13 Structural Equation Modeling

The association between the interactive and diagnostic use of financial and non-financial performance measures with individual creativity: The mediating role of perceived fairness

This study examines the associations between top management’s interactive and diagnostic use of financial and non-financial performance measures with individual manager’s (i.e. middle and lower level managers) creativity, and the mediating role of middle and lower level manager’s perceived fairness of their performance appraisal on such associations. Using data from a survey of 220 middle and lower level managers from manufacturing organisations in Australia, the structural equation model revealed direct positive associations between both the diagnostic use of financial performance measures and the interactive use of non-financial performance measures with individual creativity. Further, the positive effect of the interactive use of financial performance measures on individual creativity is positively and fully mediated by distributive, interpersonal and informational fairness, while the positive effect of the interactive use of non-financial measures is positively and partially mediated by interpersonal and informational fairness. In addition, procedural fairness positively and partially mediates the effect of the diagnostic use of financial performance measures on individual creativity, and interpersonal fairness positively and fully mediates the effect of the diagnostic use of non-financial performance measures on individual creativity. The findings contribute to the performance measurement and appraisal literature examining the interactive and diagnostic use of both financial and non-financial performance measures and extends the sparse literature on the role of perceived fairness in explaining the behavioural effect of performance measurement systems. The findings also provide implications for practice, revealing the importance of the interactive and diagnostic use of financial and non-financial performance measures, and manager’s perception of the fairness of performance appraisal processes as a mechanism through which individual manager’s creativity can be enhanced.

The effect of latent and error non-normality on corrections to the test statistic in structural equation modeling

In structural equation modeling, several corrections to the likelihood-ratio model test statistic have been developed to counter the effects of non-normal data. Previous robustness studies investigating the performance of these corrections typically induced non-normality in the indicator variables. However, non-normality in the indicators can originate from non-normal errors or non-normal latent factors. We conducted a Monte Carlo simulation to analyze the effect of non-normality in factors and errors on six different test statistics based on maximum likelihood estimation by evaluating the effect on empirical rejection rates and derived indices (RMSEA and CFI) for different degrees of non-normality and sample sizes. We considered the uncorrected likelihood-ratio model test statistic and the Satorra–Bentler scaled test statistic with Bartlett correction, as well as the mean and variance adjusted test statistic, a scale-shifted approach, a third moment-adjusted test statistic, and an approach drawing inferences from the relevant asymptotic chi-square mixture distribution. The results indicate that the values of the uncorrected test statistic—compared to values under normality—are associated with a severely inflated type I error rate when latent variables are non-normal, but virtually no differences occur when errors are non-normal. Although no general pattern regarding the source of non-normality for all analyzed measures of fit can be derived, the Satorra–Bentler scaled test statistic with Bartlett correction performed satisfactorily across conditions.