Jerry,
You could write your model for each time point. Variables are denoted by _t1,... _t4 for each of them.
Below is some information I provided previously for a user's question. The path is not the same as yours but the basic idea should be the same.
You might specify the following model for time point 1 -- LINEQS V1_t1 = b12 * V2_t1 + b13 * V3_t1 + E1, V2_t1 = b24 * V4_t1 + b25 * V5_t1 + b26 * V6_t1 + b27 * V7_t1 + E2, V3_t1 = b34 * V4_t1 + b35 * V5_t1 + b36 * V6_t1 + b37 * V7_t1 + E3;
Now, suppose you have two time points, the problem becomes more complicated. Suppose that initially, you simply stack the time_2 variable models to the previous specifications:
LINEQS
V1_t1 = b12 * V2_t1 + b13 * V3_t1 + E1, V2_t1 = b24 * V4_t1 + b25 * V5_t1 + b26 * V6_t1 + b27 * V7_t1 + E2, V3_t1 = b34 * V4_t1 + b35 * V5_t1 + b36 * V6_t1 + b37 * V7_t1 + E3 V1_t2 = b12_t2 * V2_t2 + b13_t2 * V3_t2 + E4, V2_t2 = b24_t2 * V4_t2 + b25_t2 * V5_t2 + b26_t2 * V6_t2 + b27_t2 * V7_t2 + E5, V3_t2 = b34_t2 * V4_t2 + b35_t2 * V5_t2 + b36_t2 * V6_t2 + b37_t2 * V7_t2 + + E6; Here you also add a new set of coefficients with suffix “_t2”. But this is not necessary if your theory would hypothesize b’s is invariant across time, that is b=b_t2 for all b’s.
Then, you can ask that wouldn’t it make sense to assume V1_t2 is predictable by v1_t1? Sure, then you modify the fourth equation by adding an effect: V1_t2 = b12_t2 * V2_t2 + b13_t2 * V3_t2 + a11_t21 * V1_t1 + E4, But can V1_t2 be affected by V2_t1 too? If so, you could do: V1_t2 = b12_t2 * V2_t2 + b13_t2 * V3_t2 + a11_t21 * V1_t1 + a12_t21 *V2_t1 + E4,
Then you can keep asking about the effects of other t1 variables on V1_t2. You might expand the above equation by including non-negligible effects---but you must make your own judgment about what effects are negligible or not. Then, the next consideration is about the modification of equations for V2_t2 and V3_t2---basically, you are trying to specify how variables in different time periods could relate to each other. You might also add equations for other t2 variables like: V4_t2 = * V4_t1 + … + E7 Yes, this will become very tedious and difficult to manage! But this is the precisely nature of using a very general modeling method to study repeated multivariate measures.
CALIS or SEM is a flexible modeling tool that you cannot expect one to tell you a generic model to fit. For longitudinal data, there are quite many possibilities. Questions that might guide you to specify the model are: 1. Can I assume some effects to be invariant across time points (e.g, b12 = b12_t1 = b12_t2)?
2. Are variables at time point 2 affected by variables at time point 1? 3. Can my research questions be answered by simpler statistical techniques? SEM is not the best modeling techniques in all occasions.
I recommend you to try out some models with fewer time points (say, the first, and the last) and see if you can understand the modeling and interpret the results. Then you can build more complicated models.
Hope this helps,
Jill Tao
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