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The statistical tests used in the analysis of structural equation models with unobservable variables and measurement error are examined. A drawback of the commonly applied chi square test, in addition to the known problems related to sample size and power, is that it may indicate an increasing correspondence between the hypothesized model and the observed data as both the measurement properties and the relationship between constructs decline. Further, and contrary to common assertion, the risk of making a Type II error can be substantial even when the sample size is large. Moreover, the present testing methods are unable to assess a model's explanatory power. To overcome these problems, the authors develop and apply a testing system based on measures of shared variance within the structural model, measurement model, and overall model.

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Several issues relating to goodness of fit in structural equations are examined. The convergence and differentiation criteria, as applied by Bagozzi, are shown not to stand up under mathematical or statistical analysis. The authors argue that the choice of interpretative statistic must be based on the research objective. They demonstrate that when this is done the Fornell-Larcker testing system is internally consistent and that it conforms to the rules of correspondence for relating data to abstract variables.

ABSTRACT:The empirical research examining the association between typical measures of corporate governance and various accounting and economic outcomes has not produced a consistent set of results. We believe that these mixed results are partially attributable to the difficulty in generating reliable and valid measures for the complex construct that is termed ''corporate governance.'' Using a sample of 2,106 firms and 39 structural measures of corporate governance (e.g., board characteristics, stock ownership, institutional ownership, activist stock ownership, existence of debtholders, mix of executive compensation, and anti-takeover variables), our exploratory principal component analysis suggests that there are 14 dimensions to corporate governance. We find that these indices have a mixed association with abnormal accruals, little relation to accounting restatements, but some ability to explain future operating performance and future excess stock returns.