Claes Fornell

Claes Fornell, David F. Larcker, Structural Equation Models with Unobservable Variables and Measurement Error: Algebra and Statistics, Journal of Marketing Research, Vol. 18, No. 3 (Aug., 1981), pp. 382-388

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.

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 addit...

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.