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?