variance attributable to individual level in negative binomial regression

[vahid yazdi]

I am working on a two-level (negative binomial regression model) in Stata software. I selected an outcome variable (a count variable related to behavior of students). this variable is a variable with over-dispersion (no equality of variance and mean). I have a question that how can I calculate the variance of bottom level (e.g individual level in case of students within schools) in final model. The output of Stata give a var(cons) for school level which is statistically significant. However it does not show as for individual level. I want to know that how much the variance of outcome variable is explained by individual level (i.e students). please guide me more.

[Clyde Schechter]

What you are asking for is actually very complicated, and, in a strict sense, does not exist.

When you fit a linear regression model, the individual level variance is a parameter of the model: it is the variance of the error distribution, which is taken to be normal with a constant variance. But in a negative binomial model, the error distribution has a negative binomial distribution, and the variance of that distribution is actually a function of the predicted value. (Just as it would be in a Poisson distribution, where variance = mean; it's just more complicated for negative binomial.)

I suppose it is possible, in principle, to actually calculate the corresponding variance for each individual observation in your data, and then somehow combine all of those into some summary statistic (though that statistic would not itself be the variance of any distribution related to the model). But it could be time consuming and complicated to code this, and I can't really see any way that the result would actually be useful for anything.

[vahid yazdi]

Dear schechter so many Thanks for your guidance.