8. Consider the data in Example5 8.odc on religious affiliation for 133 small area populations in North East London (2001 UK Census). These are Christian, Buddhist, Hindu, Jewish, Muslim, Sikh, Other religion, No religion, Religion not stated. Compare the fit of the fixed effects multinomial, namely

(with c j = 1 all j) to that of the Dirichlet-multinomial and the multivariate logit-MVN model of (5.9)–(5.10) for multinomial smoothing. Consider both the DIC and posterior predictive checks.

(yil, yi2, YiJ) ~Mult(ni, [il, Ti2, ..., ;J]) (iii)~Dir(c..... c1)