Past exam of the mathematics course of the University of Cambridge / 2021 / iii / Paper 218 / 2 / c / Solution

For $m_j$ exchangeable Bernoulli responses of mean $p_j$ and pairwise correlation $\rho$,A standard quasi-binomial model uses a common dispersion multiplier $\varphi$. It cannot represent this variance simultaneously when the offer counts $m_j$ vary, because the multiplier $1+(m_j-1)\rho$ then varies by user.