion
Subscale Item Analyses
The item loadings for each of the eight subscales are presented in Table 1.
The item numbers correspond to those in the 8SQ instrument itself. Most items
designated by the test authors as contributing to the respective subscales have held
up, while only a small proportion of items have failed to exhibit adequate
loadings. In refining the item content of the 8SQ, those items in Table 1 with
inadequate loadings might need to be deleted from the instrument. However,
cross-validational replication of findings is required before any firm conclusions
are drawn regarding the adequacy of the respective items, for use in the Australian
context.
The 8SQ is comprised of 96 items which require about 20 minutes of
testing time. A shortening of the instrument, retaining only the best items for each
subscale, might result in a more efficient and useful measure of mood states.
Admittedly, mood states fluctuate momentarily in response to changes in stimulus
input and other influences, including even the task of responding to the items. It is
10
undesirable if administration of the instrument itself brings about changes in the
very dimensions which it is measuring. Table 1 suggests that at least three of the
items in both the Stress and Regression subscales are inadequate predictors of
these respective mood-state dimensions. Two items appear to be questionable
contributors to the Arousal subscale. On the other hand, for the Fatigue, Guilt, and
Extraversion subscales, all items have exhibited significant relationships with the
corresponding factors.
Item Factor Analyses
Examination of the item loadings for the eight separate subscales (see
Table I) enabled selection of the "best" six items in each instance (items exhibiting
the highest subscale loadings) for inclusion in the subsequent factor analyses of
the 8SQ instrument. The resulting 48 x 48 intercorrelation matrix served as the
starting point for the factor analyses. Examination of the latent roots for the
unrotated principal components suggested that no more than seven factors should
be extracted on the basis of the Scree test. Using a maximum-likelihood
procedure, convergence of communality estimates required five iterations of the
initial factor matrix, with extraction of seven factors. The Kaiser-Meyer-Olkin
(KMO) measure of sampling adequacy (an index of the observed versus partial
correlations) was 0.976, indicating the correlations between variables were
appropriate for an exploratory factor analysis to be conducted. The KMO is
defined algebraically in Norušis (1985, p. 129). In addition, Bartlett's Test of
Sphericity (see Norušis, p. 128) was 28815.218 (P<.001), indicating that the
correlation matrix was not an identity matrix, and therefore that it was suitable for
subsequent factor analysis. The direct Oblimin factor-pattern solution converged
11
Table 1
Item Loadings for Each 8SQ Subscale
(N = l,lll)
Item Loading Item Loading Item Loading Item Loading Item Loading
Anxiety
1
-.60
9 .76
17
-.24
-
25
-.47
33 .64
41
-.62
49 .70
57
.43
65
-.77
73
-.76
81 .67
89 .76
Stress
2 .66
10 -.15
18
.64
26 .54
34 -.63
42
-.77
50
.42
58
.22
66
.21
74 .46
82
-.44
90
-.45
Depression
3 .70
11
.08
19 -.58
27 .50
35
.55
43
-.49
51
-.72
59
-.51
67 .62
75
.55
83
-.67
91 .74
Regression
4 .46
12
.01
20 .54
28 .02
-
36
.65
44 -.30
52
.61
60
-.58
68 -.53
76
-.56
84 .60
92
-.22
-
Guilt
6
.45
14 -.33
22 .59
30 .56
38 -.44
46 .48
54 .63
62 -.60
70 .71
78 -.71
86
-.62
94
-.70
Extraversion
7
-.32
15 .67
23 .51
31 .51
39 .60
47 -.37
55 -.65
63 -.70
71 -.41
79 -.58
87
.34
95
.60
Arousal
8
-.44
16
.11
24 .36
32 .60
40 .65
48 -.25
56 -.68
64 -.32
72 .74
80 .48
88
-.65
96
.39
12
in 73 iterations, suggesting a somewhat unstable factor resolution (the smaller the
number of iterations required, the more reliable is the solution). With the SPSSX 6
(delta) shift parameter set at zero, the ±.10 hyperplane count for the maximum-
likelihood solution was 53.3% (cf. Cattell, 1978; Gorsuch, 1983), indicating only
moderate approximation to simple structure of the final rotated solution. Variation
of the 6 shift parameter enabled maximization of the hyperplane count with 6 = -
0.2, wherein the degree of obliquity of the factors was reduced slightly (± .10
hyperplane count of 54.2%). This factor-pattern solution is presented in Table 2.
Table
2
Oblique
Seven-Factor Pattern Solution
Factor Number
8SQ Item
No.
Anxiety
2
3
4
5
6
7
h2
09
.37
-.04
.33
.01
.14
.06
.11
.58
49
.22
-.16
.20
.04
.09
.20
.19
.50
65
-.56
-.01
-.13
.17
-.09
-.08
-.06
.63
73
-.51
-.01
-.08
.24
-.20
-.01
-.12
.67
81
.44
-.16
.01
.03
.12
.10
.12
.48
89
.30
-.01
.36
-.04
.07
.02
.29
.63
Stress
02
-.09
.07
.68
-.03
.09
.09
.14
.55
18
-.03
-.01
.66
-.05
-.01
.05
.08
.48
26
.12
-.09
.47
-.02
-.01
-.02
-.05
.29
34
-.52
.05
-.19
.10
.07
-.17
.00
.54
42
-.19
.03
-.51
.10
-.01
-.08
-.17
.62
74
.20
-.04
.40
.02
.06
-.06
-.09
.25
Depression
03
-.14
-.09
-.13
.26
-.38
.02
-.22
.54
19
.07
-.09
.24
.02
.11
.12
.31
.40
51
.09
-.10
.11
.08
.33
.18
.34
.58
67
-.02
-.07
-.03
.13
-.09
-.08
-.65
.60
83
.30
-.20
.05
.08
.20
.18
.15
.52
91
-.16
.10
-.09
.35
-.38
.03
-.10
.62
Regression
20
-.22
.13
.02
.10.
-.35
-.12
.06
.40
36
-.04
.28
-.11
.35
-.01
-.14
-.16
.53
52
-.14
.03
-.02
.09
.03
-.50
-.10
.46
60
.08
.15
.04
.08
.09
.43
.10
.40
76
.06
-.08
.31
.03
.04
.07
.48
.55
84
-.09
.15
.03
.35
.04
-.23
-.12
.40
13
Fatigue
13
-.08
.61
.07
.09
-.12
-.10
.03
.59
21
.03
-.67
.14
-.08
.08
.OS
-.07
.65
29
.01
.37
-.03
.33
-.27
-.07
-.08
.65
53
.03
-.45
.07
-.20
-.08
.13
-.07
.46
85
-.04
.40
.00
.45
.05
-.07
-.03
.53
93
.13
-.52
.08
-.26
.05
.01
.02
.60
Guilt
54
.34
-.10
.02
.22
-.03
.19
.27
.41
62
-.24
-.06
.01
.07
-.01
-.21
-.26
.33
.
70
.27
-.12
-.02
.27
.18
.18
.33
.52
78
-.19
-.05
.02
.19
-.10
-.12
-.49
.61
86
-.18
-.02
-.13
.14
.12
-.15
-.41
.45
94
-.24
-.07
-.06
.12
-.
11
-.04
-.52
.61
Extraversion
15
.01
.02
-.01
.09
-.70
-.04
.01
.57
39
.03
.04
-.05
.46
-.29
-.11
.05
.47
55
.06
-.01
.04
.08
.36
.48
-.06
.50
63
.07
-.04
.11
-.08
.38
.28
-.06
.46
79
-.04
-.17
.03
-.18
.41
.01
.12
.41
95
-.20
-.02
.02
.29
-.16
-.20
-.10
.43
Arousal
32
.07
-.58
.10
.01
.10
.12
-.01
.55
40
.08
-.18
.07
-.03
.06
.41
.14
.50
56
.02
-.02
.00
.29
-.04
-.63
.02
.57
72
-.01
-.38
-.07
-.05
.16
.35
.12
.57
80
.04
-.30
-.07
.03
.22
.06
.18
.29
88
-.08
.06
-.03
.51
-.18
-.08
-.13
.57
Latent Root: 18.27 3.15 1.85 1.54 1.20 1.01
.96
Percent
Variance:
38.1 6.6 3.9 3.2 2.5 2.1
2.0
Hyperplane
Count
.10): 25 29 30 27 25 24
22
Notes. Factor
loadings
are
reported
to two decimal places
only.
Factor
loadings
>
.30 are shown in
bold.
14
Factor 1 (38.1% of the unrotated principal-components variance)
represented the 8SQ dimension labeled Anxiety. No fewer than five of the six
items exhibited significant (>.30) loadings with respect to this dimension (Items 9,
65, 73, 81, and 89, respectively). In addition, one Stress item (Item 34), one
Depression item (Item 83), and one Guilt item (Item 54) contributed significantly.
Curran (1974) reported the results of an exploratory factor analysis of item parcels
(each comprising four 8SQ items from Forms A and B together), using a sample of
155 American university students as subjects. Curran provided strong evidence for
the construct validity of the Anxiety subscale, with all six item parcels (comprised
of known marker variables) exhibiting significant factor loadings as predicted.
Accordingly, there seems little doubt as to the validity of the Anxiety dimension,
although the present findings suggest some refinement of the actual items in the
subscale may be required.
As for Factor 2 (6.6% of the unrotated component variance), all six of the
Fatigue items (Items 13, 21, 29, 53, 85, and 93) exhibited significant loadings as
predicted, along with three of the Arousal items (Items 32, 72, and 80). This factor
supported the 8SQ Fatigue subscale as a discrete mood-state construct. It is
possible that the responses to the Fatigue items may have been influenced partly
by the time required for administration of the instrument, although typically this
involved only about 20 minutes, or so. Previously, Curran (1974) also had reported
strong factor support for the Fatigue subscale items. The fact that only three of the
Arousal items lined up on this factor suggests that the Arousal subscale needs
refinement.
Factor 3 (3.9% of unrotated component variance) loaded predominantly on
Stress items (with the exception of item 34), as well as on two of the Anxiety
15
items (Items 9 and 89), and one of the Regression items (Item 76). While strongly
supporting the Stress subscale as defined in the 8SQ, this factor also suggested
some association of stress and anxiety. Curran (1974) had reported that three of six
marker variables for Stress exhibited significant loadings on Anxiety. While
Curran obtained no significant loadings on the Stress factor, the present findings
support the validity of this subscale. Curran used a sample of only 155 subjects
(three subjects per variable), whereas the present analysis was based on a much
larger sample, providing a firmer base on which to investigate the validity of the
8SQ subscale structure.
Seven items contributed significantly to Factor 4 (which accounted for
3.2% of the unrotated component variance). Perusal of the content of these
particular items (Items 29, 36, 39, 84, 35, 88, and 91) suggests that this factor
represented a specific mood-state dimension of Adventurousness, not delimited as
such in the existing 8SQ subscale structure. This factor may represent the
sensation-seeking dimension (Zuckerman, 1979). The 8SQ may benefit by
addition of items intended specifically to measure the sensation-seeking
emotional/mood-state dimension. This would necessitate inclusion of an additional
subscale into the structure of the instrument, thereby providing a more
comprehensive measurement of the mood-state domain.
Factor 5 (accounting for 2.5% of the unrotated component variance) clearly
loaded on the Extraversion subscale items (only Item 95 failed to exhibit a
significant loading). Three of the Depression items (Items 3, 51, and 91) also
contributed to this factor, along with one Regression item (Item 20). The "non-
Extraversion" items which contributed significantly to this factor may need to be
16
redefined as Extraversion items. Even though the eight states measured in the
8SQ are conceptually distinct, the particular items allocated to each subscale may
need some revision.
As for Factor 6 (2.1% of the unrotated component variance), significant
factor loadings occurred for three Arousal items (Items 40, 56, and 72), two of the
Regression items (Items 52 and 60), and one Extraversion item (Item 55). The
overall interpretation of this factor suggests confusion and sluggish intellectual/
cognitive functioning. This factor seems to represent the negative pole of the 8SQ
Arousal dimension. The items defining the Regression subscale failed to load
together as a single entity, but instead were scattered among five of the seven
extracted factors. The Regression subscale is not supported by the present findings
as a discrete factorial construct. Curran (1974) reported that only one of six marker
variables was loaded significantly (>.30) on the Regression dimension.
Correspondingly, his marker variables exhibited significant loadings which were
scattered widely across the remaining mood-state factors in his analysis. Hence,
the factor analytic support for the 8SQ Regression subscale seems uncertain. The
8SQ would probably be a more efficient instrument with removal of the
Regression subscale.
Factor 7 (2.0% of unrotated component variance) contrasted three of the
Depression items (Items 19, 51, and 67) with four of the Guilt items (Items 70, 78,
86, and 94), thereby suggesting a Guilt/Depression interpretation. This factor
loaded significantly on one Regression item (Item 76), suggesting that Guilt/
Depression represents a distinct mood-state dimension. The Depression items were
evenly divided between factors 5, and 7, in accord with reports of the complexity
of depressive mood states (see Boyle, 1985b, for a review). A number of
17
8SQ items contributed substantially to more than one of the eight subscale
dimensions, thereby inflating the subscale intercorrelations, and also raising
doubts about the purported subscale structure of the instrument.
Subscale intercorrelations tend to be rather high in the psychometric mood-
state area. Not only is the 8SQ hampered by high subscale correlations (Cattell &
Curran, 1976, p. 16), but also other multidimensional instruments such as the
Multiple Affect Adjective Check list (MAACL-R; Zuckerman & Lubin, 1985), the
POMS (McNair et al., 1981), and the DES-IV (Izard et al., 1974) demonstrate this
difficulty. Such a finding is not unexpected, as mood states tend to fluctuate
concurrently, in response to provocative stimuli. As Cattell (1978, p.163) stated,
"Researchers in the field of psychological states have repeatedly found decidedly
larger correlations among primaries in state than in trait factors, due to time-
coordinated ambient situation changes.... the dynamics of situations often cause
them to occur together."
In the present study, the intercorrelations for the seven extracted and
rotated factors generally were moderate, rather than being excessively high (Table
3). However, in view of the apparent interdependence of the seven derived factors,
obliquity of the final factor solution was reduced somewhat by use of the SPSSX 8
shift parameter, in an attempt to achieve a greater approximation to simple
structure. It might be argued that differences in the obtained factor-pattern solution
as compared with that defined by the 8SQ subscales were due partly to cross-
cultural influences (since Australian rather than North American subjects were
used). However, a similar investigation of the POMS factor structure, using
Australian college students as subjects (Boyle, 1987b), supported the groupings of
items designated as contributing significantly to each factor.
18
Table
3
Factor Pattern
Intercorrelations
Factor No. 1 2 3 4 5 6
7
1
2
-.30
3
.42
-.18
4
-.22
.34
-.17
5
.36
-.38
.22
.38
6
.46
-.41
.20
-.31
.43
7
.51
-.16
.30
-.21
.31
.44
Notes.
Correlations
are shown to two decimal places
only.
All correlations are statistically significant, although only
those
which are not trivial (.30) are shown in bold.
The present attempt to cross-validate the factor structure of the 8SQ
instrument has resulted in only partial replication. Good support for the subscales
labelled Anxiety, Stress, Fatigue, and Extraversion was forthcoming, while the
dimension labelled Arousal combined with Fatigue and with Regression.
Depression and Guilt emerged as a single dimension. A number of the 8SQ items
contributed significantly to more than one subscale, thereby making the separation
of some of the factors unnecessarily problematic. While the Scree test suggested
seven separate factors, examination of the percentage variance accounted for by
each factor, together with the significant intercorrelations observed between the
factors, suggested a smaller number of factors. To test this possibility, and the
appropriateness of removing the Regression subscale (since it failed to emerge
from the seven-factor solution), a six-factor solution was also taken out.
19
The six-factor solution (Table 4) also involved an iterative maximum-likelihood
method of analysis requiring five iterations of the initial factor matrix. The direct
Oblimin factor pattern converged after only 47 iterations as compared with the 73
iterations required for the seven-factor solution. The total ± .10 hyperplane count
associated with the six-factor solution, with the delta shift parameter set at zero,
was 45.8%, suggesting a rather unsatisfactory approximation to simple structure
(variation of the SPSSX o shift parameter to reduce the obliquity of the derived
factors did not result in a greater approximation to simple structure criteria).
Ideally, the ± .10 hyperplane count should be at least 75% or better (Kline, 1979;
Boyle, 1988).
Table
4
Oblique Six-Factor
Pattern
Solution
Factor
Number
8SQ Item
No.
Anxiety
2
3
4
5
6
h2
09
.34
.00
.38
.14
.13
.02
.58
49
.17
-.18
.24
.25
.07
.12
.50
65
-.59
.03
-.14
-.02
-.13
-.05
.64
73
-.55
.02
-.11
.04
-.26
-.10
.68
81
.41
-.14
.04
.22
.10
.02
.48
89
Stress
.27
.02
.44
.11
.06
.20
.63
02
-.13
.06
.73
.00
.11
.12
.54
18
-.07
-.05
.70
-.03
-.02
.06
.47
26
.09
-.09
.50
-.03
-.04
-.11
.29
34
-.52
.14
-.19
-.07
.07
-.03
.53
42
-.17
.08
-.57
-.02
-.02
-.14
.61
74
.15
.00
.43
-.01
.03
-.17
.25
Depression
03
-.17
-.08
-.18
.08
-.49
-.19
.53
19
.03
-.08
.30
.19
.10
.23
.40
51
.04
-.04
.17
.31
.33
.22
.58
67
-.06
-.07
-.13
-.12
-.13
-.59
.58
83
.25
-.18
.08
.29
.17
.05
.52
91
-.18
.17
-.13
.14
-.47
-.11
.62
Regression
20
-.22
.16
.03
-.07
-.40
.07
.40
20
36
-.07
.49
-.13
.10
-.05
-.25
.53
52
-.16
.23
.02
-.21
-.05
-.25
.40
60
.06
-.25
.02
.33
.10
.13
.38
76
.02
-.04
.41
.20
.00
.35
.54
84
-.14
.40
.05
.08
-.04
-.28
.39
Fatigue
13
-.04
.71
.07
-.12
-.08
.11
.58
21
-.03
-.77
.15
.08
.01
-.17
.64
29
.01
.52
-.04
.08
-.33
-.09
.64
53
.01
-.62
.06
-.01
.08
-.05
.47
85
-.08
.67
.02
.22
.01
-.16
.54
93
.12
-.66
.10
-.06
.03
-.01
.59
Table
4
(Continued)
Guilt
54
.28
-.04
.06
.39
-.11
.15
.41
62
-.27
.01
.00
-.14
-.05
-.29
.33
70
.20
.00
.04
.46
.11
.16
.51
78
-.23
-.01
-.04
-.09
-.16
-.49
.60
86
-.19
.06
-.19
-.08
.10
-.45
.46
94
-.26
-.10
-.14
-.
11
-.14
-.45
.59
Extraversion
15
.01
-.04
-.02
-.05
-.80
.09
.57
39
-.03
.25
-.03
.26
-.44
-.11
.46
55
.05
-.11
-.01
.29
.42
.01
.44
63
.06
-.13
.09
..
12
.46
.00
.44
79
-.05
-.19
.06
.00
.47
.07
.40
95
-.25
.14
.03
.04
-.26
-.22
.42
Arousal
32
.01
-.64
.12
.19
.02
-.12
.55
40
.07
-.33
.06
.25
.09
.20
.48
56
-.06
.32
.09
-.06
-.20
-.26
.41
72
-.03
-.52
-.08
.25
.17
.14
.57
80
.00
-.27
-.03
.20
.19
.06
.27
88
-.15
.27
-.03
.25
-.32
-.28
.58
Latent
Root: 18.27 3.15 1.85 1.54 1.20
1.01
Percent
Variance:
38.1 6.6 3.9 3.2 2.5
2.1
Hyperplane
Count(±
.10):
23
21
26
22
23
17
Notes. Factor
loadings
are
reported
to two
decimal
places
only.
Factor
loadings.30
are shown in
bold.
21
Factor 1 again represented the 8SQ Anxiety dimension, but this time both
Items 49 and 89 failed to exhibit significant (2': .30) factor loadings. However,
Items 83 and 54 (Depression and Guilt items, respectively) no longer were
significantly associated with the Anxiety factor. Factor 2 again supported the SSQ
Fatigue subscale, with all six items contributing significantly to the dimension. In
addition, four of the Arousal subscale items (Items 32, 40, 56, and 72) exhibited
significant loadings, providing further support for collapsing the Fatigue and
Arousal subscales into a single scale. Arousal and Fatigue seem to represent
extremes on a bipolar dimension. Factor 3 clearly represented the SSQ Stress
dimension, and again only Item 34 failed to exhibit a significant loading.
However, a Depression item (Item 19) now loaded significantly. Factor 4
comprised a few scattered significant loadings suggestive of general negative
affect. It did not resemble the fourth factor from the seven-factor solution. Factor
5 again suggested an Adventurousness interpretation, while Factor 6 partially
represented the Guilt dimension. The factor intercorrelations are presented in
Table 5, suggesting a high level of interdependence between the six factors.
Evidently, the seven-factor solution is not particularly challenged by the six- factor
solution, and the latter would not appear to replicate better the findings of either
Curran (1974) or Curran and Cattell (1976).
22
Table
5
Factor Pattern
Intercorrelations
Factor
No.
1
1
2
3
4
5
6
2
-.45
3
.53
-.31
.36
-.22
.24
5
.46
-.62
.33
.23
6
.49
-.31
.30
.25
.42
Notes.
Correlations
are shown to two decimal places
only.
Non-trivial correlations (.30)
are shown in
bold.
Congeneric and Confirmatory Factor Analyses
As congeneric and confirmatory factor analyses via SIMPLIS and LISREL
(Jöreskog & Sörbom, 1986, 1987, 1989) had not been reported, and given the
uncertainty surrounding the exploratory factor analytic results above, LISREL
analyses of the 8SQ item intercorrelations were also carried out. Both congeneric
and confirmatory factor analytic methods enable statistical model testing, unlike
the traditional data-driven, exploratory factor analytic approaches (cf. Anderson,
1987; Bentler, 1985; Long, 1983; McDonald, 1980; Muthén, 1984). Separate
PRELIS runs (Jöreskog & Sörbom, 1988) were carried out for subsets of 48 items
(due to practical limitations of the computer hardware it was not possible to
conduct a confirmatory factor analysis on the intercorrelations of all 96 8SQ items
simultaneously). Use of the PRELIS program is particularly important if the
variables are skewed or kurtotic. Given that the item responses were measured on
23
a four-point Likert-type scale, computation of Pearson product- moment
correlation coefficients was not justified, as such estimates have been shown to be
significantly biased when the variables are ordinal (Jöreskog & Sörbom, 1989).
Use of PRELIS enabled the computation of polychoric correlation coefficients.
Had product-moment correlations been used, the resulting parameter estimates, as
well as the various goodness of fit indices (Chi-Square or x2 , Goodness of Fit
Index or GFI, Adjusted Goodness of Fit Index or AGFI, and Root Mean square
Residual or RMR)1would have been significantly biased (Jöreskog & Sörbom,
1986; Olsson, 1979; Poon & Lee, 1987). The resulting 48 x 48 intercorrelation
matrices for each respective 8SQ subset of 48 items served as the point of
departure for the subsequent confirmatory factor analyses (see below), wherein the
measurement model is expressed algebraically as:
x=A
x
ξ + δ
such that the observed variables/8SQ items are represented by the x's, and the
latent variables are represented by the g's, respectively. The vector of measurement
errors in the x variables is represented by o (cf. Cuttance & Ecob, 1987). The
corresponding equation for the covariance matrices reported below (Tables 8, 10,
and 12), is given as:
Σ=Λ
Φ
Λ’ +Ɵ
δ
where Λ represents the matrix of loadings for the latent traits (8SQ subscales), Φ
represents the matrix of covariances between the latent traits, and Ɵ represents
the matrix of error variances and covariances among the x variables (8SQ items).
A similar procedure was employed using a combination of PRELIS and LISREL
in undertaking separate congeneric factor analyses of the best six items for each of
24
the 8SQ subscales, as determined from the SIMPLIS standardized regression
equations. Together with the corresponding maximum-likelihood goodness of fit
estimates, the congeneric factor analytic results are shown in Table 6 for each 8SQ
subscale, respectively.
Table
6
Congeneric Factor Models for 8SQ
Subscales
Subscales
(X
Variables)
Standardized (AJ LISREL Estimates
(ML)
Parameter Standard Significance
R
2
Value Error of
T-
V
alue
Anxiet
y
QOl
(
1
)
0.63
0.00
<.01
0.40
Q17
0.34
0.06
<.01
0.12
Q25
0.52
0.06
<.01
0.27
Q33
-0.67
0.07
<.01
0.45
Q41
0.66
0.07
<.01
0.44
Q57
-0.47
0.06
<.01
0.23
Coefficient of Determination for X Variables =
0.742
Goodness of Fit Statistics: GFI = 0.983; AGFI = 0.961; RMR =
0.033
Stress
(
Q02
2
)
0.77
0.00
<.01
0.60
Q18
0.73
0.04
<.01
0.53
Q26
0.57
0.04
<.01
0.33
Q34
-0.61
0.04
<.01
0.37
Q42
-0.82
0.04
<.01
0.67
Q74
0.50
0.04
<.01
0.25
Coefficient of Determination for X Variables
=
0.835
Goodness of Fit Statistics: GFI = 0.953; AGFI = 0.890; RMR =
0.045
Depressio
Qll
n (
3
)
0.23
0.00
<.01
0.05
Q27
-0.54
0.39
<.05
0.29
Q35
-0.62
0.43
<.05
0.38
Q43
0.56
0.40
<.05
0.32
Q59
0.50
0.36
<.05
0.25
Q75
-0.68
0.47
<.05
0.46
Coefficient of Determination for X Variables
=
0.715
Goodness of Fit Statistics: GFI = 0.982; AGFI = 0.957; RMR =
0.039
Regression
( )
Q20 0.58 0.00 <.01
0.34
Q36 0.69 0.07 <.01
0.48
25
Q52 0.68 0.07 <.01
0.46
Q60 -0.61 0.07 <.01
0.37
Q76 -0.60 0.07 <.01
0.36
Q84 0.63 0.07 <.01
0.40
Coefficient of Determination for X Variables =
0.793
Goodness of Fit Statistics: GF!
=
0.983; AGFI
=
0.960; RMR =
0.030
As is evident from the congeneric factor results, the various goodness of fit
indices for each of the eight subscales were all highly supportive of the construct
validity of the respective 8SQ dimensions. However, this result was obtained only
by exclusion of the least-adequate six items for each subscale. The congeneric
factor results and associated goodness of fit estimates were less than satisfactory
when all 12 items for each subscale were included in the analyses. It would seem
desirable, therefore, that the item content of the 8SQ instrument be revised by
eliminating those items which account for the least amount of shared variance
associated with the respective subscales. Concomitantly, it might be necessary to
include new items, in view of the congeneric factor results.
The present findings suggest that the existing item content of the 8SQ
instrument requires modification. Separate maximum-likelihood confirmatory
factor analyses were carried out on the sets of 48 items, consisting of the best six
items from each subscale, as determined initially from the principal-component
analyses reported in Table 1, and subsequently from the standardized regression
coefficients produced from the congeneric factor analyses for each subscale. In
addition, for purposes of comparison, a confirmatory factor analysis was also
undertaken on the 48least- adequate items, as determined from the standardized
regression equations for each subscale.
26
Using the best 48 items as shown in Table 1 for the principal-component
analyses on each 8SQ subscale (see Table 7), the GFI was found to be 0.623, the
AGFI was 0.578, and the RMR was 0.214, indicating an inadequate fit of the
empirical data to the purported eight-factor model of the 8SQ.
Table
7
Confirmatory Factor Analysis of Best 48
Items
(from the principal components scale
analyses)
8SQ
Subscales
Standardized LISREL Estimates (ML)
Factor
No.
1
2
3
4
5
7
8
R2
Anxiety (
1
)
Q09
Q49
Q65
Q73
Q81
Q89
Stress (
2
)
0.02
-0.78
0.30
-0.69
-0.75
-0.81
0.02
0.45
0.08
0.43
0.51
0.59
Q02
0.76
0.43
Q18
0.63
0.36
Q26
0.51
0.23
Q34
-0.78
0.54
Q42
-0.86
0.67
Q74
-0.85
0.65
54
27
Depression
(
3
)
Q03
Ql9
Q51
Q67
Q83
Q91
Regression
( )
Q20
Q36
Q52
Q60
Q76
Q84
Fatigue
( 5
)
Q13
Q21
Q29
Q53
Q85
Q93
Guilt
( )
Q54
Q62
Q70
Q78
Q86
Q94
Extraversion
(
7
)
Ql5
Q39
Q55
Q63
Q79
Q95
Arousal
(
8
)
Q32
Q40
Q56
Q72
Q80
Q88
Table 7
(Continued)
0.02
0.67
0.79
0.23
0.82
-0.79
0.69
0.78
0.66
-0.63
0.65
0.67
0.01
0.79
-0.86
0.75
-0.79
0.85
0.01
0.46
0.58
-0.71
0.65
0.76
0.01
-0.58
0.66
-0.62
-0.82
-0.72
0.01
-0.73
0.71
-0.42
-0.65
0.77
0.02
0.41
0.56
0.05
0.60
0.56
0.39
0.55
0.40
0.36
0.39
0.40
0.01
0.58
0.69
0.52
0.58
0.67
0.02
0.18
0.30
0.46
0.37
0.52
0.01
0.31
0.39
0.35
0.61
0.47
0.01
0.49
0.46
0.16
0.38
0.54
28
Notes. GFI = 0.623; AGFI = 0.578; RMR = 0.214
Factor loadings are shown to two decimal places only.
Perusal of communality estimates indicates that Items 3, 9, 13, 15, 26, 32, 54, 62,
65, and 67 account for the least amount of common factor variance for the
respective 8SQ subscales.
All A, factor loadings (except for Items 3, 9, 13, 15, 32, 54) are statistically
significant at the 1% level or better, using univariate two-tailed tests (cf. Boyle &
Langley, 1989). As can be seen from Table 7, use of the principal-components
analyses to select the "best" six items per subscale has not been particularly
successful, as several of the selected items have very low communalities (<.30)
associated with them. Moreover, a number of the factor loadings are trivial,
suggesting that the 8SQ instrument needs considerable psychometric improvement
at the item level, for optimal use in the Australian context. The covariances
obtained for the eight factors are shown in Table 8. It is clear that the subscales are
very highly intercorrelated, suggesting that a reduction in the number of 8SQ
mood-state dimensions would seem desirable.
For the confirmatory factor analysis of the best 48 8SQ items (as
determined from the two-stage least squares standardized regression equations)
(Table 9), the GFI was found to be 0.738, the AGFI was 0.707, while the RMR
was now 0.095. Cuttance (1987, p. 260) has pointed out that "models with an
AGFI of less than 0.8 are inadequate ... most acceptable models would appear to
have an AGFI index of greater than 0.9." Accordingly, even though these
goodness of fit indicators represented an improvement, they still suggested the
inadequacy of the overall eight-factor model proposed by Curran and Cattell
29
(1976) for the 8SQ instrument. The corresponding phi matrix of covariances for
these items is presented in Table 10. Again, the 8SQ subscales are generally quite
highly intercorrelated, suggesting that there is significant item redundancy (cf.
Boyle, 1985b). This finding is further evidence that the item composition of the
8SQ subscales needs revision, at least for use in the Australian context.
Table
8
Covariances
between
Exogenous
Latent Traits
(<I>
Matrix)
8SQ Subscale AX ST DE RG FA GI EX
AR
AX
ST
-0.95
DE
-1.00
0.90
RG
FA
0.97
-0.80
-0.83
0.68
-0.97
0.83
-0.93
GI
1.00
-0.95
-1.00
0.99
-0.82
EX
-0.92
0.85
0.97
-0.98
0.77
-1.00
AR
0.91
-0.79
-0.97
1.00
-0.90
0.95
1.00
Notes. Covariances are shown to two decimal places only.
AX=
Anxiety;
ST =Stress; DE= Depression; RG =Regression; FA
=Fatigue;
Gl =Guilt; EX= Extraversion; AR
=Arousal
30
-0.60
Table
9
Confirmatory Factor Analysis of Best 48
Items
(from the standardized regression
equations)
Standardized
LISREL Estimates
(ML)
Factor No.
8SQ Subscales
1;1
1;2
1;3
Ss
1;7
1;8
Anxiety
(
/;
1
)
QOl 0.67 0.65
Q17 0.23 0.04
Q25 0.51 0.23
Q33 -0.66 0.36
Q41 0.70 0.44
Q57 -0.43 0.18
Stress
(S
2
)
Q02 0.73 0.66
Q18 0.66 0.50
Q26 0.52 0.30
Q34 -0.71 0.39
Q42 -0.86 0.66
Q74 0.46 0.24
Depression
(
/;
3
)
Regression
( )
Q20 0.63 0.85
Q36 0.71 0.50
Q52 0.63 0.28
Q60 -0.59 0.28
Q76 -0.62 0.13
Q84 0.60 0.30
Fatigue
(
/;
5
)
Q13
0.78
0.75
Q21
-0.79
0.55
Q29
0.84
0.81
Q53
-0.73
0.48
Q85
0.74
0.48
Q93
-0.81
0.61
Guilt( )
Q06
0.67
0.68
Q14
-0.45
0.17
Q22
0.66
0.38
Q30
0.54
0.23
Q38
-0.44
0.16
Q46
0.62
0.35
57
31
MULTIVARIATE
EXPERIMENTAL CLINICAL RESEARCH
Table 9
(Continued)
Extraversion
(
7
)
Q07
O.Ql
0.21
Ql5
0.69
0.13
Q23
0.52
0.10
Q31
0.59
0.11
Q71
-0.42
0.07
Q79
-0.70
0.14
Arousal (
8
)
Q08
Q32
Q40
Q56
Q80
Q88
O.Ql
0.69
0.69
-0.65
0.50
-0.70
0.18
0.11
0.14
0.10
O.Q7
0.06
32
Notes. GFI = 0.738; AGFI = 0.707; RMR = 0.095
Factor loadings are shown to two decimal
places only.
Perusal of communality estimates indicate that Items 7, 14, 15, 17, 23, 24, 25, 27, 30,
31, 35, 38, 43, 52,
57, 60, 71, 75, 76, and 79 account for little of the common factor variance for the
respective 8SQ subscales. All A, factor loadings (except for Items 7, 8 and II) are
statistically significant at better than the 1% level, using univariate two-tailed tests.
Table 10
Covariances between Exogenous Latent traits
(<!>
Matrix)
8SQ
Subscale
AX
ST
-0.96
DE -0.85
0.68
RG 1.00 -0.79
-1.00
FA 0.68 -0.55 -0.96
0.89
GI -0.98 0.77 0.81 -0.93
-0.63
EX 0.67 -0.54 -0.96 0.86 0.82 -0.60
AR -0.88 0.67 1.00 -1.00 -0.96 0.83
-0.89
Notes. Covariances are shown to two decimal places only.
AX=
Anxiety;
ST =Stress; DE= Depression: RG =Regression; FA= Fatigue; Gl =Guilt; EX= Extraversion:
AR
=Arousal
The goodness of fit estimates for the confirmatory factor analysis of the
least-adequate 48 items (Table 11) were as follows: GFI (0.723); AGFI (0.691);
and RMR (0.108), indicating again, a poor fit to the 8SQ model. The number of
iterations for the maximum-likelihood analysis exceeded 250 (as was also the case
for the confirmatory factor analyses reported in Tables 7 and 11), thereby
indicating the extensive "measurement noise" associated with these subsets of
8SQ items. Even so, these goodness of fit estimates were slightly better than those
for the analysis based on the principal components (from Table 1). Hence, the
33
combined use of PRELIS and LISREL enabled a more accurate assessment of the
adequacy and construct validity of item structure of the 8SQ instrument. As for the
matrix of covariances (Table 12), it is evident that there is multicollinearity (cf.
Pedhazur, 1982) associated with this particular subset of 48 items, thereby
pointing to the inadequacy of these items, and to the possible need for their
removal from the existing instrument.
Table
11
Confirmatory Factor Analysis of Worst 48
Items
(from standardized regression
equations)
8SQ
Subscales
Standardized LISREL Estimates
(ML)
Factor
No.
3
!;.;
5
Anxiety (
1
)
QOl
Q17
Q25
Q33
Q41
Q57
Stress
( :J
0.59
0.35
0.25
0.06
0.54
0.29
-0.71
0.51
0.67
0.45
-0.46
0.21
Q10
0.01
0.00
Q50
0.24
0.06
Q58
0.28
0.08
Q66
0.21
0.04
Q82
-0.67
0.45
Q90
-0.57
0.32
Depression
(
3
)
Q11
0.01
0.00
Q27
-0.59
0.35
Q35
-0.52
0.26
Q43
0.63
0.40
Q59
0.54
0.29
Q75
-0.59
0.35
59
34
MULTIVARIATE
EXPERIMENTAL CLINICAL RESEARCH
Regression
(/;,.)
Q04
Q12
Q28
Q44
Q68
Q92
Fatigue
(/;
5
)
QOS
Q37
Q45
Q61
Q69
Q77
Guilt (/;;)
Q06
Q14
Q22
Q30
Q38
Q46
Extraversion
(/;
7
)
Table 11
(Continued)
0.44
0.00
0.03
-0.31
-0.56
-0.21
0.01
0.64
-0.74
0.52
0.52
-0.75
0.67
-0.45
0.65
0.52
-0.44
0.64
0.20
0.00
0.00
0.09
0.31
0.04
0.01
0.41
0.54
0.27
0.27
0.57
0.44
0.21
0.42
0.27
0.20
0.41
35
Notes. GFI
=
0.723; AGFI
=
0.691; RMR
=
0.108
Factor loadings are shown to two decimal places only.
Perusal of the communality estimates indicates that only one-third of the subscale items (Items I, 6, 22,
27,
31, 33, 37, 41, 43, 45, 46, 68, 75, 77, 82, and 90) have communalities which are non-trivial (<:.30).
All factor loadings (except for Items 5, 10, 11, 12, and 28) are statistically significant at
the 1% level or better, using univariate two-tailed tests.
Table
12
Covariances between Exogenous Latent Traits
(<I>
Matrix)
8SQ Subscale AX ST DE RG FA GI EX
AR
AX
ST
-1.00
DE -0.84
1.00
RG 1.00 -1.00
-1.00
FA 0.84 -0.98 -0.98 1.00
GI -0.99 1.00 0.81 -0.95
-0.84
EX 0.69 -0.88 -1.00 0.89 0.83
-0.66
AR -0.91 1.00 1.00 -1.00 -1.00 0.71
-1.00
Notes. Covariances are shown to two decimal places only.
The multicollinearity among these 8SQ is clearly evident.
AX=
Anxiety;
ST =Stress; DE= Depression; RG
=Regression;
FA= Fatigue; GI
=Guilt;
EX= Extraversion; AR
=Arousal
36
Conclusions
Evidently, the 8SQ is potentially a useful mood-state instrument. However,
in view of the apparent factor complexity of several ofthe8SQ items (contributing
to more than one mood-state dimension), and given the apparent lack of construct
validity of at least half of the items, it would seem desirable to remove both
complex items and those with trivial (< .30) factor loadings from the 8SQ
instrument. An abbreviated version of the instrument (comprising at least 48
psychometrically sound items) should minimize effects on mood states brought
about solely through the process of responding to the items. While the exploratory
factor analysis (Table 7) provided partial support for the construct validity of the
8SQ subscale structure, and while the congeneric factor analyses for the best six
items in each subscale also provided somewhat encouraging GFI, AGFI, and RMR
estimates, the evidence from the confirmatory factor analyses based on subsets of
48 items each was somewhat discouraging for the eight-factor nomological model
proposed by Curran and Cattell (1976). It is evident from the obtained results that
the 8SQ instrument is affected by problems associated with multicollinearity.
Given the less-than-adequate confirmation of the eight-factor model, it may be
necessary to revise the structure of the instrument by reducing the number of
subscales. A shortened 8SQ would be more efficient psychometrically, enabling
quicker measurement of transitory mood states. The present findings suggest that a
reallocation of items to a number of the 8SQ subscales also may be needed. Such a
psychometrically refined version of the instrument should enable better research to
be undertaken within the mood-state area.
37
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Footnote
The GFI and AGFI indices are independent of sample size, whereas the Chi-Square is directly
affected by sample size, such that virtually all models are rejected when the sample size is large, as
in the present instance. The AGFI is the statistic of choice, together with the RMR (mean residual
variance-covariance resulting from comparison of the obtained vs. predicted covariance matrices).
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Structural Modeling by Example offers a comprehensive overview of the application of structural equation models in the social and behavioural sciences and in educational research. It is devoted in roughly equal proportions to substantive issues and to methodological ones. The substantive section comprises case studies of the use of these models in a number of disciplines. The authors emphasize the reasons for modeling by these methods, the processes involved in defining the model, and the interpretation of the results. Each substantive chapter includes an exemplary data set and formal model construction of give readers practice in setting up the models and interpreting the results. The methodological section comprises investigations of the behaviour of structural equation modeling methods under a number of conditions. The aim is to clarify the situations in which these methods can usefully be applied and the interpretations that can be made. Introductory and concluding chapters relate structural equation models to the mainstream statistical methods, regression and factor analysis, of which they are a synthesis and generalization, and place in perspective the current status, scope, and limitations of these models with reference to other methodological studies.
Chapter
Structural Modeling by Example offers a comprehensive overview of the application of structural equation models in the social and behavioural sciences and in educational research. It is devoted in roughly equal proportions to substantive issues and to methodological ones. The substantive section comprises case studies of the use of these models in a number of disciplines. The authors emphasize the reasons for modeling by these methods, the processes involved in defining the model, and the interpretation of the results. Each substantive chapter includes an exemplary data set and formal model construction of give readers practice in setting up the models and interpreting the results. The methodological section comprises investigations of the behaviour of structural equation modeling methods under a number of conditions. The aim is to clarify the situations in which these methods can usefully be applied and the interpretations that can be made. Introductory and concluding chapters relate structural equation models to the mainstream statistical methods, regression and factor analysis, of which they are a synthesis and generalization, and place in perspective the current status, scope, and limitations of these models with reference to other methodological studies.
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