Overdispersion in clinical mastitis ata from dairy herds: a negative binomial approach

Cases of clinical mastitis on diary farms were modelled using a negative binomial distribution. The negative binomial distribution is a gamma mixture of Poisson distributions, hence it is possible that the number of cases per farm had a Poisson distributions and the mean of these Poisson distributions had a gamma distribution. Risk factors associated with the number of cases per farm can be modelled with a negative binomial distribution but calculations involving the negative binomial likelihood are not straightforward. However, a very close approximation to the negative binomial is the Poisson model with an extra parameter for overdispersion. Fitting the Poisson model with overdispersion is illustrated.