Conceptual Shell Games in the Four-Step Debate

Abstract

The exchange between Hayduk and Glaser (2000) and Mulaik and Millsap (2000) sheds new light on the use of multistep procedures for testing structural equation models. Nonetheless, the fundamental concepts of the discussion remain murky. The notion of a correct number of constructs (interpreted latent variables) rests on a conflation of the model with the reality it models. The articulation of what is tested in terms of model constraints encounters an analogous difficulty. Finally, the appeal to analysis into clear and distinct ideas holds the potential to clarify some of these issues, but still awaits the necessary exposition and application to structural equation modeling. A common thread shows itself in an over-reliance on single languages of description. This calls for greater attention to the active engagement of multiple languages of description.