Past exam of the mathematics course of the University of Cambridge / 2023 / iii / Paper 218 / 1 / c

With $X$ having rows $x_i^T=(1,g_i,m_i)$ and ${\mu }_i(\beta )=e^{x_i^T\beta }$, the quasi-score equation isIt is the same coefficient equation as for Poisson maximum likelihood, explaining why the two models have identical coefficient estimates.

Let $W=\mathrm{diag}({\hat{\mu }}_1,\dots ,{\hat{\mu }}_n)$ and let coordinate $2$ denote gender. The model-based standard error is