Specifying and Testing Differences Between Variables in Structural Equation Modeling Using the H–O Specification

Differences, such as gaps or contrasts, are crucial to theories in the social sciences. However, modeling these differences in structural equation modeling (SEM) remains challenging. Existing approaches have limitations that prevent researchers from modeling and testing differences flexibly. This paper introduces the H–O specification for modeling differences, a flexible SEM specification that overcomes these limitations. Our specification enables differences to be modeled as both independent and dependent variables, allows for differences between latent variables, and facilitates testing of the equal importance and full transmission assumptions. Using an empirical example from marketing research, we demonstrate that the H–O specification can reproduce the results of existing approaches while offering greater modeling flexibility and more opportunities to test differences.