[R-sig-ME] weights in mixed modelling

[Mollie Brooks]

Hi Alex,

I was previously thinking about ways to do a meta-analysis on beta distributed data. The discussion here might be relevant to your problem https://github.com/glmmTMB/glmmTMB/issues/156#issuecomment-276046838 <https://github.com/glmmTMB/glmmTMB/issues/156#issuecomment-276046838>

You might want to use the dispersion formula instead of weights and transform the uncertainties to be on the right scale of the dispersion model.  In glmmTMB and betareg's formulation of beta regression, var = mu*(1-mu)/(1+phi). Solving that equation for phi gives phi = mu*(1-mu)/var -1.

So if you have a collection of estimated proportions (mu_hat) and variances (var_hat), where mu_hats are beta distributed, then it might make sense to use dispformula =~ mu_hat*(1-mu_hat)/var_hat -1 or dispformula =~ mu_hat*(1-mu_hat)/var_hat in a meta-analysis. As Ben says in comments further down the Github issue, you would want to simulation test this idea to make sure it works. 

I’m not sure about breaking up observations that you mention.

Cheers,
Mollie


> On 14Jan 2021, at 18:00, Baecher,Joseph Alex <jbaecher using ufl.edu> wrote:
> 
> Hi everyone,
> 
> I’m looking for advice and/or information about using weights in mixed modelling. My colleagues and I are conducting an analysis and we’ve attempted to use weights to solve two issues. As is likely obvious, I am not a statistician, so please excuse my ignorance! We’re using data gathered from several hundred studies. The studies represent a spectrum of quality and robustness and therefore we have created an standardized “index of study quality” to rank each of the data sources. It was our (perhaps dubious) understanding that we could use such an index as model weights in our analysis. There are also instances in which studies’ presented data in aggregate, and therefore we had to break data into multiple observations. We had hoped weights could mitigate any issues arising from pseudoreplication. For this, we created an “observation weight”, in which each independent observation was assigned a weight of 1 and observations which were broken into multiple observations were given a weight = 1/(# of observations). We thought combining the “index of study qualities” with the “observation weight” via multiplication could give us a composite weight… The model we are using is a Beta-distributed mixed effects model, fitted using  ‘glmmTMB’.
> 
> If you have any advice or suggestions or relevant reading materials, I would greatly appreciate it.
> 
> Thank you in advance for your time and patience,
> 
> All the Best,
> 
> -Alex B.
> ~~~~~~~~~~~~~~~~~~~~~~~~~~~
> J. Alex Baecher (he, him, his)
> PhD student, Research Assistant
> School of Natural Resources and Environment
> University of Florida
> 354 Newins-Ziegler Hall
> Gainesville, Florida 34611 (USA)
> --
> phone: ‪(352) 575-0454
> e-mail: jbaecher using ufl.edu<mailto:jbaecher using ufl.edu>
> website: www.alexbaecher.com<http://www.alexbaecher.com/>
> ~~~~~~~~~~~~~~~~~~~~~~~~~~~
> 
> 
> 
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