The beta-binomial model mixes binomials over a beta-distributed success probability. The random-intercept generalized linear mixed model instead takes
$$
\operatorname{logit}(P_j)=z_j^T\beta+b_j,\qquad b_j\sim N(0,\tau^2).
$$
Both create within-user dependence and overdispersion, but use different mixing distributions. The mixed-model coefficients are conditional on the random effect, while beta-binomial regression is naturally phrased through a marginal mean.


Solution

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

 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2021/iii/paper-218/2/e/solution