Hello, I am conducting a multiple indicator lgm with continuous variables. Three time points are modeled and the latent variable at each time-point is measured by three indicators. These indicators are item-parcels, i.e. the average of three items of a nine-item scale intended to measure the construct under consideration. Also, while the first two slope loadings are fixed at 0 and 1 in the lgm, the last loading is freely estimated. Furthermore, I estimate the model with the restriction of strict measurement invariance. This LGM fit the data very well (CFI = .996). Interestingly, the slope variance did not differ from zero, which is a surprise as this contradicts earlier research findings. However, when I compute a “manifest” form of the lgm (the nine items are averaged at each time point), I obtain a significant slope variance (the overall model fit is good: CFI = .994). Similar results emerge when I compute manifest lgms for each of the item parcels I had used in the multiple indicator lgm (p-values are: p = .04, p = .09, p = .12). This is confusing (for me, at least) and I was wondering whether you have ever had such a case, and whether I should interpret the manifest or the latent result? 2. What explains this pattern? Apparently, changing to multiple indicator lgms does not always yield smaller standard errors for growth parameters (as I thought); why did this not occur in my case? Thanks in advance, Steffen
Multiple indicator growth modeling is described in the Topic 4 video and course handout on the website. One of the first steps is to fit a growth model for each indicator. If the indicators do not have the same shape, a multiple indicator growth model is not appropriate for the data. This may be the case for your data.
Dear Dr. Muthen, thanks for your reply and your advice. However, I believe that the indicators have approximately the same shape (although I am not sure if they are similar "enough"). The third (the other two loadings are fixed at 0 and 1) loading of the first indicator is .935, .952 for the second indicator and 1.007 for the third indicator. Is this OK or is the loading of the third indicator to high? Thanks, Steffen