Tiina posted on Friday, January 06, 2006 - 3:30 am
I'm using Mplus version 3, and wondering the following questions concerning multiple and regular growth models (with three time scores). The questions are timely also for several of my colleagues.
1) If there is a possibility to use multiple indicator GM, is this always a better option? I understand the difference in parametrization between the two types of LGMs, but does the multiple indicator model do better job in controlling for the measurement error in the examined variables, given that the time scores are already latent? I suspect that I'm seeing this happening in my data, because I'm getting a higher regression coefficient among a covariate and the slope factor with a multiple than regular LGM. Both models fit well to the data. Are there any conditions under which you would recommend to use the one over the other?
2) About model identification: If I'm letting the program to estimate one of the time score loadings on the slope factor, thus ending up with only two "known" indicators for the latent variables, do I need to fix one time score to zero for the model to be identified, or does the parametrization of the LGM make sure that the model is identified anyway? Are there any differences in this between multiple indicator and regular GM? I'm asking this because sometimes I'm able to run such a model, and sometimes not. Further, do these issues depend on whether I'm using the "BY" or the random slope (|) statement in the syntax?
3) When constructing a multiple growth process model including effects from 1) a covariate to the intercept and slope of a growth curve, 2) which (intercept) again has an effect on the intercept and slope of another growth curve, and 3) it is known that the predictor variable predicting the intercept and slope of the first growth curve has similar effects on the second growth curve when tested separately, is it possible to test mediational effects trough the first growth curve to the next when all of these components are included in the same model (i.e., one predictor variable measured at T1, and two growth processes including three time scores, and the level and linear slope factors)? This would make theoretical sense, and I quess that my interest would be to model the mediation trough the slope-component of the first growth curve. In other words, may the intercept and slope factors be treated as regular latent variables, allthough they are specified components of growth curves?
4) When regressing an intercept and slope of a LGM on a covariate, does one need to specify the relationship among the intercept and the level as a regression path to say that "...varible x predicts increases in variable y while CONTROLLING FOR THE INITIAL LEVEL of...", or is this true also in case these components are simply allowed to correlate? If not, if X predicts the slope of an Y only when the intercept and the level are correlated but not when the path is defined as a regression, can one really say that the X predicts increases in Y in similar manner as in traditional, longitudinal SEM model (allthough in LGM, the latent factors represent different things than traditional latent variables). If not, is this really "longitudinal" information (which would be essential for my paper)?
5) I noticed a discussion about the difference in obtained covariate effects on growth components when letting the intercept and the slope to be correlated vs. including a regression among them, in a situation where these factors are heavily negatively correlated: Significant effects from the covariate to these factors were obtained only when including a regression among the level and the slope. I have a similar situation, and wanted to ask if this effect is specific/common for the situation when the intercept and slope are negatively correlated? What may account for this?
Thank you Bengt and Linda for your time, and excellent website!!
1. If the factor model fits well and measurement invariance across time has been established, the multiple indicator model would be best. In this model time-specific variance and measurement error can be separated unlike a regular growth model where the two are combined.
2. See Chapter 16, Growth Models, to see the difference between the BY and | specifications of growth models and to see how to specify a multiple indicator growth model.
3. Yes, growth factors can be treated as any latent variable.
4. All covariates are controlled for in the regression of a dependent variable on a set of independent variables.
5. The is nothing special about a negative covariance that would require special modeling techniques.
Tiina posted on Monday, January 09, 2006 - 7:07 am
Thank you for your timely response. I still wanted to specify the question 4. I meant controlling for the initial level of the dependent variable/growth curve, rather than control for other independent variables. That is, if I'm obtaining a significant effect on the linear slope factor (and possibly also on the level factor), is the meaning of this effect similar in case when there is a correlation among the level and slope factor, and when the slope is regressed to the level? Or is it so that including the regression among the level and the slope is the only way to indicate that some covariate in fact predicts increases/decreases in some variable over time?