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

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- Solution e

Solution

The beta-binomial model mixes binomials over a beta-distributed success probability. The random-intercept generalized linear mixed model instead takes

logit (P_{j}) = z_{j}^{T} β + b_{j}, b_{j} \sim N (0, τ^{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.

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