Choosing count models

I have 2 questions on count models

  1. based on the research question below, what model should I use: poisson, negative binomial regression or zero-inflation? How are they different?
  2. Is this count model or multivariate model?

My research question is what factors determine the location of a nonprofit organization. There are two categories of factors: industrial features determining the type of organizations, and government spending determining the number of organizations. the outcome might be:
county 1: 3 schools + 20 museums + 5 research centers + 1 church = 29 org
county 2: 2 schools + 0 museum + 0 research centers + 0 church + 1 hospital = 3 org
county 3: 0 schools + 0 museum + 0 research centers + 0 church + 0 hospital + 1 food pantry + 2 thrift stores = 2 org

Essentially, I am interested in both the type of organization and the number of organizations.

Please also provide the following information in addition to your question:

  • Operating System: Microsoft Windows
  • brms Version: 2.4.0
  1. I would suggest fitting all three models and then compare them, for instance via pp_check and loo.

  2. If you have just one response variable, it’s a univariate model. If you have multiple response variables, it’s a multivariate model. Responses may be counts in both cases.