Modeling sigma to account for cluster heteroskedasticity

I’m not entirely certain where to put this question but was hoping for a little direction/help in finding some literature.

I have panel data of newspaper-days. I am testing how newspaper level covariates predict their daily coverage (several different measures). I know I should account for heteroskedasticity within newspapers, one obvious way to do this seems to be to use the distributional modeling approach discussed here. So I have modeled the sigma as a random intercept for each paper.

My problem is that I am having trouble finding literature that actually supports this method. I was hoping someone might have a suggestion of where I can look.

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There are article and books about glm that support the approach, you can search for “joint modelling of mean and dispersion” in the glm litterature (several paper/chapters between 1980 and 1995)

There is also information in the classical beta regression paper, as precision and mean are often modeled together.

Finally, there are papers and books related to GAMLSS, an article around 2006 or 2008 and all the paper around the associatrd package.

I am not actually on my computer, so I cannot find the exact papers, sorry. I would be able to send the exact reference tomorrow, but they should be easy to find. They are also listed in my preprint (method part) :

Have a good day!


You may want to look into “Location scale models” or “MELSM” (mixed effects location scale model).