Violating Homogeneity

#1
Hi,
if in regression models homogeneity is violated, the variance can in principle depend on both: Predictor and outcome variable(s).

In case of a dependency on categorical or continuous predictor variables, there are many ways to model different dependencies, e.g. using GLS models.

In contrast, regarding a dependency of the variance on the outcome, I only know Poisson regression where the variance equals the expected value and thus increases with the outcome. But if I have another dependency of the outcome (e.g. variance = outcome^2), does somebody know ways to model this?

Thanks
 

hlsmith

Less is more. Stay pure. Stay poor.
#2
So you have count data? Sounds like overdispersion. There is quite a bit of literature on it. I believe the negative binomial model is an option.
 
#3
I don't have a special problem in mind, and you are right, in case of count data one could use quasi-Poisson or negative binomial models, or indtruducing an observation level random factor. But in all of these cases (including a regular Poisson model) you model in principle the same: A linear increase of the variance with the outcome. But now I am wondering if
1.) qualitative other relationships between variance and outcome (nonlinear dependency of variance on the outcomes or a variance decreasing with the outcome) make sense / appear in real world problems, and
2.) how to model this
 

hlsmith

Less is more. Stay pure. Stay poor.
#4
This sucks, but an option is to trim your data. So just use those data with homogenuous errors. Though, I am not overly experienced with count base regression models
 

Dason

Ambassador to the humans
#5
This sucks, but an option is to trim your data. So just use those data with homogenuous errors. Though, I am not overly experienced with count base regression models
Doesn't seem like a great approach. You can specify in a model that your variance is increasing in some fashion. It's not quite as nice as just doing a vanilla linear model but it's definitely possible.