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.
A follow-up question regarding modeling cross-lagged path analysis (involving three time points). It is my understanding from a few published works that one should constrain the stability effects to be equal, as well as the cross-lagged paths. If this is done, as you noted above, the unstandardized estimates will be the same but the standardized estimates are likely to be different for paths constrained to be equal. In this scenario, how does one test for mediation effects, given that one would use the same labels to constrain the relevant paths to be equal. Testing for mediation using path labels under model constraint (e.g., Med1 = a*b*c, where b is the label for two cross-lagged paths or two stability paths constrained to be equal) would be problematic. Thank you.
Below is a Sample syntax involving crossed lagged effects of two team processes each measured at three time points (T2, T3, T4), and subsequent effect on team performance (measured once at time 5):
TmCd_T3r on TmCd_T2r (b1); TmCd_T4r on TmCd_T3r (b1);
Gcoh_T3 on Gcoh_T2 (b2); Gcoh_T4 on Gcoh_T3 (b2);
Gcoh_T2 with TmCd_T2r; GCoh_T3 with TmCd_T3r; GCoh_T4 with TmCd_T4r;
TmCd_T3r on Gcoh_T2 (b3); TmCd_T4r on Gcoh_T3 (b3);
Gcoh_T3 on TmCd_T2r (b4); Gcoh_T4 on TmCd_T3r (b4);
TeamPerf on Gcoh_T4 (q) TeamPerf on TmCd_T4r (s);
One possible indirect path from Gcoh_T2 to TeamPerf is: Gcoh_T2 --> Gcoh_T3 --> Gcoh_T4 --> Team perf. However, given that (Gcoh_T2 --> Gcoh_T3) is constrained to be equal to (Gcoh_T3 --> Gcoh_T4) as denoted by the label b2, the mediation effect would be b2*b2*q. Is it a problem in this case because b2 (unstandardized) is the same value? In calculating the indirect effect, it seems to me that mplus will only actually multiple b2*q rather than b2*b2*q. If these paths were not constrained to be equal, this would not be a problem because the paths would have different labels.
Please let me know if i am thinking about this correctly. Thanks
Yan Liu posted on Monday, November 18, 2019 - 4:56 pm
Dear Dr. Muthen,
I want to make sure if I am right about computing the indirect effects. We have three treatment conditions (x1, x2); the mediator was measured at time-2 and time 3 (m1, m3); the outcome was obtained at time-3 and time-6 (yt3,yt6). The yt6 is zero inflated. Here is my model:
Note that Y3 influences Y6 so you need to label that coefficient and bring it into the effects on Y6.
Also, it seems like it is possible that M3 could influence Y3 as well.
Yan Liu posted on Saturday, November 23, 2019 - 1:57 pm
Dear Dr. Muthen, Thank you very much for your reply! I would like to confirm two issues with you. First, one outcome yt6 is zero inflated, but the other is not. Is this the correct way to define them?
COUNT = yt3 yt6(i);
Second, I modified the model based on your advice with some considerations of Y3 influences Y6, and M1 influence M3 and Y6. However, I didn't link M3 and Y3 as they are collected at the same time. How would you think this model:
MODEL: !autoregressive effects M3 ON gis1 (d); yt6 ON yt3 (f);
!cross-lagged regression effects m1 ON x1 (a1) x2 (a2) male;
is a problematic model when yt3 is a count variable. There is not a good way to treat a count variable as a predictor. There is no underlying continuous latent response variable that can be referred to as with categorical variables y*. Mplus simply treats it as continuous. Perhaps you can categorize it and treat it as ordinal, that is, categorical in Mplus language. But to get a y* variable, you can't use ML but have to use WLSMV or Bayes.
Yan Liu posted on Saturday, November 23, 2019 - 4:03 pm
Dear Dr. Muthen,
Thanks for pointing this out! Our outcome yt3 is the attendance to exercise classes, ranging form 0 to 36. yt6 is zero inflated, which has to be treated as a count variable. Given that yt3 is skewed to a small degree, can we treat it as a continuous variable using MLR?