Poisson regression model: Multi-level mixed, fixed or random effects

[Sabrina Chapman]

I am currently exploring the relationship between funding of health centers (9000) and mortality of patients registered in these centers over a 5-year period. My omitted variables are likely to be correlated with the explanatory variables in which case a random effects models may not be appropriate. Given that there is very little year-on-year variation within health centers with regards to funding and deaths and greater greater variation between these centers, a fixed effects model may also be inappropriate. My data is over dispersed, therefore was hoping to deal with this incorporating robust standard errors. Would a Multi-level mixed Poisson regression an option given that neither a fixed or random effects model seem appropriate? Thank you for your time.