Table 5.

Deviance information criteria for independent modeling and multivariate modeling (M-based BYM) of the Bayesian models

	Deviance information criteria
Modeling	α(+βχ ι)	$\mathit{\alpha }+{\mathcal{V}}_{\mathit{i}}\left(+\mathit{\beta }{\mathit{\chi }}_{\mathit{\iota }}\right)$	$\mathit{\alpha }+{\mathcal{U}}_{\mathit{i}}\left(+\mathit{\beta }{\mathit{\chi }}_{\mathit{\iota }}\right)$	$\mathit{\alpha }+{\mathcal{U}}_{\mathit{i}}+{\mathcal{V}}_{\mathit{i}}\left(+\mathit{\beta }{\mathit{\chi }}_{\mathit{\iota }}\right)$	M-based BYM with fixed effects	M-based BYM with random effects
Without covariate	8141.7	8006.8	7969.5	7961.4	6947.84	7131.05
With covariate	8051.9	7941.5	7895	7900

(+βχ _ι) in case of additional covariate - $\mathcal{U}$ : Autocorrelation - $\mathcal{V}$ : heterogeneity $\mathcal{X}$ Townsend index components