Repeated measurements from one person can share persistent unobserved spending tendencies, violating model1's independent-error assumption and shifting that person's baseline. Model2 represents this <clustered data> through a common random intercept $b_i$, which induces within-person covariance $\operatorname{Cov}(Y_{ij},Y_{ik}\mid X)=\sigma^2$ for $j\ne k$.

Solution

Past exam of the mathematics course of the University of Cambridge / 2025 / iii / Paper 218 / 5 / b / Solution

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Clustered data are grouped observations for which measurements in the same group may be dependent, as with repeated measurements on one subject.


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