Dual trajectory model
Message/Author
 Anonymous posted on Thursday, November 25, 2004 - 8:07 pm
I have two processes measured over time, each with 4 time points. I have a hypothesis that one of the processes is driving the other. That is, that the causal flow is in a particular direction (i.e. an individual's value on process A at time t determines an individuals value on process B at time t+1...rather than an individual's value on process B at time t determines an individual's value on process A at time t+1. Can you recommend a model for this type of hypothesis?
 bmuthen posted on Friday, November 26, 2004 - 6:35 am
Such direct influence from the outcomes of one process on the outcomes of another process can for example be combined with a growth model for both if that is a substantively relevant model. Or combined with an auto-regressive model for each if that is more relevant.
 Anonymous posted on Saturday, November 27, 2004 - 7:10 am
Thank you. In the case of a dual growth model that includes the cross lagged effects to examine the direction of causation, is the syntax below correct and how should one specifiy the contemporaneous effect?

int_PROCA slp_PROCA|T1PA@0 T2PA@1 T3PA@2 T4PA@3;
int_PROCB slp_PROCb|T1PB@0 T2PB@1 T3PB@2 T4PB@3;

T2PA ON T1PB; T3PA ON T2PB; T4PA ON T3PB;
T2PB ON T1PA; T3PB ON T2PA; T4PB ON T3PA;
 bmuthen posted on Saturday, November 27, 2004 - 8:03 am
The syntax is correct. Contemperanous relations could for example be handled by correlating the residuals of the outcomes for the two processes.
 Anonymous posted on Wednesday, December 08, 2004 - 1:47 pm
I have a related question. Imagine two models. In one model, both the repeated measures of x and the repeated measures of y are modeled as growth models and all of the growth factors are correlated. In addition, the contemporaneous effect of y on x at each measurement occassion is specified.

iy sy|t1y@0 t2y@1 t3y@2 t4y@3;
ix sx|t1x@0 t2x@1 t3x@2 t4x@3;
t1y on t1x; t2y on t2x; t3y on t3x; t4y on t4x;

In the second model, only y is modeled as a growth model and x is treated as a
time varying covariate.

iy sy|t1y@0 t2y@1 t3y@2 t4y@3;
t1y on t1x; t2y on t2x; t3y on t3x; t4y on t4x;

How would you interpret the time-varying effect of x on y differently given these two models?
 Linda K. Muthen posted on Thursday, December 09, 2004 - 9:19 am
I think if the growth factors are correlated, then in the parallel process model, the regressions of y on x would be the regression of the residual of y on x. I would run it both ways and then look at the results and think about it.
 Anonymous posted on Thursday, December 09, 2004 - 9:43 am
Thanks, I've done that and I find that the effect of the tvc in the second model is much stronger. I had interpreted it in the same way that you have, but I wanted to make sure that my thinking was correct. I guess the choice of the model will depend on one's hypothesis, that is, whether it is conceptually necessary to control for time in both constructs or if it makes more sense to assess the full effect of x on y after adjusting for change over time in y. Thank you.
 Renee Thompson posted on Wednesday, April 25, 2007 - 8:25 pm
What is the command to correlate residuals? I am trying to run a path diagram with longitudinal data.
 Linda K. Muthen posted on Thursday, April 26, 2007 - 5:37 am
The WITH option of the MODEL command is used for this purpose. See Chapter 16 of the Mplus User's Guide.
 Thomas Olino posted on Tuesday, February 09, 2010 - 4:49 am
I am interested in examining growth of two count outcomes negative binomial (counts; 0-10 range). In running the models as a latent growth curve, the models are able to be estimated. However, there are multiple errors that prevent the model estimation when including predictors of the growth parameters.

I was interested in running the same model in a long data format to attempt to work around this problem. Is it possible to model the growth of two different outcomes using TYPE=TWOLEVEL RANDOM?

Two issues seem to make this difficult. First, each outcome would be regressed on time, however, if modeled as ~ Outcome1 ON Time1; Outcome2 ON Time2; ~ then Time1 would be perfectly correlated with Time2.

Second, I am interested in looking at prediction of intercept and slope variation. However, this would require more than one random effect - one for each outcome.

Are there ways of specifying this model?

Thanks,

Tom
 Linda K. Muthen posted on Tuesday, February 09, 2010 - 9:50 am
 Amy Krentzman posted on Wednesday, December 07, 2011 - 12:09 pm
Greetings!

I am running:

x1 on y1 y2 y3;
x2 on y1 y2 y3;

and I'd like to improve the model fit so I'd like to allow the error terms of the DVs to covary.

x1 with x2;

But the model fit information is identical to when I just had the regression commands. Running the same model in AMOS, once I allowed the error terms of the DVs to covary (by drawing a curved arrow), the model fit improved a whole lot. I wonder what I'm doing wrong?

Thanks!
Amy
 Linda K. Muthen posted on Wednesday, December 07, 2011 - 12:26 pm
x1 and x2 correlate by default in Mplus. So when you added x1 WITH x2 you did not change the model.
 Laura Alexandra posted on Wednesday, September 17, 2014 - 12:00 am
Dear Mrs./ Mr. Muthen

I am running a dual domain latent growth curve model (2 linear growth trajectories), which seems to terminate well.
Just to get some further insight (not the main focus) I am running the same dual domain growth curve model for two groups with different educational levels using the subgroup command in mplus. (For one group the model-fit is not very well particularly because I (need to) include a lot of control variables as predictors of latent parameters which for this group seem not to be highly relevant)

As it is not my intention to make a comparison of latent growth parameters across groups but only to get some idea/check if covariates included in the conditional model work in the same direction across both groups would this procedure be ok?

Thank you very much!
 Bengt O. Muthen posted on Wednesday, September 17, 2014 - 9:23 am
Model fit should not be hurt by control variables that do not have significant influence on the growth factors. I would make sure the model fits well in each group separately.
 Laura Alexandra posted on Wednesday, September 17, 2014 - 10:57 pm
Thank you for this fast reply.

So if the model fit is appropriate for each group , meaning that I may have to allow for correlations across different residuals for each group separately, can I still proceed with using the subgroup command to get an intuitive understanding whether the influence of some covariates on slopes and intercepts is similar across these subgroups- or would this then be no more a valid procedure?

Thank you very much!
 Bengt O. Muthen posted on Thursday, September 18, 2014 - 1:53 pm
When you say subgroup command, I assume you mean the GROUPING option of the VARIABLE command. If the groups differ only in terms of correlated residuals for the outcomes, I think you can still make a meaningful study of group differences in covariate influence on the growth factors.
 Laura Alexandra posted on Friday, September 19, 2014 - 5:28 am
Dear Mr. Muthen

The multigroup LGM-model I estimate is the following:

VARIABLE: (…)
grouping is high1 (0=low 1=high);
cluster etc.

ANALYSIS:
ESTIMATOR= MLR; Type is complex;

MODEL:
iw sw | w1@0 w2@1 w3@2 w4@3 w5@4;
il sl | l1@0 l2@1 l3@2 l4@3 l5@4;
iw sw on x1 etc;
il sl on x1..;

l2 with w2; sl with iw@0;..

MODEL low: sw with iw@0;
MODEL high: sw@0;

1)I fixed the slope variance for the group high at 0 because it was negative and not significant- resulting in a non-pos-def PSI. Is it ok to specify this solemnly for group high?

2)When I am only interested in seeing if some of the time-invariant measures affect the latent intercepts and slopes in both groups in a similar way (only direction, not if size of coef is equal) – do I then also need to constrain intercepts etc?

3) As I fixed the variance of one latent slope for the group high at 0 I am surprised to find significant effects of covariates on this slope- how is this possible?

Thank you so much for your great support!
 Linda K. Muthen posted on Saturday, September 20, 2014 - 2:52 pm
1. This is okay.
2. No.
3. In a conditional model, you fix the residual variance to zero not the variance.
 Laura Alexandra posted on Friday, June 26, 2015 - 5:42 am
Dear Mr. & Mrs.Muthen

I am estimating the following (conditional) dual trajectory growth model.

ANALYSIS:
ESTIMATOR= MLR; Type is complex;

MODEL:
iw sw | w1@0 w2@1 w3@2 w4@3 w5@4;
il sl | l1@0 l2@1 l3@2 l4@3 l5@4;
iw sw on x1 x2 x3 etc;
il sl on x1 x2 x3 etc;

First I include only x1 as a regressor, while then I add other predictors of the intercepts and slopes such as x2, x3 etc. to the model (with the intention to control for their effect)- as changes in the effect of x1 are very minor when adding other control variables I was wondering if it could be that by default x1, x2, x3 etc. may not be allowed to be correlated? Or is the procedure I am following ok and the effect of x1 on the intercepts and slopes is robust concerning additional controls added?

Thank you very much for your help.
 Bengt O. Muthen posted on Sunday, June 28, 2015 - 10:30 am
Q1. No

Q2. Yes.
 Shichen Li posted on Wednesday, May 16, 2018 - 7:13 pm
Dear Mrs./ Mr. Muthen

I am new to Mplus and I am trying to test if the latent category of two variables are related using the dual trajectory model. After GMM analysis, I found both variable 1 and variable 2 has 2 latent categories. I used the LTA (example 8.7) to do the anlaysis. The model I used is the following:

MODEL:
%OVERALL%
i1 s1 | y2@0 y3@1 y4@2 y5@3 y6@4;
i2 s2 | y7@0 y8@1 y9@2 y10@3 y11@4;
c2 ON c1;
MODEL c1:
%c1#1%
[i1 s1];
%c1#2%
[i1*1 s1];
MODEL c2:
%c2#1%
[i2 s2];
%c2#2%
[i2*-1 s2];

I am not sure if the model is correct as I assume that if the model is significant then the trajectory of the two variables would be correlated. However, I can't find Chi-squre test or Wald test for the model in the results. Can I use this model? If so how can I know whether the model is significant or not? Or should I use other method?

Thank you very much.
 Bengt O. Muthen posted on Thursday, May 17, 2018 - 4:32 pm
I don't know what it means to say "if the model is significant". You should look at the

c2 ON c1

results to see if you have a significant relationship between those 2 variables.
 Shichen Li posted on Saturday, August 11, 2018 - 9:09 pm
Dear Mrs./ Mr. Muthen

(1) After GMM analysis, I found both variable 1 and variable 2 has 2 latent categories. Though varaible 1 and varaible 2 were measured at the same time, can I use the LTA (example 8.7) to test whether latent category of the two variables are related ?

(2) The results were as following:
Categorical Latent Variables

C2#1 ON
C1#1 -4.165 1.695 -2.457 0.014

Can I suggest from the result that class1 of variable 1 is negatively related to class1 of variable 2?

Thank you very much.
 Bengt O. Muthen posted on Monday, August 13, 2018 - 9:36 am
Se UG ex 7.14.
 Bengt O. Muthen posted on Monday, August 13, 2018 - 9:38 am
The answer for (2) is Yes. You can relate c1 and c2 using either ON or WITH. For different latent class variable parameterization, see the end of Chapter 14 of the UG.