124
JOURNAL OF MARKETING RESEARCH, FEBRUARY 1987
HQI The total effects of the use of reward and coercive
power sources on power and dealer satisfaction will
be no different from the direct effects.
Figure 2
FULL SECOND-ORDER MODEL
1
I
15'it«m
Scale
Ex perl
Scale
RelerenI
Scale
Uj
LegHmato
Scale
6-Item
Scale
lO-Hem
Scale
5-llem
Scale
\E3
among these alternative hypotheses is a matter of justification on the basis of theory, because any of the three
results in exactly the same model fit.'' The point is that
only when both power and satisfaction are included in
the same model can an analysis of their relationship be
performed. This is also true for the model in Figure 1,
which utilizes the three indicants of "qualitative power
sources" as individual endogenous constructs.
INTERPRETATIONS
Other issues involve the methods and data used by Gaski
in the interpretation of his results, specifically the use of
the LISREL "total effects" estimates for hypothesis testing and the use of potentially low-variance data in suggesting managerial implications.
Direct and Total Effects
As an "exploratory" null hypothesis, Gaski presents
(p. 66):
Gaski seems to have recognized (p. 67) that this hypothesis is simply a test of Hy p = 0 in his Figures 5
and 6. That is, if reward and coercion are related to qualitative power sources (H, and H, in Gaski's article), and
if qualitative power sources are related to power and satisfaction (P ^ 0), the total effect of reward and coercion
on power and satisfaction musl be different from the direct effect. As Gaski's HQ is indistinguishable in practice
from H,: p = 0, Gaski's argument that "the absence of
prior theoretical development on this issue seems to dictate an exploratory approach" (p. 67) seems to be irrelevant.
Further, caution must be exercised in the interpretation of the "total effects" output generated by the
LISREL software. These effects are the direct plus indirect effects computed from the unstandardized solution. Even when the correlation matrix is used as input
and the variances of the ^'s are fixed to 1.0. the variances of the endogenous constructs {r\s) normally will
not be equal to 1.0 in the unstandardized solution. Thus
Gaski's direct comparisons between the structural coefficients ofthe standardized solution and LISREL's "total
effects" based on the unstandardized solution (p. 74) are
not appropriate. There are at least three reasonable approaches to this problem. First, one could confine comparisons to unstandardized coefficients and effects. Second, one could follow standard path-tracing techniques
on the standardized coefficients (Duncan 1975). Third,
in complex models where path tracing is difficult, the
methods provided by Fox (1980, 1985) can be applied
to the standardized coefficients matrices. In particular,
when one is interested in estimating the direct effects
channeled through one or a subset of the endogenous
variables in a complex model, the methods provided by
Fox (1985) may be useful.
It should also be recognized that the standard enors
associated with "total effects" can be very large, especially when several variables with "large" standard errors are included in the computation of indirect effects.
When nonsignificant variables (whose confidence intervals include zero and possibly estimates of the opposite
sign) are included in the multiplicative computation of
indirect paths, as is the case in Gaski's analysis, results
can be particularly misleading, again suggesting the preferability of simply testing the equivalent hypothesis that
Managerial Implications
illustrative of the problem of drawing causal inference from
a saturated structural submodel. The inclusion of either 3J2, pj^, or
i|t,2, though certainly having different causal interpretations, results in
exactly the same mode) fit, because any of the three specifications
results in estimating a structural model equivalent to a measurement
model with all 10 among-construct covariances estimated. This further illustTiites that any lack of fit in the model in Figure 2 must be
due to the measurement of TI,. given the saturated structural model
and fixed measurement for the other constructs.
Referring to his Table 2, Gaski suggests that, "Managerial recommendations are . . . to capitalize on the
realization that some punishments might be used without
fear of undesirable consequences. For example, 'refuse
to seir is the one action in this study without a significant relationship with any of the qualitative power
sources" (p. 75).
COVARIANCE STRUCTURE MODELING A N D MEASUREMENT ISSUES
It is difficult to understand why a relatively extreme
supplier action such as refusing to sell to a dealer would
fail to affect dealer perceptions of referent and expert
power sources when other (less extreme) forms of punishment relate negatively. Recall that punishments were
measured as "Please indicate how often Clark Equipment
takes each of the following kinds of action in their dealings with your organization" with four response categories ranging from "never" to "often" (p. 67). Before
one would be willing to refuse to sell to a dealer "without fear" of a negative impact on qualitative power
sources, one would need to know the likelihood that a
sample of current Clark Equipment dealers would include several dealers to whom Clark Equipment "often"
refuses to sell; that is, the variance in the variable. If
recurrent use of the "refuse to sell" punishment results
in a termination of the supplier-dealer relationship, the
empirical results reported by Gaski would follow, but
with exactly the opposite managerial implications. The
same general problem could account for other weak relationships involving elements of the "coercion" construct.
125
lated more strongly to expert and referent sources than
to the legitimate power source, and that reward and coercion are related to power and satisfaction only indirectly.
The results in Table 3 corresponding to the model in
Figure 2, which incorporates the second-order representation of power sources, suggest similar conclusions about
the explanatory power of the model with respect to power
and satisfaction, and their relationship. These revised estimates are provided for comparison with Gaski's estimates.
Deriving meaningful managerial conclusions from these
(and Gaski's) "causal" models is as difficult as attempting to draw conclusions from an examination of the (disattenuated) among-construct covariance or correlation
matrix. It is only through the a priori imposition of overidentifying restrictions that the goodness of fit of the
models can be examined or causal interpretations made.
Because (1) the model in Figure I is a "saturated submodel," (2) any lack of fit in the model in Figure 2 is
due only to the measurement model for TII, and (3) any
Table 3
REANALYSIS
In view of these problems with the measurement and
structural models presented by Gaski, two models were
reformulated and estimated with Gaski's correlation matrix as input. The model estimated in Figure 1 uses the
three sources of power individually whereas the model
in Figure 2 uses them as indicants of a second-order
"qualitative power source" construct. Both models include power and satisfaction simultaneously as endogenous constructs.
An examination of the results in Table 2 suggests that
(1) power is related directly only to the legitimate power
source, (2) satisfaction is related directly only to the referent power source, (3) the observed correlations among
the expert, referent, and legitimate power source constructs are not fully accounted for by reward and coercion (as evidenced by the 4*,;), and (4) in the context of
the model, power and satisfaction appear to be unrelated/ These fmdings suggest that there is value in examining the three power sources as first-order constructs
and that information can be gained by including power
and satisfaction in the same model. For example, the
preceding conclusions cannot be examined under Gaski's model formulations. In agreement with Gaski. these
results further suggest that reward and coercion are re-
PARAMETER ESTIMATES,
FULL SECOND-ORDER MODEL
Standardized
USREL
estimates
.912
.787
.821
.848
.522
.930
.874
.308
.771
.070
.489
-.488
.102
,017
-.037
,024
-.231
,431
,864
,420
.168
.381
.325
,281
,727
,135
.236
Parameter
X,
X2
X3
x/
X,
x/
^21
pll
&n
7ij
721
731
732
4i
?3
5,"
e,
«3
€4"
"The distributional properties of the x' statistic and the standard
error estimates produced by the LISREL program are based on the
asymptotic variances and covariances of the sample variance-covariance matrix, not the sample correlation matrix. Thus, tests on individual parameters are conducted here by fixing one structural parameter to zero, reestimating the model, and examining the difference in
X^ with one degree of freedom. In an importani article, Steiger, Shapiro, and Browne (1985) show that sequential chi square difference
statistics are asymptotically uncorrelated.
€,'
X
=
13.70
p = .090
d.f. = 8
R'it],) = .587
x'
P<
-
4.44"
28,07
\-
.02
.00
.23
.00
,00
.21
.89
,70
,80
.96
44,60
38.40
.92
.02
.15
.05
,
' F
i
.]
•
' 1-
RH-(]2)
=
.136
R^T],) = .580
GFI = .984
AGFI = .943
RMSR = .027
'Fixed parameter in unstandardized solution.
V difference statistic with 1 d.f. for model with this parameter
fixed.
JOURNAL OF MARKETING RESEARCH, FEBRUARY 1987
126
overidentifying restrictions that might be added would,
of course, be post hoc, causal inferences from both Gaski's models and these reformulations must be avoided.
CONCLUSIONS
Gaski's basic conclusions about the interrelations among
power sources are not changed substantially by this reanalysis. However, the parameter estimates themselves are
important and correct estimates should be reported.
The basic message of this note is that measurement
assessment and covariance structure modeling should be
performed on the individual indicants constituting one's
measures whenever possible and applicable. Coefficient
alpha is inadequate in assessing the unidimensionality
and discriminant validity of measurement scales. Further, it is suggested that the use of LISREL with single
indicants of all constructs and fully recursive models is
unnecessary; in the absence of multiple indicators and
overidentified models, the LiSREL method is simply a
cumbersome alternative to more straightforward procedures. When all possible structural relationships are estimated, any lack of fit must be due to the measurement
model; when multiple indicators are not available, no
measurement model can be estimated and thus the advantages of the covariance structure modeling approach
are lost.
Perhaps this note will underscore the piitential complexity in the specification, estimation, and interpretation of covariance structure models. Many informed
judgments are catted for in the process, each of which
requires justification based on the specific goals of the
research, the nature of the data, the context of the analysis, and the assumptions underlying the available techniques.
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