Modeling the influence of time-varyin... PreviousNext
Mplus Discussion > Growth Modeling of Longitudinal Data >
 Jason Bond posted on Friday, November 15, 2002 - 6:03 pm
Hello. In the paper:

Curran P. J., Muthen B.O., Harford T.C. (1998). "The Influence of Changes in Marital Status on Developmental Trajectories of Alcohol Use in Young Adults," Journal of Studies on Alcohol, 59: 647-658.

an analysis method which allows the effect of a covariate to propagate to current and subsequent response variables is proposed in a growth curve analysis. Upon implementing this, I have run into a identitication problem. The problem is with the the Time 1 additional factor (whose effect propagates to the time 1 through time 4 (the last time) response). Specifically, there is co-linearity between the intercept of the latent intercept term and the intercept of the time 1 additional factor, as shown in the ALPHA portion of the Technical 1 output. As both the intercept and the time 1 additional factor both have all paths from the factor to the response fixed to 1, this is expected. So I constrained their intercepts to be equal. A similar problem exists for the additional factor at Time 4. The factor mean is not defined. After fixing this to 0 (should this be fixed to the mean of the reponse at the last time point?), the problem then arises that the variances of the Time 1 and the Intercept factor are not uniquely estimable. I assume that fixing the factor variances of the intercept and this time 1 additional factor is the way to go. Is there a way to constrain factor variances to be equal? In the paper referenced above, a citation is given:

Muthen B.O. (paper in preparation). "Modeling the influence of time-varying covariates in latent curve analysis".

Is this paper available? Any input is greatly appreciated,

 Linda K. Muthen posted on Friday, November 15, 2002 - 7:48 pm
If you send the output to, I will take a look at it.
 Linda K. Muthen posted on Wednesday, November 20, 2002 - 2:23 pm
Thank you for sending the output. You need to fix the intercepts of AAt1, AAt2, AAt3, and AAT4 to
zero. Also you must fix the covariances of AAt1, AAt2, AAt3, and AAT4 with int and slope to zero.
 Shane Allua posted on Tuesday, May 30, 2006 - 2:42 pm
I have a model with 37 participants, each of whom provides 5 mood (DV) and 5 pain ratings (covariate) during two exercise sessions, which differ in intensity (E = easy, H =hard). Can I include both of the intensities (repeated factor)in the model? If my MODEL statement is correct for one of the intensities with time-varying covariates, can I just include a second i (i2) and s (s2)? The model, however, did not converge. Part of the problem may reside in the small sample size. Your help is appreciated.

MODEL: i1 s1 | em20@0 em40@1 em60@2 em80@3 em100@4 ;
i2 s2 | hm20@0 hm40@1 hm60@2 hm80@3 hm100@4 ;

stvch | hm20 ON hp20 ;
stvch | hm40 ON hp40 ;
stvch | hm60 ON hp60 ;
stvch | hm80 ON hp80 ;
stvch | hm100 ON hp100 ;
stvce | em20 ON ep20 ;
stvce | em40 ON ep40 ;
stvce | em60 ON ep60 ;
stvce | em80 ON ep80 ;
stvce | em100 ON ep100 ;

i1 WITH s1 ;
i2 WITH s2 ;

stvce WITH i1 ;
stvch WITH i2 ;

stvce WITH s1 ;
stvch WITH s2 ;
 Linda K. Muthen posted on Tuesday, May 30, 2006 - 8:30 pm
If I understand your question correctly, yes you can have more than one growth process in a model. Sometimes with this type of model, it is necessary to have residual covariances at each time point, for example, em20 WITH hm20; I would run each growth process separately to make sure they fit as a first step before putting them together. I would not add the time-varying covariates until this models is stable.
 Shane Allua posted on Tuesday, June 27, 2006 - 3:10 pm
As a follow up to the above model, I have set up the two intensities (hard=H and easy=E)as a parallel process model where the DV is regressed on the respective covariate for each time point for both intensities.
MODEL: i1 s1 | em20@0 em40@1 em60@2 em80@3 em100@4 ;
i2 s2 | hm20@0 hm40@1 hm60@2 hm80@3 hm100@4 ;
hm20 ON hp20 ;
hm40 ON hp40 ;
hm60 ON hp60 ;
hm80 ON hp80 ;
hm100 ON hp100 ;
em20 ON ep20 ;
em40 ON ep40 ;
em60 ON ep60 ;
em80 ON ep80 ;
em100 ON ep100 ;

em20 WITH hm20 ;
em40 WITH hm40 ;
em60 WITH hm60 ;
em80 WITH hm80 ;
em100 WITH hm100 ;

It appears that the Mplus default is to correlate the covariates with the intercept and slopes of both processes. In my model, most of them are not significant. What is the importance of having the covariates correlate with the intercept and slope factors? Thanks for your time.
 Linda K. Muthen posted on Wednesday, June 28, 2006 - 8:23 am
Mplus does not covary covariates with other variables as far as I know. You would need to send your input, data, output, and license number to Say which covariances are the issue.
 Jan Hochweber posted on Tuesday, September 15, 2015 - 8:29 am

when specifying a standard latent growth model with a time-varying covariate (TVC), it seems that regressing the repeated measurements on the covariate does not imply that covariances between the covariate and the growth factors are estimated.

1) Considering, for example, Preacher et al.'s (2008) LGM book (Figure 2.7, p. 47) or Curran and Hussong (2003, Figure 5), I would assume that these covariances would have to be part of the model, by specifying, for instance:

i s | y1@0 y2@1 y3@2;

y1 on x1;
y2 on x2;
y3 on x3;

i s with x1-x3;

On the other hand, User's Guide Example 6.10 (also, e.g., the model in Curran, Muthén, & Harford, 1998) does not include any direct relationships between the TVC and the growth factors (albeit with time-invariant covariates). What would be your recommendation with respect to the TVC's association with the growth factors?

2) Do I assume correctly that specifying covariances between the TVC and the growth factors (as done above) implies a multivariate normality assumption on the covariates? If so, is there a reasonable way to include categorical TVC?

Many thanks in advance.
 Bengt O. Muthen posted on Tuesday, September 15, 2015 - 7:41 pm
It's good question. It seems like one should let growth factors and TVCs correlate - the question is how (what influences what - and, is WITH ok). We discuss that in our short course Topic 3; see the video and handout on our website. Slides 138-159 go through various models, such as "M3".

2) Multivariate normality should be ok when you condition on the covariates, that is, they are not DVs.
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