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Mplus Discussion > Latent Variable Mixture Modeling >
 Chris Blanchard posted on Thursday, November 18, 2010 - 4:55 am
i'm new to MPlus and have a question. I have data where we tracked patients with heart disease for 1 year and have physical activity measurements at baseline, 3, 6, 9, and 12 months. I performed a growth-mixture model to identify the number of classes for two intensities (i.e., light and moderate) controlling for age and gender. I identified two classes for each intensity. Now that I have this information, I want to know the probability of a patient transitioning from a light intensity trajectory into a moderate intensity trajectory (and vice versa). I believe this can be done via dual trajectory analysis, but I'm not sure this can be done in MPlus. If it is, can someone direct me to an example. Thanks very much,
 Bengt O. Muthen posted on Thursday, November 18, 2010 - 7:46 am
Is "intensity" a dichotomous covariate?

What are the two processes in the dual trajectory analysis you have in mind?
 Chris Blanchard posted on Thursday, November 18, 2010 - 7:58 am
No. I ran a separate growth mixture model for light intensity and one for moderate intensity (syntax for light is below).

USEV ARE age gender light1 light2 light3 light4 light5;



CLASSES = c(2);

STARTS 20 2;

i s | light2@0 light3@1 light4@2 light5@3;
i s on light1;
i s on age;
i s on gender;

is this syntax correct? If so, i'm hopoing to show that as time goes on, patients transition into doing more moderate intensity PA...from reading the lit., i thought i had to do a dual trajectory analysis, but perhaps there is another type of analysis I could do? Thanks for your help in advance!
 Bengt O. Muthen posted on Thursday, November 18, 2010 - 5:30 pm
There is no transitioning in the GMM. Perhaps you want to use Latent Transition Analysis and include both light and moderate.
 Chris Blanchard posted on Friday, November 19, 2010 - 4:19 am
Thank you! Final question, if I run a growth mixture model with 2 classes for light intensity and 2 classes for moderate intensity, will the output be able to provide me with the probabilities of being in class 1 for light intensity conditional on the moderate classes and vice versa? In speaking with my collegue, he also wants to identify the most at risk group. I think this is a dual trajectory analysis approach. I apologize if I confused the issue...chris
 Bengt O. Muthen posted on Friday, November 19, 2010 - 10:21 am
Hmm. I understood the light and moderate intensities to correspond to different groups of subjects, in which case one cannot talk about conditional probabilities of one given the other. But perhaps I am misunderstanding. A dual process would be 2 different types of outcomes observed on the same individual.
 Chris Blanchard posted on Friday, November 19, 2010 - 2:52 pm
They are actually the same participants. The questionnaire asked them about light intensity and moderate intensity. I ran the growth mixture models separately and identified 2 classes for each intensity. I was hoping to then combine them into a dual trajectory-type analysis to establish the probability of a participant being in class 1 for light intensity conditional on the moderate intensity classes...is this possible to do? Sorry about the confusion.
 Bengt O. Muthen posted on Saturday, November 20, 2010 - 7:29 am
You can do that by using 2 latent class variables in a dual process model, one latent class variable for each process. You can relate the 2 latent class variables to each other.

To do this you say in the Overall part of the mixture model:

c1 with c2 (or c2 on c1)

And then

Model c1:


where you mention the growth factor means for process 1 in latent class 1


where you mention the growth factor means for process 1 in latent class 2

Model c2:

where analogously you mention the growth factor mean for process 2 in the different proc 2 classes
 Chris Blanchard posted on Wednesday, November 24, 2010 - 11:01 am
thank you very much! I've pasted part of my syntax below and was wondering if a) it is correct, and b) if I interpret the latent transition probabilities based on the estimated model output to determine the probabilities of being in light class 1 condition on mvpa class 1, etc...or do I have to save the probabilities and get this information from the saved data file. Sorry, that is my last MPLUS newbie question!

ilight slight | mild_m2@0 mild_m3@1 mild_m4@2 mild_m5@3;
imvpa smvpa | mvpa_m2@0 mvpa_m3@1 mvpa_m4@2 mvpa_m5@3;
ilight slight on mild_m1;
imvpa smvpa on mvpa_m1;
ilight slight on age;
imvpa smvpa on age;
ilight slight on gender;
imvpa smvpa on gender;
c2 on c1;
[ilight slight];
[ilight slight];
[imvpa smvpa];
[imvpa smvpa];
 Bengt O. Muthen posted on Thursday, November 25, 2010 - 8:26 am
This looks correct.
 Chris Blanchard posted on Friday, December 03, 2010 - 11:18 am
Hi there, in redoing the analyses, I decided to do a simple latent class growth analysis for light intensity (identified 2 classes: class 1 = 177; class 2 = 46) and moderate intensity (identified 2 classes: class 1 = 186; class 2 = 37). Then, when I run the dual trajectory analysis to obtain the latent transition probabilities, the class membership get's flipped for light intensity (class 1 = 46; class 2 = 177), but not moderate intensity. Unfortunately, this is confusing me because the demographic make-up of the trajectories also get reversed when I examine them in SPSS. Below is my syntax, am I doing something wrong?

il sl | mild_m1@0 mild_m2@1 mild_m3@2 mild_m4@3 mild_m5@4;
im sm | mvpa_m1@0 mvpa_m2@1 mvpa_m3@2 mvpa_m4@3 mvpa_m5@4;
c2 ON c1;
[il sl];
[il sl];
[im sm];
[im sm];
 Linda K. Muthen posted on Sunday, December 05, 2010 - 11:14 am
You can use the results of the two prior analyses as starting values in the current analysis to keep the classes straight.
 Andrea Mata posted on Wednesday, March 09, 2011 - 2:14 pm
Hello. I am familiar with running LCGAs and GMM's in mplus, however, I need to run a dual trajectory model using LCGA. I was hoping you could provide references for examples of syntax to guide me in this task. Thank you in advance.
 Bengt O. Muthen posted on Wednesday, March 09, 2011 - 6:10 pm
Use the UG to combine an LCGA setup and a parallel process setup and you have what you want. Check to be sure that your growth factor variances are zero since you want LCGA. One question is if you want one latent class variable for both processes or one for each. I can't think of a reference off hand.
 Laura Wray-Lake posted on Thursday, January 24, 2013 - 9:17 pm
We separately ran latent class growth analyses (LCGA) for our two constructs: PYD (continuous) and SU (count). Three classes were found for PYD; two classes were found for SU (we used a zero-inflated poisson model for SU). Then we wanted to run a dual trajectory analysis to obtain latent transition probabilities, so we conducted a latent transition analysis. WWe used the below model specifications we got a class breakdown for PYD that closely resembles our original LCGA breakdown, but the class breakdown for SU is very different from our original LCGA (i.e., 48-52 split vs. 10-90 split). We could not find sample syntax for conducting LTA with a ZIP model, and we suspect that we have misspecified the ZIP (SU) portion of the model. Is below correct? If it isn't, how should it be changed?

ipyd spyd | PYD1@0 PYD2@1 PYD3@6;
isu ssu | SU1@0 SU2@1 SU3@6;
iisu sisu | SU1#1@0 SU2#1@1 SU3#1@6;
c2 ON c1;

[ipyd spyd];
[ipyd spyd];
[ipyd spyd];

[isu ssu iisu sisu];
[isu ssu iisu sisu];
 Bengt O. Muthen posted on Friday, January 25, 2013 - 4:39 pm
It looks like you are setting it up correctly. I wonder if the model assumption is what causes the discrepancy - your model says that the PYD items influence the SU items only through their latent class variables. For instance, some of the PYD items may have direct effects on some of the SU items (which I think could be handled but leads to a more complex model).

If you instead said c1 ON c2, you might similarly see the PYDS classes shift.

Another possibility is to use 3-step LTA analysis, locking down the class formations from the LCGAs. See our web note 14. Although this would then mask the potential model misfit matter that I mentioned.
 J.D. Haltigan posted on Thursday, November 14, 2013 - 9:03 pm

I just wanted to follow-up on this thread with an additional question:

When deriving conditional probabilities using TECH 15 (i.e., in a dual trajectory analyses) is it necessary to have separate runs where you condition c1 on c2 and c2 on c1 (which is what I have done to get the full set of conditional probabilities) or can this be done in a single run?

Apologies if I have been unclear in what I am asking.
 Bengt O. Muthen posted on Friday, November 15, 2013 - 4:45 pm
It has to be done in two runs. The setup was mainly intended for LTA where the influence goes one way.
 J.D. Haltigan posted on Friday, November 15, 2013 - 7:25 pm
Thank you.

One other question: When saving the class probabilities and classes from a dual trajectory model, is there any way (other than running frequencies on the exported class variable) to tell which class is which (i.e., classes 1, 2, ...x) don't necessarily map onto latent transition patterns 1, 2, ...x). In my case, I ran a dual trajectory model resulting in a 2x2 or 4 class output.

 Bengt O. Muthen posted on Saturday, November 16, 2013 - 6:02 pm
The top of the output that gives the model-estimated probabilities for the 4 classes shows the order of the classes. I hope that's what you are asking.
 J.D. Haltigan posted on Saturday, November 16, 2013 - 10:22 pm
Thanks much! This clarifies it.
 J.D. Haltigan posted on Saturday, June 07, 2014 - 1:15 pm

I am back running joint trajectory models and I have a few questions I am unclear on.

My setup is that I am modeling the joint probabilities of 5-group and 6-group constructs (i.e., 30 total possible joint groups).

In specifying the joint models, I am setting the intercept and growth parameters of process 1 and 2 classes to their respective estimates obtained in the univariate models. Is this OK? or should simply starting values at these estimates be used instead?

Secondly, as is expected with 30 possible combinations, a few of the posterior probabilities are quite low. I read a paper (Fanti & Henrich, 2010) where the authors omitted the intercept and growth terms representing such low probability classes and re-ran the joint trajectory model. Since I am not specifying the intercept and growth terms for the joint trajectories in the input, how precisely is what they did accomplished? In other words, I would like to re-run the joint trajectories omitting these combinations.

Thank you.
 Bengt O. Muthen posted on Saturday, June 07, 2014 - 5:45 pm
Q1. I would not fix the parameters of the joint analysis to the values from the separate analyses. Using them as starting values while still using Starts is ok.

Q2. If you specify the model so that the growth parameters (means,variances, covariances) for each process are only varying across the latent classes of that process, the small cell sizes in the 5 x 6 latent class table don't hurt. What hurts is if cell sizes are small among the 5 and 6 classes, respectively, because that is what supports the estimation of those growth parameters.
 J.D. Haltigan posted on Saturday, June 07, 2014 - 11:11 pm
Thank you. What is troubling me is that when I use the growth parameter estimates from the separate univariate runs as starting values (rather than fixed) for the process portions of the dual model, the resultant latent class memberships for each process are hard to link back to the latent classes from the original univariate runs. How is it possible to map the classes of the process portion of the dual model back to their original univariate classes?
 Bengt O. Muthen posted on Sunday, June 08, 2014 - 4:10 pm
The fact that the joint model for the two processes gives different results for each process than when they are analyzed separately indicates that the joint model is not well specified. That is, the relationship between the two processes is not well captured.
 J.D. Haltigan posted on Wednesday, June 25, 2014 - 10:03 pm
Thank you! It seems to me that there is no 'best practice' in the developmental psychopathology literature re: dual trajectory modeling. In virtually every paper I have examined, the authors state something to this effect: "...the intercept and growth parameters from the individual class memberships for construct x and construct y were used to predict the probability of multiple class membership in a joint statistical model." I read this as they simply fixed those values in the dual run and just wanted the conditional probabilities (rather than capturing the relationship between the two processes).

In a more technical paper, Xie et al., note that in the dual run "the number of optimal trajectory groups in the dual model is *usually consistent* with those id'd in the univariate models." In this paper they also note that they fit a number of different dual models with varying classes for each construct, determining the one with the best fit.

I guess it depends on the research question and how you frame the dual approach?
 Bengt O. Muthen posted on Thursday, June 26, 2014 - 2:32 pm

I would still want to see the same "marginal" model for each process remain essentially unchanged when doing the joint analysis. But it is not always easy to find the right joint model that produces that.
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