I'm wondering how to test the significance of factor(s) and/or covariate(s) along with modeling the causal relationship among responses. Let me explain this with a concrete example.


Suppose a researcher observed four responses Y1, Y2, Y3, and Y4 along with three covariates X1, X2, and X3 from an experiment involving ab treatment combinations from a fixed factor A with a levels and a random factor B with b levels. Based on past experience, it is assumed four responses are correlated and Y1 is also influenced by the other three (Y2, Y3, and Y4).


  • How can I test the significance of Factors (A and B) and covariates (X1, X2, and X3) and causality among responses (Y1, Y2, Y3, and Y4) using a single model?
  • $\begingroup$ As far as the 'causality' part goes, this sounds like testing for mediation, but as the lead of that Wikipedia article says, the possibility of / methods for testing for mediation using empirical data have been challenged. I haven't made a thorough study of this, but i'd number myself among the skeptics. $\endgroup$
    – onestop
    Apr 12, 2011 at 12:18

1 Answer 1


I don't believe you can definitively do so. The most difficult aspect will be the relationships among the 4 Y variables. That there are "assumed" causal relationships among them does not help us to test causality. In my limited understanding, a structural equation approach would assess the plausibility of an hypothesized model but would not test the correctness of such a model in any strict sense.


Your Answer

By clicking “Post Your Answer”, you agree to our terms of service and acknowledge you have read our privacy policy.

Not the answer you're looking for? Browse other questions tagged or ask your own question.