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Levels within the multilevel model were patient (level 1) within practice (level 2).

Most of the prior distributions of hyperparameters used in our multilevel model were not conjugate.

Levels within the multilevel model were persons (level 1) within geographical area (LSOA, level 2).

Appropriately reflecting the between-hospital heterogeneity, the 95% confidence intervals for hospital-level variables in the marginal and multilevel model were wider than in the ordinary logistic regression.

The patients' demographic and clinical characteristics to be included in the multilevel model were identified in a preliminary stepwise logistic regression model (significance level of entry = 0.05; significance level of removal = 0.10).

Overall the 95% CIs for hospital-level variables in the marginal and multilevel model were wider than in the ordinary logistic regression, reflecting the between-hospital heterogeneity that is erroneously not accounted for in the latter model.

The resulting multilevel model is fit with RJMCMC (Richardson and Green 1997) to obtain posterior distributions for the number of sources and their individual parameters.

The resulting multilevel model is fit with reversible jump Markov chain Monte Carlo (RJMCMC) to obtain posterior distributions for the number of sources and their individual parameters.

Second, a multilevel model was employed for the substantive statistical analyses, in which villagers were nested within villages.

The multilevel model was applied to the villager dataset alone, and to the villager and village datasets combined.

Changing patterns of diversity projected from the multilevel model are very similar to the patterns of diversity projected from Maxent.