This paper addressed important theoretical differences
of contingency fit and the methods to test them in management
accounting.
We first discussed different forms of fit, arguing that
overview papers in management accounting have mentioned
sub-types of fit that do not belong to contingency
theory (mediation form of fit), while specific sub-forms of
matching fit that appear in the broader management literature
(matching forms of fit with iso-performance versus
hetero-performance on the fit-line and/or with asymmetric
effects of mis-fit on performance) have not been explicitly
addressed. We also discussed the methods used in management
accounting research to test ‘fit’ and assessed their
ability to effectively test the specific sub-form of fit they
postulate as well as to discriminate between rival forms
of fit. We focused on the methods used to test matching
and moderation forms of fit that entail effects of (mis-) fit
on performance. Our review and analyses lead to several
recommendations for future empirical contingency work.
First, polynomial regression analysis represents a powerful
approach to testing matching versus moderation form
of fit models that represent competing theoretical explanations.
Polynomial regression analysis simultaneously tests
for any bivariate moderation and matching form of fit and
thereby avoids the weaknesses related to the traditional
methods to test fit outlined in Section 3. Second, we recommend
accepting moderation effects after ruling out the
possibility of a matching form of fit and a curvilinear effect
only of the MCS variable. As explained earlier, any path
model with performance as a dependent variable (referred
to as mediation form of fit) is not a suitable alternative.
This recommendation is based on theoretical and empirical
arguments that question the “no relation” condition
between the moderator and the independent variables. The
central insight of our Monte Carlo simulations is that simple
path models easily conceal existing moderation effects.
Moreover, we presented an overview of the computational
procedures now available for probing interactions,
including the application of the Johnson-Neyman technique
(the suitability of which had previously been
questioned in the management accounting literature).
These procedures allow researchers to conclusively test
sub-forms of moderation fit.
Third, we provided an overview and recommendations
on how to use covariance-based SEM when testing
contingency theory. In particular, we recommend not
using covariance-based SEM to test matching form of
fit hypotheses, but instead using polynomial regression
analysis. Due to the linearity constraints of covariancebased
SEM, this technique is not yet advanced enough to
provide reliable estimates similar to those obtainable from
This paper addressed important theoretical differencesof contingency fit and the methods to test them in managementaccounting.We first discussed different forms of fit, arguing thatoverview papers in management accounting have mentionedsub-types of fit that do not belong to contingencytheory (mediation form of fit), while specific sub-forms ofmatching fit that appear in the broader management literature(matching forms of fit with iso-performance versushetero-performance on the fit-line and/or with asymmetriceffects of mis-fit on performance) have not been explicitlyaddressed. We also discussed the methods used in managementaccounting research to test ‘fit’ and assessed theirability to effectively test the specific sub-form of fit theypostulate as well as to discriminate between rival formsof fit. We focused on the methods used to test matchingand moderation forms of fit that entail effects of (mis-) fiton performance. Our review and analyses lead to severalrecommendations for future empirical contingency work.First, polynomial regression analysis represents a powerfulapproach to testing matching versus moderation formof fit models that represent competing theoretical explanations.Polynomial regression analysis simultaneously testsfor any bivariate moderation and matching form of fit andthereby avoids the weaknesses related to the traditionalmethods to test fit outlined in Section 3. Second, we recommendaccepting moderation effects after ruling out thepossibility of a matching form of fit and a curvilinear effectonly of the MCS variable. As explained earlier, any pathmodel with performance as a dependent variable (referredto as mediation form of fit) is not a suitable alternative.This recommendation is based on theoretical and empiricalarguments that question the “no relation” conditionbetween the moderator and the independent variables. Thecentral insight of our Monte Carlo simulations is that simplepath models easily conceal existing moderation effects.Moreover, we presented an overview of the computationalprocedures now available for probing interactions,including the application of the Johnson-Neyman technique(the suitability of which had previously beenquestioned in the management accounting literature).These procedures allow researchers to conclusively testsub-forms of moderation fit.Third, we provided an overview and recommendationson how to use covariance-based SEM when testingcontingency theory. In particular, we recommend notusing covariance-based SEM to test matching form offit hypotheses, but instead using polynomial regressionanalysis. Due to the linearity constraints of covariancebasedSEM, this technique is not yet advanced enough toprovide reliable estimates similar to those obtainable from
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