Models for status inconsistency and mobility: a comparison of the approaches by Hope and Sobel with the mainstream square additive model

This paper is about the analysis of effects of status inconsistency and mobility on a dependent variable. We compare the mainstream square additive baseline model to alternative designs by Hope (1971, 1975) and Sobel (1981, 1985). Both writers claim that the square additive baseline model also contains some status inconsistency effects. An examination of the relationships between the square additive model, Hope's halfway/difference model, and Sobel's simple diagonal reference model shows that the effects uncovered by Sobel and Hope pertain to the inequality of the effects of the status variables on the dependent variable. These salience difference effects are therefore distinct from the non-additive status inconsistency effects which would be detected using the square additive approach. Less restricted versions of the diagonal reference model, the DM-1 and DM-2 models as well as a recent model by Weakliem (1992), are also examined with regard to additive/non-additive components and symmetry of effects.