Table 3. Model fit and comparison statistics.

Model	$\overline{D}$	pD	DIC
Partial
(1a)	1320	81	1401
(1b)	1345	114	1459
Covariate£
(2)	952	32	984

$\overline{D}$ = posterior mean deviance, calculated as $\overline{D}={\rm E}\left[D\right].$ where D = −2log p(y|θ).

p_D = Posterior mean deviance—deviance of posterior means, calculated as p_D = E_θ|y [D]−D(E_θ|y[θ]).

DIC = Deviance information criterion, analogous to the frequentist AIC estimate and estimated as $DIC=D\left(\overline{\theta }\right)+2p_D.$

^£Several covariate models (which also included random effect terms) were fitted starting with a model that included all covariates that were screened in the univariate procedure with a liberal p ≤ 0.2, followed by the removal of one covariate at a time from the Bayesian hierarchical models. The removal of % grassland area, minimum land surface temperature and an interaction term, ‘diurnal temperature range x % mixed forest area’ one at a time, in that order resulted in models with DIC values of 1261, 1014, and 1008. To the final covariate model, a random effect space-time term, Ψ_ij was inserted, which resulted in a DIC value of 1023, indicating poor performance. Other previously removed covariates did not re-enter the final covariate model.