A Double-Structure Structural Equation Model for Three-Mode Data

Structural equation models are commonly used to analyze 2-mode data sets, in which a set of objects is measured on a set of variables. The underlying structure within the object mode is evaluated using latent variables, which are measured by indicators coming from the variable mode. Additionally, when the objects are measured under different conditions, 3-mode data arise, and with this, the simultaneous study of the correlational structure of 2 modes may be of interest. In this article the authors present a model with a simultaneous latent structure for 2 of the 3 modes of such a data set. They present an empirical illustration of the method using a 3-mode data set (person by situation by response) exploring the structure of anger and irritation across different interpersonal situations as well as across persons.