Abstract

Testing a causal model, based on empirical data, through covanance structure modeling, often leads to the observation that any particular hypothesized model may have equivalent models. Model equivalence occurs when two or more covariance structure models generate identical covariance matrices. These covariance matrices, commonly referred to as model estimates of covariance matrices or reproduced covariance matrices, must be distinguished from empirically observed or sample covariance data. When two or more models are equivalent, the result is that they are equally fit to any observed data and thus are not distinguishable by data analysis. In proposing a model which supports the hypotheses of interest, an investigator is obliged to rule out the equivalent models by substantive interpretation.