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[R-meta] Plotting the correlation among true/random effects across categories

5 messages · Wolfgang Viechtbauer, Yuhang Hu

Wolfgang Viechtbauer
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You get the estimated variation in the underlying true means of each category (around the fixed effects, which correspond to the expected value of the underlying true means of each category) and the correlation of that variation between the two categories. I have now added the model to the write-up of this example here:

https://www.metafor-project.org/doku.php/analyses:berkey1998

so you can see exactly what the code (given on that page) corresponds to model-wise.

Best,
Wolfgang
15 days later
Yuhang Hu
# 
Hi Wolfgang,

Thank you very much for your response. I wanted to ask two
questions regarding your responses.

1-- If instead of struct="UN", I use struct="GEN" (below), then what does
the correlation reported between AL and PD represent?

My understanding is that it represents the correlation between the
'differences' (not between the means of AL and PD) between AL and PD across
the trials, right?

model <- rma.mv(yi~ outcome, vi, data =  dat.berkey1998,
                random = ~ outcome | trial, struct = "GEN")

2-- You mentioned that the estimated variation by the model (say tau2)
accounts for an additional piece (i.e., E(var(u_i|y_i))) in random effects
(ui) that is not present in the BLUPs.

My question is then, is the variation, or correlation obtained by the model
preferred over (and more reliable than) that obtained by hand-calculating
them from the BLUPs?

Many thanks,
Yuhang

On Thu, Jun 1, 2023 at 8:18?PM Viechtbauer, Wolfgang (NP) <
wolfgang.viechtbauer at maastrichtuniversity.nl> wrote:

            

      
      
      
    

        

  
  


  


      

    

    
4 days later

    

      
      

        


  

        

      Wolfgang Viechtbauer
    

    

      
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Hi Yuhang,

1) In the model below, 'outcome' turns into a dummy variable that is 1 for PD and 0 for AL. So the intercept random effect represents variation in the treatment effects for AL, while the outcomePD random effect represents variation in how much the treatment effects differ for PD compared to AL. The correlation is then the correlation between these two random effects.

2) That depends on what you are interested in. But if you want to know how much variance there is in a random effect, I would take the variance estimate (and not compute the variance of the BLUPs) and similarly if you are interested in the correlation between two random effects.

Best,
Wolfgang

            

      
      
      
    

  
  


  


      

    

    
2 days later

    

      
      

        


  

        

      Yuhang Hu
    

    

      
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Thanks, Wolfgang.

Just curious, if not useful for variance and correlation estimation, then I
wonder when and how BLUPs are needed in practice?

Thanks,
Yuhang

On Wed, Jun 21, 2023 at 8:57?PM Viechtbauer, Wolfgang (NP) <

        
wolfgang.viechtbauer at maastrichtuniversity.nl> wrote:

        

            

      
      
      
    

        

  
    

      
      
    

  


  


      

    

    
2 days later

    

      
      

        


  

        

      Wolfgang Viechtbauer
    

    

      
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They can be useful for various things:

1) for diagnostic purposes (e.g., assessing normality assumptions),
2) they can provide an estimate of the treatment effect in particular studies (that not only takes the observed effect from the study into consideration, but borrows information from the other studies),
3) there might be circumstances where one uses the BLUPs as predictors for other things (in a two-stage type of analysis).

Best,
Wolfgang