Decomposable Models: A New Look at Interdependence and Dependence Structures in Psychological Research

Decomposable models represent interdependence structures for observable variables. Each model is fully characterized by a set of conditional independence restrictions, and can be visualized with an undirected as well as a special type of a directed graph. As a consequence each decomposable model can be interpreted either in terms of interdependencies only or as a particular kind of dependence structure, as a recursive system or path analysis model. Under the assumption of normally distributed variables, decomposable models determine the structure of correlation matrices, and maximum-likelihood estimates of these can be calculated with the help of ordinary least squares estimation. Using several examples from psychological research, we discuss the interpretation of decomposable models. Furthermore, it is demonstrated how recursive dependence structures can be specified with the help of decomposable models in a hypothesis generating (exploratory) as well as in a hypothesis testing (confirmatory) manner.