The July-Sept issue of the SEM journal just came out with an article on this topic by Blozis and Cho which looks good.
In Mplus you simply handle this by the TSCORES option of the VARIABLE command and the AT option in the growth model specification using the | approach - see the User's Guide ex 6.12 (without the time-varying covariates and their random slope "st").
Bengt - Do you have a paper that discusses the model that results with TSCORES? It seems to be more than the traditional multilevel (tall data) formulation. It appears more flexiable (in some ways) than mixed efects models because endogenous covariates with missing data are handled, and also you can have occasion-specific residuals, while MLR offers only one residual.
Oh well. It is good to have, even without a paper.
I am wondering about the residuals for each growth-curve outcome/indicator. For example, in an age-based model with six yearly outcomes for subjects with six-years of age-heterogeneity at baseline, are these time-in-study residuals or age-residuals? Or a hybrid of the two?
They are age-related residuals. I would hold them equal across the occasions because a given occasion corresponds to different ages for different subjects. More elaborate modeling is possible using Model Constraint, but this equality would be the standard I think.
Is there any way to get traditional fit indices such as the CFI or the RMSEA for LGMs that use individually-varying time scores (i.e., when using the Tscores option)? If not, what might one say to reviewers who want to get some sense of the absolute level of fit of models, not just the relative fit (using the BIC, etc.).
There are no absolute fit measures in this case. Nested models can be compared using loglikelihood difference testing. Models with the same set of dependent variables can be compared using BIC.
burak aydin posted on Monday, November 30, 2009 - 3:22 pm
Hi, I have an ECLS data set with 9484 cases. I try to see if there would be a significant difference on estimations when using interindividually varying time points. type=random command requires mlr estimation process, and it gives only AIC and BIC values for the model fit. Is there any way to get other indicies. like CFI, NFI and RMSEA? Thanks
This approach falls within the domain of random slopes for observed covariates, in this case time. With random slopes you don't have a single covariance matrix as in CFA/SEM - the outcome variances vary as a function of the covariate values - so the usual fit indices are not developed.
burak aydin posted on Monday, November 30, 2009 - 7:21 pm
Do you mean this estimation process is similar to what HLM does? or this is a more complex estimation method for LGM? I would like to learn more about this estimation process. Because I get different results between 1)ML estimation method- fixed time points,like; y1@email@example.com@1.5 2)MLR estimation method- type=random model: y1-y3 AT c1-c3 where c1 is all zeros,c2 is all 0.5s and c3 is all 1.5s.