I am currently working on methods for a thesis project. I will be modeling the outcome of disease incidence for two different diseases using negative binomial regression. It will most likely be zero-inflated negative binomial regression. The predictor variables will be the same for each model, and I would like to compare the beta coefficients. My models will look as follows:
$_1=β_1+β_2+…+β_$
$_2=β_1+β_2+…+β_$
where all betas are the same variables and observations, and $Y_1$ is incidence for one disease and $Y_2$ is incidence of another disease.
Would it be possible and make more sense to concatenate the two datasets and build nested models via making each predictor variable an interactive term with a dummy variable stating that it is a part of one disease outcome? This is shown below:
$(\text{incidence})=_1_1 + _1_2 + _2_1 + _2_2 +...+ __1 + __2$
Where $_1$ is a $1$ or $0$ indicating it is an observation from the original $_1$ dataset and $_2$ is a $1$ or $0$ indicating it is an observation from the original $_2$ dataset?
I have found some information on doing this method using linear regression, but I am unsure if it would apply to negative binomial regression.