Anonymous posted on Thursday, April 14, 2005 - 1:33 pm
These questions come on the heels of my reading Nagin's (2005) book on Group-based modeling of development.
The first question is that Nagin appears to find the definition of group used in GGMM problematic. Nagin defines a group as a collection of individuals who follow approximately the same developmental trajectories and suggests that the groups are points of support on the population distribution of trajectories. He goes on to say that population variability is captured principally by differences across groups in the shape and level of their trajectories. GGMM, he argues, adds individual differences in the expected trajectory of group members, which alters the definition of a group. This implies that belonging to group A might actually have a trajectory that more closely correspondes to the mean trajectory of group B, which creates "group cross-overs", which undermines the definition of a group. Is this an accurate depiction of the GGMM model, why or why not?
The second question is that Nagin goes on to critcize the GGMM framework for modeling heterogeneous individuals that can nonetheless be described by a single probability distribution. He specifically says that GGMM describes population heterogenity with multiple layers of heterogenity. He purports that this is the source of the group cross-over problem. Is this accurate?
I have read your response to Bauer and Curran (2003) in psychological methods. However, I was wondering if you wouldn't mind clarifying this issue for me a little more. As an avid Mplus user, I would like to be able to use the GGMM framework for future research and would like to be able to develop cogent counter arguments to make the case. Thank you in advance for addressing these issues.
BMuthen posted on Friday, April 15, 2005 - 7:46 am
I will have to answer you more fully after I have read Nagin's book. Re your 1st q., my 2004 chapter in the Kaplan handbook gives my discussion of the 2 view points. I can appreciate Nagin's viewpoint about groups representing support points of a latent variable distribution -- this is referred to as non-parametric estimation. However, I think it is a strength of the GGMM framework that you not only allow typical developmental patterns (groups) but also variations within those typical patterns. I think it is ok if some extreme variations within 2 different classes are close to each other. If you have within-group variation, Nagin's approach would result in a proliferation of groups. The strength of the Mplus program is that both the Nagin and the GGMM models can be studied to see which is most appropriate for the application.
Re your 2nd q., I don't agree with the premise that there is a cross-over problem.
Feel free to raise more question later when I have read the book.
Anonymous posted on Friday, April 15, 2005 - 1:53 pm
Thank you so much. I will check back with you about more issues. Thanks for addressing these for me.
Anonymous posted on Monday, April 25, 2005 - 10:08 pm
I have been reading your articles and thinking about what you have written on this topic. I was wondering if I have your central premise correct. My interpretation is as follows:
The Nagin model is incorrect in its specification of individuals into classes because it does not consider the effect of covariates on the intercept and slope when developing the classes. Further, the Nagin model does not consider distal effects in this calculation either. Therefore, if a user of Nagin's model is fortunate enough to develop the correct number of classes without these influences, then they will still have biased estimates of intercept and slope factors. This is the case becasue in the Nagin model the intercept and slope factors using PROC TRAJ require that multinomial logit analyses be performed in an additional step after posterior probabilites have been used to determine the individual cases that belong in the different classes. Therefore, the Nagin model may lose information and is rather inefficient to perform. Further, it may be more efficient to have a few overlapping individual cases in the trajectories due to heterogenity as long as the intercepts and slopes are properly estimated by the covariates and if necessary the distal effects.
Is this close to correct? I probably overstated somethings, but is the gist here?
bmuthen posted on Monday, April 25, 2005 - 10:18 pm
This not quite how I would portray it. My 2004 chapter in the Kaplan handbook gives a fuller account, but here are a few corrections. First, Nagin's modeling differs from mine not because of covariate influence being different, but because he does not have growth factor variances within classes (with or without these growth factor being influenced by covariates). Second, as far as I understand, TRAJ does not require " that multinomial logit analyses be performed in an additional step after posterior probabilites have been used to determine the individual cases that belong in the different classes.", but can do this step together with the first step. Third, allowing for within-class variation does not necessarily imply "a few overlapping cases in the trajectories". I think the central difference between the two approaches is that Nagin's modeling tries to capture all the trajectory heterogeneity in terms of distinct classes (which is then a form of non-parametric estimation of latent variable distributions), whereas my modeling tries to distinguish heterogeneity of a fundamental kind (classes) from heterogeneity that is merely slight variations on a theme (the within-class variation). Hope that helps somewhat - perhaps I should write more on this topic.
Anonymous posted on Monday, April 25, 2005 - 11:24 pm
This does help. It would be great if you did write more that directly addressed the advantages and disadvantages of the two approaches. I am partial to GGMM because I am trained in the SEM tradition. The GGMM is much more intuitive to me. However, the Nagin model appears to be gaining popularity and his recent writings have cast doubt on the utility of GGMM. I understand that Mplus contains both models, but the GGMM just has intuititve appeal. So, by all means please write some more about these two models, at least for us SEMers that really want to use GGMM. Thanks for addressing these issues thus far and clearing up the differences. I will continue the think about these differences to make sure that I completely understand them.
The Nagin model is a special case of GGMM where the growth factor variances and covariances are zero. If you think of it that way rather than as two separate approaches/models, it may be easier to understand. The choice of the model would be which one best fits the theory you are interested in studying. Do you believe that all people are exactly alike in different classes or do you believe that there is some variability with the people in one class being more similar to each other than to people in other classes. In the first case, you would choose the Nagin model. In the second case, you would choose GGMM.
bmuthen posted on Monday, April 25, 2005 - 11:55 pm
Let me order the Nagin book and see what is said there and what needs to be clarified.
Anonymous posted on Wednesday, April 27, 2005 - 12:20 pm
Thank you Linda this makes the issue crystal clear for me now. I went back and reread Bengt's paper in Kaplan's (2004) book and he refers to Mplus programs that examine Moffitt's theory using the Cambridge data. I can't seem to locate these on the examples web-site. How may I obtain the input and output for these analyses?
bmuthen posted on Wednesday, April 27, 2005 - 12:29 pm
These examples are not on the Mplus web site but we are happy to send them to you. Just email us and specify which input you want.
IYH Boon posted on Tuesday, May 03, 2011 - 8:31 pm
Could you send the examples mentioned by @Anonymous at 6:20 to me too? Thanks.