Why include covariance in the interaction model? 
Hi,
The above image is from "Latent Variable Models" by Loehlin and Beaujaean.
Given the model above the structural equation for Y is, Y = cX + dZ + e*XZ + W.
So it's an interaction model.
My question is as follow.
Why is the covariance betwen X and Z (i) included in the model despite the presence of the interaction variable (XZ)?
Because we are talking of partial coefficient, the effect of one independent variable on Y when all the other variables are held constant, it seems to be that the covariance between X and Z would be negated by the presence of the interaction variable XZ.
Any help would be much appreciated!

Here by definition, the latent random variables $X, Z$ are correlated exogenous source variables in the sense of causal inference, each of which is common factor for several observed variables and also forms an interaction factor for observable $Y$. And note the SEM you referred uses different path as compared to correlation between variables, say $r_{X,Y}$, as the latter uses compound paths. With your diagram $r_{X,Y}=c+id$, while $r_{XZ,Y}=e$. The given correlation $i$ between source variables $X,Z$ are non-causal thus you cannot interpret $i$ as partial path (regression) coefficient, unlike $c,d,e$. But from above it's obvious $i$ participates in the total correlation coefficients between variables such as $r_{X,Y}$ and $r_{Z,Y}$.
