Cross-lagged analysis. Interpretation of Coefficients and Covariates

Question

I am currently, for the first time, conducting cross-lagged panel analyses to test for temporal precendence in the relationship between two variables. I have two questions:

How do you interpret, in words, the respective cross-lagged coefficients. Is it similar to regression as in (given they are unstandardized): one unit increase in X from t1 to t2 leads to ß increase in Y from t1 to t2?

Secondly, do you typically include time-constant covariates/control variables in the model, if yes how would you do that? - simply running them as multiple regression on X1 and Y1 within the cross-lagged analysis?

Any help would be greatly appreciated.

Answer 1

The interpretation of the path coefficients is the same as the interpretation of partial regression coefficients in multiple regression. I would say something like: "A one-unit increase in X at Time 1 is associated with a ß-unit increase in Y at Time 2, controlling for the autoregression of Y on itself over time."

One would typically use path analysis for autoregressive/cross-lagged models because path models allow you to consider multiple dependent and independent variables simultaneously. You can then simply add covariates at whichever time point is theoretically appropriate. You could, for example, include time-invariant covariates ("traits") as additional predictors at each time point.