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Mplus Discussion > Multilevel Data/Complex Sample >
 Jennifer Lloyd posted on Thursday, June 12, 2008 - 5:34 pm

I have *three waves* of data for individual children:

(1) Time 0 = Kindergarten (readiness for school measure)
(2) Time 1 = Grade 4 (academic achievement measure)
(3) Time 2 = Grade 7 (academic achievement measure)

My ultimate interest is seeing the way in which children's developmental trajectories (from Time 0 to Time 1 to Time 2) vary across residential neighbourhoods.

Here is the rub: Because the Time 0 measure is 'non-equatable' with the Time 1&2 measures (they measure different constructs), then I *cannot* include the measures in a three-wave growth model, or else the results would simply be uninterpretable (as per Singer & Willett, 2003).

Therefore, can I instead run a regular two-level HLM model (kids within neighbouhoods) within the SEM framework, in which the Time 2 measure is my DV and the Time 0&1 measures simply serve as Level-1 predictors?

If so, can I use SEM to explore both (a) the effect of particular Level-1 mediators and (b) the role of particular Level-2 predictors?

Thanks for any guidance!
 Linda K. Muthen posted on Friday, June 13, 2008 - 10:55 am
It is hard to do growth modeling even with three repeated measures. I would stick with a simple model of either:

y2 ON y1;
y1 ON y0;


y2 ON y1 y0;
y1 ON y0;

How many neighborhoods do you have and how many children per neighborhood?
 Jennifer Lloyd posted on Monday, June 16, 2008 - 11:05 am
Dear Dr. Muthen,

Thanks so much for your reply. I have 30 neighbourhoods, and approximately 40-100 children per neighbourhood.

I figured that a simple two-level model was going to be the way to go, rather than a growth model. Therefore, I am leaning towards [y2 ON y1 y0].

Thanks again!
 Christoph Schaefer posted on Wednesday, August 14, 2019 - 11:41 am
Dear Professors,

In a study with repeated measures, there are ten waves. The research question is whether an observed continuous UV influences an observed continuous AV. One is not interested in whether there is a trend in time. One would like to know, instead, whether the UV at t influences the AV at t+1.

My questions:
Q1: Is it possible to model this case as a two-level model in Mplus (with the individuals at level 2 and the measures of the waves at level 1?)
Q2: Given that one is not interested in the trends, is it possible to ignore the sequence of the waves (except the fact that the UV at t is assigned to the AV at t+1)?

Best regards,
 Bengt O. Muthen posted on Wednesday, August 14, 2019 - 5:14 pm
Q1: Check our Time series page for ways to do this:


The UG has many such examples in Chapter 9. Also, we have Short Course Topics 12 and 13 with videos and handouts on this. 10 times points is a bit small for this, but your model seems simple.

Q2: Don't know what you mean by "ignore the sequence" but I think the above sources will answer this.
 Christoph Schaefer posted on Thursday, August 15, 2019 - 3:03 am
Many thanks.

If I may specify my question a bit: If I am not interested in the effect of time or any trends, but only interested in the effect of a measured continuous UV, could I simply specify a multilevel model (with individuals at level 2, and time points at level 1)? Is there a problem with this two-level design?
 Bengt O. Muthen posted on Thursday, August 15, 2019 - 5:29 pm
Q1: Regular multilevel modeling does not easily allow for UV at t influencing the AV at t+1 (the time points need to be the same). But the time series approach I referred to does allow this in a very straightforward way. And it also allows for auto-regression.

Q2: See above.
 Christoph Schaefer posted on Friday, August 16, 2019 - 7:57 am
Thank you! The short courses, the examples, and your comments were very helpful.
If I may double-check whether I specify my model correctly: The aim of following model is to test whether x has an effect on y. (For the sake of simplicity, there is only an immediate effect of x on y modelled in this example.)

sy| y on y&1;
sx| y on x;
y on xm;
y sy sx with y sy sx;
 Christoph Schaefer posted on Friday, August 16, 2019 - 12:59 pm
(The background for that preceding post: I was wondering whether one could specify "s | y on y&1 x;" but since I have not found this line in an example, I guess that this is not advisable.)
 Bengt O. Muthen posted on Friday, August 16, 2019 - 5:45 pm
With only 10 time points, you need to keep the model simple and not use random slopes, only random intercepts. So say:

y on y&1;
y on x&1;
x on x&1;
y on x;

Regarding number of time points and N, see

Schultzberg, M. & Muthén, B. (2018). Number of subjects and time points needed for multilevel time series analysis: A simulation study of dynamic structural equation modeling. Structural Equation Modeling: A Multidisciplinary Journal, 25:4, 495-515, DOI:10.1080/10705511.2017.1392862. (Supplementary material).
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