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?
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)?
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?
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.
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.)
%Within% sy| y on y&1; sx| y on x; %Between% y on xm; y sy sx with y sy sx;
With only 10 time points, you need to keep the model simple and not use random slopes, only random intercepts. So say:
%Within% y on y&1; y on x&1; x on x&1; %Between% 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).