

Adding AR1 Structure in MLM SEM 

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Hi, I have three variables repeatedly measured over seven timepoints, and I want to model their within and betweenperson 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. VARIABLE: NAMES ARE 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); CLUSTER IS ID; ANALYSIS: TYPE IS TWOLEVEL RANDOM; MODEL: %WITHIN% 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; %BETWEEN% 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; OUTPUT: TECH1 TECH3; 


I think you want to switch to a singlelevel, 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 autoregressions. 


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 crosslag panel analysis. However, with that representation, I lose the capability to model the withinperson process. Are you suggesting that I cannot model the first order autoregressive effects using SEM MLM? Thank you! 


Which withinperson process would you not be able to model? 


That is the withinperson effects as is the case with multilevel modeling. 


Explain it to me in terms of what you model in your Twolevel input. 


Okay, so I am attempting to model the relationship between affect, effort, and performance. All three measures are assessed seven time. In the withinperson model, I want to examine the extent to which withinperson changes in affect are related to withinperson changes in effort and performance. At the betweenlevel, I want to examine whether general affect is related with effort and performance. At the withinlevel, 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 t1). By taking into account the previous timepoints 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 withinperson relationships. I hope I am clear in my description. Thank you! 


Seems like a singlelevel 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 singlelevel 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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