In Example 4.3, apply the existing ZIP regression, but using a mixed predictive check based on replicate

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In Example 4.3, apply the existing ZIP regression, but using a mixed predictive check based on replicate \(t_{r e p, i} \sim \operatorname{Bern}(\zeta)\). This should show the proportion of underpredicted cases to be around \(4 \%\).

Data from Example 4.3
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