Comments on an article by Grice, Shlimgen and Barrett (GSB): “Regarding Causation and Judea Pearl’s Mediation Formula”
Stan Mulaik called my attention to a recent article by Grice, Shlimgen and Barrett (GSB) (linked here http://psychology.okstate.edu/faculty/jgrice/personalitylab/OOMMedForm_2011A.pdf ) which is highly critical of structural equation modeling (SEM) in general, and of the philosophy and tools that I presented in “The Causal Foundation of SEM” (Pearl 2011) ( http://ftp.cs.ucla.edu/pub/stat_ser/r370.pdf.) In particular, GSB disagree with the conclusions of the Mediation Formula — a tool for assessing what portion of a given effect is mediated through a specific pathway.
I responded with a detailed account of the disagreements between us (copied below), which can be summarized as follows:
1. The “OOM” analysis used by GSB is based strictly on frequency tables (or “multi-grams”) and, as such, cannot assess cause-effect relations without committing to some causal assumptions. Those assumptions are missing from GSB account, possibly due to their rejection of SEM.
2. I define precisely what is meant by “the extent to which the effect of X on Y is mediated by a third variable, say Z,” and demonstrate both, why such questions are important in decision making and model building and why they cannot be captured by observation-oriented methods such as OOM.
3. Using the same data and a slightly different design, I challenge GSB to answer a simple cause-effect question with their method (OOM), or with any method that dismisses SEM or causal algebra as unnecessary.
4. I further challenge GSB to present us with ONE RESEARCH QUESTION that they can answer and that is not answered swiftly, formally and transparently by the SEM methodology presented in Pearl (2011). (starting of course with the same assumptions and same data.)
5. I explain what gives me the assurance that no such research question will ever be found, and why even the late David Friedman, whom GSB lionize for his staunch critics of SEM, has converted to SEM thinking at the end of his life.
6. I alert GSB to two systematic omissions from their writings and posted arguments, without which no comparison can be made to other methodologies:
(a) A clear statement of the research question that the investigator attempts to answer, and
(b) A clear statement of the assumptions that the investigator is willing to make about reality.