Hypothesis Formulation, Model Interpretation, and Model Equivalence: Implications of a Mereological Causal Interpretation of Structural Equation Models

Abstract

One can distinguish statistical models used in causal modeling from the causal interpretations that align them with substantive hypotheses. Causal modeling typically assumes an efficient causal interpretation of the statistical model. Causal modeling can also make use of mereological causal interpretations in which the state of the parts determines the state of the whole. This interpretation shares several properties with efficient causal interpretations but also differs in terms of other important properties. The availability of alternative causal interpretations of the same statistical models has implications for hypothesis specification, research design, causal inference, data analysis, and the interpretation of research results.

ACKNOWLEDGMENTS

Material from this article was presented to the 2001 International Meeting of the Psychometric Society and the Doctoral Faculty in Educational Psychology at the CUNY Graduate Center.

PSC-CUNY Research Award 62700-00-31 partially supported the research reported here.

Lisa Caltabiano, Donna Griffith, Tammy Trierweiler, Claire Miller, and Sarah Torneten provided feedback on a draft of this article; assisted in various phases of the ongoing research; and have helped clarify many key concepts related to mereological causation and mereology of statistical variables. Raj Bhatia and Frank Coffaro assisted in an earlier phase of the research and also helped clarify key concepts. This article has also benefited from discussions with Ken Bollen, Denny Borsboom, Michele Galietta, Bill Gottdiener, Steve Penrod, and particularly Bill Rozeboom. Stuart Kirschner brought the Roberts & Golding (1991) article to my attention.

Notes

¹In the interest of fair disclosure, I note that one reviewer found this interpretation intolerable and indeed contrary to the very title of this journal. Obviously, I found the argument unpersuasive and hope that this and other passages make clear that multivariate research need not entail causation between variables themselves as the only viable interpretation of multivariate models. Indeed, one reviewer claimed that (a) variables exist in the head; (b) causation exists outside the head; and (c) variables literally cause variables, not events coded as variables. I find it less than obvious how to make these three claims cohere.