where V( · ) denotes the variance function. In Eq. (10), the variance of Y is proportional to an unknown constant σ 2
and the extra variation in the data can thus be handled without affecting the structure of the mean response. σ 2
> 1
implies over-dispersion, while 0 < σ 2
< 1 implies under-dispersion. In a QL model, the usual parameter of interest
is µ . Adopting the notation of McCullagh and Nelder (1989), the quasi-log-likelihood is defined as,