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 anonymous_04 posted on Thursday, August 07, 2014 - 10:55 am

I have three variables repeatedly measured over seven time-points, and I want to model their within and between-person structure using SEM MLM. So far the model is working perfect (see example code). Now, I want to test the robustness of these relationships by taking into account past influences of the same variable (i.e., I want to add an autoregressive term). How do I incorporate that in the model below? Thank you for your help.

ID x1 x2 x3 x4 m1 m2 m3 m4 y1 y2 y3 y4;

USEVARIABLES ARE ID x1 x2 x3 x4 m1 m2 m3 m4 y1 y2 y3 y4;

MISSING ARE all (-99);




Xw BY x1 x2 x3 x4 ;
Mw BY m1 m2 m3 m4 ;
Yw BY y1 y2 y3 y4l

Mw ON Xw;
Yw ON Mw;
Yw ON Xw;


Xb BY x1 x2 x3 x4 ;
Mb BY m1 m2 m3 m4 ;
Yb BY y1 y2 y3 y4l

Mb ON Xb;
Yb ON Mb;
Yb ON Xb;

 Bengt O. Muthen posted on Thursday, August 07, 2014 - 1:42 pm
I think you want to switch to a single-level, wide format approach. So you consider your variables to be the x's, m's, and y's at all the time points. Then it is easy to add auto-regressions.
 anonymous_04 posted on Thursday, August 07, 2014 - 2:06 pm
Thank you Prof Bengt for the quick reply. I agree that formatting the data to wide format would allow me to test to autoregression. And, I have done so in the past using cross-lag panel analysis. However, with that representation, I lose the capability to model the within-person process. Are you suggesting that I cannot model the first order autoregressive effects using SEM MLM?

Thank you!
 Bengt O. Muthen posted on Thursday, August 07, 2014 - 3:34 pm
Which within-person process would you not be able to model?
 anonymous_04 posted on Thursday, August 07, 2014 - 3:40 pm
That is the within-person effects as is the case with multilevel modeling.
 Bengt O. Muthen posted on Thursday, August 07, 2014 - 4:11 pm
Explain it to me in terms of what you model in your Two-level input.
 anonymous_04 posted on Thursday, August 07, 2014 - 4:32 pm
Okay, so I am attempting to model the relationship between affect, effort, and performance. All three measures are assessed seven time. In the within-person model, I want to examine the extent to which within-person changes in affect are related to within-person changes in effort and performance. At the between-level, I want to examine whether general affect is related with effort and performance.

At the within-level, I do find a significant relationships between all three variables, which is great. Now, I want to know whether those relationships hold once I take into account the effects of previous time point of the same variable (i.e., the effect of t-1). By taking into account the previous time-points of the same variable, any significant relationship I find can be interpreted as an incremental effect. I believe this is a more conservative test of the within-person relationships.

I hope I am clear in my description. Thank you!
 Bengt O. Muthen posted on Friday, August 08, 2014 - 1:58 pm
Seems like a single-level model would work. So for each time point you have a path model for 3 variables: affect, effort, and performance. And you have 7 time points, so a single-level model would have 21 outcome variables. The sets of 3 variables are correlated across time, e.g by lagged effects. The "between variable" predicts the 3 variables (or some of them) the same or different ways over time.
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