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I am interested in running a multivariate multi-level model with longitudinal data, and I'm having a hard time conceptualising the hierarchy levels.

My variables are:

  • Multivariate outcome: Quality of life scores (continuous) with 5 domains (Physical, Psychological, Autonomy, Peer, and School).
  • Individuals are repeatedly measured every 6 months for 2 years (4 time-points).

Is the hierarchy:

  1. Level 1 (Time: T1, T2, T3, T4)
  2. Level 2 (Quality of Life Domain: Physical, Psychological, Autonomy, Peer, and School)
  3. Level 3 (Individual)

OR

  1. Level 1 (Quality of Life Domain: Physical, Psychological, Autonomy, Peer, and School)
  2. Level 2 (Time: T1, T2, T3, T4)
  3. Level 3 (Individual)

Basically, what is my Level 1 variable here? Is it time? Or the different outcomes?

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  • $\begingroup$ Welcome to CV. The hierarchy depends on your research question. What are your predictors (independent variables)? Just time? If so, I wouldn't use time as a random effect, but as a predictor, in which case time wouldn't be in the random effect hierarchy. In that case individual would be on Level 2 and individual quality of life ratings would be on Level 1. QoL domains status depends on whether you'll use it as a fixed predictor or a random effect. $\endgroup$
    – Sointu
    Commented Aug 11, 2023 at 21:12
  • $\begingroup$ Thanks for your reply @Sointu - My predictors would be Time (just to explore if/ how QofL changes over time), and then next I would explore the influence of a categorical independent variable (class membership from a separate latent class growth model I'm running). When looking at the influence of the categorical IV on QofL over time, which hierarchy would it be? $\endgroup$
    – Emma L
    Commented Aug 20, 2023 at 20:19

1 Answer 1

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Edited to put the thing you actually asked first: you don't have a random effect hierarchy. All your potential random effects (participant, domain and time) are on the same "level". You can specify them as crossed random effects in your model. Using the multilevel language, your individual QoL observations are on level 1, and participant, domain and time are all on level 2.

As I mentioned, I wouldn't use time as a random effect in your situation though.

So using time as predictor, you first need to decide whether you want to use time as continuous (if assuming a linear change in QoL over time) or categorical predictor.

If continuous, I'd probably predict QoL ratings with continuous time and and your class variable and their interaction, including random intercepts of participant and QoL domain.

If you want time as categorical, I'd use the same model, just specifying time as categorical. In both of these cases, you'd put participant id and QoL domain in as independent (crossed) random effects. In R, this would go

model<-lmer(QoL ~ (1|participant)+(1|QoLdomain)+time*class, data=data)

Possibly, you'd want to include a random slope of time, which would give you estimates of time on QoL separately for each participant. For instance like this

model2<-lmer(QoL ~ time*class+(time|participant)+(1|QoLdomain), data=data)

I personally might consider using QoL domain as categorical fixed predictor too, maybe like this because I'd like to know if QoL changes differently in different domains.

model3<-lmer(QoL ~ time*class+time*QoLdomain+(1|participant), data=data)

You can use time and/or QoL domain as random effects if you want, but in that case you don't get the estimates of these variables predicting QoL, just estimates of how much variance out of QoL they explain. And you can't put a variable in as both categorical fixed predictor and as random effect, as those estimates use the same variance and would be "estimated twice" if you did that (it is possible to put in time as a continuous predictor and as random effect if you feel that would give relevant info).

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