Having obtained estimates for the loadings and errorvariances for the interaction terms, two nested models werethen specified. In both models, the loadings and error variancesfor the interaction terms were fixed at their previouslyestimated values. The first model was a restricted model inwhich the γ parameters linking the ‘formalization–environment’,the ‘centralization–environment’, and the ‘coordination–environment’ interaction terms to EMO behavior werefixed at zero, and the remaining γ parameters were freelyestimated. The second model was an unrestricted model inwhich those γ parameters originally fixed at zero were freed.As is shown in Table 1, moving from the restricted model tothe unrestricted model resulted in a decrease in χ2 of 2.84, withan associated decrease of 3 degrees of freedom. Although thisis an improvement in fit, it is not significant at p<.05, anddoes not provide conclusive evidence that the unrestrictedmodel is superior to the restricted model. However, by testingfor interactions, nonnormal variables are included in themodel: this violates the assumption of multivariate normality,and (often severely) biases the χ2 statistic (West, Finch, &Curran, 1995), rendering formal comparisons of the teststatistic in our nested models inappropriate. Thus, our ability todetermine which model is superior based on traditional fitindexes is compromised. As a result, we look for other factorsto inform our decision on this front. To this end, we comparethe percentage of variance explained in EMO behavior acrossthe two models. For the restricted model, the reduced formsquared multiple correlation is .655, while for the unrestrictedmodel, the squared multiple correlation is .730. Thus, inabsolute terms, we are explaining an additional 7.5% of thevariance in the EMO behavior measure in the unrestrictedmodel. This is a substantial increase in variance explained.Furthermore, all three interaction terms return significant pathcoefficients in the unrestricted model. Given this additionalinformation, we can see that the unrestricted model provides anon-trivial improvement over the restricted model: thus, weuse the results from the former when evaluating thehypotheses.
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