A new index of structure for the analysis and summary description of models for mobility tables and other kinds of cross-classifications is proposed. For a given model, this index measures model misfit (or lack of fit) as the minimum possible proportion of the population outside the specified model. It measures structure in relation to a given model or hypothesis. The framework that gives rise to this index consists of embedding a specified model (independence, quasi-independence, uniform association, etc.) in a special kind of "saturated" latent class (or mixture) model. We define this index and describe its properties, apply the framework to analyze several classical mobility tables using different baseline models, show how the framework can be used to explore local misfit or local structure, and to provide some guidelines for applying the framework in comparative analysis. This framework can be used to summarize model misfit, to compare the misfit of different models, and to compare model misfit across samples of varying sizes.

* Pennsylvania State University, State College, PA
** Eötvös University, and TÁRKI, Budapest, Hungary