= Solution
For the common <Bayesian deviance> convention $D=-2\log L$ used in all three models,
$$
p_D=\overline D-D(\overline\theta),\qquad
\operatorname{DIC}=\overline D+p_D=D(\overline\theta)+2p_D.
$$
Here `Dhat` is $D(\overline\theta)$, an at-posterior-mean fit measure, and $p_D$ is an effective parameter count. The independent model's `Dhat` of 53.1 is almost identical to the exchangeable model's 53.2; both improve on the common model's 57.8. The common model's $p_D=7$ corresponds to six intercepts plus one shared effect. Independence uses roughly twelve effective parameters. <Partial pooling> reduces the exchangeable model's effective complexity to about 8.7 while retaining nearly the same fitted <likelihood function> as independence.
\b[The exchangeable model has the lowest reported DIC, but the common model is competitive.] Their difference is only about 1.3, whereas independence is worse by about 6.3. The <deviance information criterion> measures penalized fit for a predictive comparison, not model <posterior probabilities>, and these numbers do not establish overwhelming evidence for heterogeneity. The displayed exchangeable $\overline D+p_D$ is $61.9+8.7=70.6$, rather than the printed 70.5; rounding of the underlying values can account for a tenth and does not change this interpretation.
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