Three level multilevel model, repeated measures & the effect of time

[Samantha Russell]

Dear All,
I am have decided to use a three level multilevel model and I feel somewhat unsure if the model I specified will answer my questions of interest. I am also unsure of how to assess the effect of time. I have described my data and my proposed statistical model, I would be really grateful if someone can take a look and give me some feedback.

I have searched through the earlier posts but have not found any earlier posts which could help me.

Research Aim: This study will investigate the interplay between indicators of NSC and NSD, and their shared impact on a given outcome YY.
Data Design: My data consists of young people aged 10-15, with measures collected at 5 separate time points nested with neighbourhoods. The data is organized so that there is a one year interval between each time point. In short, it is a longitudinal data (panel). However, the outcomes I am measuring are only at time point 1, 3 and 5.

Proposed Statistical Method: In order to account for the hierarchical nature of the data, and to avoid an underestimation of the standard errors, I would like to fit a three-level multilevel linear regression models. My idea is that these models will account for the fact that the data consisted of repeated measures across three waves of data- 1, 3 and 5 (at level 1) nested in individuals (at level 2) clustered within neighbourhoods (at level 3).

Questions:

1. What I now feel unsure about is the fact that variable NSC was measured at one time point (wave 3). What I would like to know is the model that I have proposed reasonable given that NSC variables are only at one time point? If no, what are my alternatives?
2. Will the syntax in model 1 below provide me with information about the proportion of variation to be found at each level (i.e. level 1, level 2 and level 3)? Is it possible to graph this variation? If yes, could you please provide me with a code for this?
3. I also wanted to assess if time (i.e. time of data collection) has a significant influence on young people’s outcome. Would the specification in model 2 provide me with this information?
4. Is the specification of model 3, the inclusion of other explanatory variables/confounders in the fixed part of the model as it should be?

Variables: (a)yy- outcome, (b) age10 – age centered, (c) wave-time of data collection, (d) id-individual identification , (e ) area-neighbourhood, (f) x1-x4- other covariates
Model 1:
mixed yy age10 || area:wave, covariance(unstructured) || id :wave, covariance(unstructured) mle nolog

Model 2:
mixed yy c.age10##c.wave || area:wave, covariance(unstructured) || id :wave, covariance(unstructured) mle nolog

Model 3:
mixed yy c.age10##c.wave x1 x2 x3 x4 || area:wave, covariance(unstructured) || id :wave, covariance(unstructured) mle nolog

Thank you kindly for your time beforehand.
Samantha

[Henrique Neder]

Dear Samantha

I'm new in mixed models but I think that your problem is somewhat near what I'm doing and my doubts.
In the model 1 you are representing the following:

y_{ijt} = beta_0 + beta1*age10_{ijt} + area_j* wave +error_{ijt}
where area_j is a random effect by area
But you are including one slope wave coefficient by area and you haven't wave in the fixed effect part. I think that this is not correct.

I suppose that you are trying to use the panel capabilities of you data. So the first level is the young people, the second level is the neighborhood and the third level is wave. The simplest model would be:

mixed yy age10 || wave: area: id, covariance(unstructured)
yy_{ijt} = beta_0 + beta_1*age10_{ijt} + u_t + u_j + u_i + error_{ijt}
u_t, u_j and u_i are random intercepts, by wave, area and subject.

Henrique