Anonymous posted on Tuesday, January 30, 2001 - 4:45 pm
Dear Linda, Bengt
I enjoyed Mplus workshop last year. Now, I want to what I leaned to actual analysis.
I have questions on multigroup latent growth modeling. Now, I have two groups: a retarded group and a normal group. The retarded group received an intervention treatment. To show the treatment is effective, I'd like to compare the growth rates of the two groupes. For both groups, linear LGMs fit well. If I simply compare the mean of the slope factors (growth factors) across the two groups, I think it is not a fair comparison because lower performing people at the initial status usually show faster growth rates (even though there is no treatment). Thus, I think it would be better to compare the means of the growth factors for the two group with the intercept factor (the initial status) controlled. Then, I have two questions:
(1) If I specify a directional path from the intercept factor to the slope factor in LGM for each group, does the mean (I know this is now an intercept) of slope indicate the growth mean with the initial status controlled? Or, it is not the mean but the intercept. If it is simply the intercept, how can I estimate the growth mean with the initial status controlled?
(2) If I can estimate the growth mean with the initial status controlled by specifying a directional path from the intercept factor to the slope factor in LGM for each group, should the path coefficients across the two group be equal (constrained to be equal)?
It sounds as if you have a quasi-experimental situation. In line with ANCOVA you want to control for pre-existing differences. ANCOVA uses an observed covariate to accomplish this controlling. In your growth model you propose using the initial status growth factor to accomplish the controlling. So, this makes sense to me. In terms of how to use this model and interpret the results I think you might want to continue using the ANCOVA analogy. That is, first you want to consider if the slope in the regression of the slope growth factor on the intercept growth factor is equal across the 2 groups (retarted and normal) If they are equal you can interpret the difference across groups in the intercept in this regression as an effect of the intervention (assuming that no other factors need to be controlled for). If they are not equal, the intervention effect has to be evaluated at different values of the intercept growth factor (the covariate that you use for controlling).
Anonymous posted on Wednesday, January 31, 2001 - 6:09 pm
Thanks for your clear answer to the question (specifying a reg path from inpt to slope). However, I couldnot understand the last sentence in your answer. What can we do if the slope in the regression of the slope growth factor on the intercept growth factor is NOT equal across the 2 groups?
In that case, in line with ANCOVA, you have to evaluate the group difference conditional on each value of the initial status factor. In ANCOVA terms, this is plotting the two lines of predicted slope values (s = a + b*i, where s is slope, a is the estimated intercept, b is the estimated slope, and i is the intercept growth factor) for the two groups with the initial status as x axis and looking to see where and by how much the two lines differ.