Today I gave my structural equation modeling class the following homework:
In Star Wars I: The Phantom Menace, Yoda presented the Jedi Theory of Emotions: “Fear is the path to the dark side. Fear leads to anger. Anger leads to hate. Hate leads to suffering.”
1. Specify the Jedi Theory of Emotions as a path model with 4 variables (FEAR, ANGER, HATE, and SUFFERING). Draw a complete path diagram, using lowercase Roman letters (a, b, c, etc.) for the causal parameters.
2. Were there any holes or ambiguities in the Jedi Theory (as stated by Yoda) that required you to make theoretical assumptions or guesses? What were they?
3. Using the tracing rule, fill in the model-implied correlation matrix (assuming that all variables are standardized):
4. Generate a plausible equivalent model. (An equivalent model is a model that specifies a different causal structure but implies the same correlation matrix.)
5. Suppose you run a study and collect data on these four variables. Your data gives you the following correlation matrix.
Is the Jedi Theory a good fit to the data? In what way(s), if any, would you revise the model?
For #1, everybody always comes up with a recursive, full mediation model — e.g., fear only causes hate via anger as an intervening cause, and there are no loops or third-variable associations between fear and hate, etc. It’s an opportunity to bring up the ambiguity of theories expressed in natural language: just because Yoda didn’t say “and anger can also cause fear sometimes too,” does that mean he’s ruling that out?
Relatedly, observational data will only give you unbiased causal estimates — of the effect of fear on anger, for example — if you assume that Yoda gave a complete and correct specification of the true causal structure (or if you fill in the gaps yourself and include enough constraints to identify the model). How much do you trust Yoda’s model? Questions 4 and 5 are supposed to help students to think about ways in which the model could and could not be falsified.
In a comment on an earlier post, I repeated an observation I once heard someone make, that psychologists tend to model all relationships as zero unless given reason to think otherwise, whereas econometricians tend to model all relationships as free parameters unless given reason to think otherwise. I’m not sure why that is the case (maybe a legacy of NHST in experimental psychology, where you’re supposed to start by hypothesizing a zero relationship and then look for reasons to reject that hypothesis). At any rate, if you think like an econometrician and come from the no true zeroes school of thought, you’ll need something more than just observational data on 4 variables in order to test this model. That makes the Jedi Theory a tough nut to crack. Experimental manipulation gets ethically more dubious as you proceed down the proposed causal chain. And I’m not sure how easy it would be to come up with good instruments for all of these variables.
I also briefly worried that I might be sucking the enjoyment out of the movie. But then I remembered that the quote is from The Phantom Menace, so that’s already been done.