The use of causal indicators in covariance structure models: some practical issues

In conventional representations of covariance structure models, indicators are defined as linear functions of latent variables, plus error. In an alternative representation, constructs can be defined as linear functions of their indicators, called causal indicators, plus an error term. Such constructs are not latent variables but composite variables, and they have no indicators in the conventional sense. The presence of composite variables in a model can, in some situations, result in problems with identification of model parameters. Also, the use of causal indicators can produce models that imply zero correlation among many measured variables, a problem resolved only by the inclusion of a potentially large number of additional parameters. These phenomena are demonstrated with an example, and general principles underlying them are discussed. Remedies are described so as to allow for the evaluation of models that contain causal indicators.