# Structural equation modeling for experimental design data

I'm wondering if this is possible to fit structural equation model for experimental design data.

Problem

Suppose a researcher observed four responses $Y_1$, $Y_2$, $Y_3$, and $Y_4$ along with three covariates $X_1$, $X_2$, and $X_3$ 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 $Y_1$ is also influenced by the other three ($Y_2$, $Y_3$, and $Y_4$).

Is it possible to model causality among responses $Y_1$, $Y_2$, $Y_3$, and $Y_4$ as well as to asses the effects of factors A , B and their interaction AB on responses $Y_1$, $Y_2$, $Y_3$, and $Y_4$?

Thanks