I am wondering how to correctly interpret and describe the coefficients (betas) in a multilevel mixed effects negative binomial regression analysis. I conducted this analysis in Stata with the menbreg command. I further standardised the independent variables. Let's assume the following regression output where restaurant visits of individuals are regressed on their financial income and age. Many of them did not visit restaurants at all, therefore the negative binomial regression analysis. Visits of different restaurant are nested in individuals.
Given that it is multilevel mixed effects negative binomial regression based on standardised predictors, how to correctly interpret the coefficients (betas) below? What does one unit change in the predictor variable mean in regards to the dependent variable? All advice would be highly appreciated.
Best Answer
Assuming that you have used the log link, and that the estimates given are on the log-odds scale:
Every 1 standard deviation change in Income is associated with a 0.32 change in the log-ods of the outcome, leaving Age unchanged. Alternatively, every 1 standard deviation change in Income is associated with a $100 \times (\exp{0.32} - 1 ) = 37.7$ percent change in the outcome, leaving Age unchanged.
Every 1 standard deviation change in Age is associated with a 0.22 change in the log-odds of the outcome, leaving Income unchanged. Alternatively, every 1 standard deviation change in Income is associated with a $100 \times (\exp{0.22} - 1 ) = 24.6$ percent change in the outcome, leaving Age unchanged.
Also, with most software, the fixed effects coefficients have an interpretation that is conditional on the random effects due to the nonlinear link function. That is, the estimates for Income and Age are for subjects visiting the same retaurant. It would be good to verify that the estimates from
menbregproduce conditional estimates - if they are marginal estimates instead, then this interpretation does not apply.