# [R-meta] Covariance matrix specification for multiple levels + specifying random slopes model

Mick Girdwood M@G|rdwood @end|ng |rom |@trobe@edu@@u
Thu Feb 23 02:00:07 CET 2023

```Hi everyone,

Thank you in advance for your help, the advice from this board is always friendly and indispensable.

I am conducting a longitudinal meta-analysis, (thank you Reza for your advice relating to a previous question to do with this https://stat.ethz.ch/pipermail/r-sig-meta-analysis/2023-January/004349.html ). I have two things I was hoping you could help me with. Similar to this previous question here https://stat.ethz.ch/pipermail/r-sig-meta-analysis/2021-April/002794.html

At the moment I had planned to use the 'longitudinal meta-analysis' per measure (outcome) of interest. However it occurred to our team that we have many similar measures of the same outcome (in this case quadriceps muscle strength). We wondered whether it would be better to use all this information in one analysis (instead of running separately for each, and use each measure to borrow strength). The reason being that the different measures are correlated with each other (as well as the timepoints). At the moment we landed on a potential model specification looking like this:

rma.mv(yi, V,
random = list( ~ timepoint | interaction(cohort, outcome), ~ outcome | cohort),
mods = ~ outcome : log(timepoint),
struct = c("CAR", "HCS”))

We have 3 different levels for outcome and timepoint is a continuous measure (hence CAR)

1. The thing I’m struggling with is how to get an appropriate V covariance matrix. Previously before including outcome I had used impute_covariance_matrix() with ‘cohort’ as the cluster. But now there is another level of correlated effects to consider - outcome. How can I account for this? Or should I just fix phi as the correlation parameter for the 2nd random component relating to outcome?

2. Another approach we considered was using a random slopes and intercept model, with a random slope for outcome (3 levels). Would this just be a case of changing the struct to “GEN” for the 2nd parameter? But then that is outcomes nested within cohorts. So it just needs to be 1 | outcome then?

Thank you so much for your help, I am indebted!

Mick Girdwood
La Trobe University | Australia

[[alternative HTML version deleted]]

```