Currently, I am working on a simple cross-lagged path analysis (i.e., not latent variables) with two variables measured at three time points. My question concerns the standardized parameter estimates. Specifically, when constraining the cross-lagged paths to be equal across time, the standardized estimates (STDYX - I'm using continuous control variables) are not equal. For example, the standardized estimate for Time 1 Variable X --> Time 2 Variable Y is not equal to Time 2 Variable X --> Time 3 Variable Y when that path is constrained to be equal in the code.
Is there a way to force these estimates to be equal? How would this be done and what would the potential implications for model fit be?
The estimates are standardized using the standard deviations of the variables involved. If these are not the same, the standardized estimates will not be the same even if the raw estimates are held equal.
You can constrain X variable variances to be equal across time but you still have the Y variances to contend with. But I would argue that you should focus on the equality of unstandardized coefficients. I would not confound them with (uninteresting) changes in variances and residual variances as you would if you focus on standardized coeffs.