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.
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;
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
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?
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.
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.