Table 1 Deviance information criterion (DIC) for five spatiotemporal models.

From: Spatiotemporal Analysis of Influenza in China, 2005–2018

Model

\(\bar{D}\)

pD

DIC

Model 1*

1129876.4

363.9

1130240.2

Model 2**

1129876.6

363.9

1130240.5

Model 3†

1129876.5

363.9

1130240.4

Model 4‡

35202.0

4467.3

39669.2

Model 5#

34664.3

4522.7

39187.0

  1. Abbreviations: D, posterior mean of the deviance; pD, the number of effective parameters; DIC, the deviance information criterion, as a measure of the trade-off between model fit and complexity.
  2. Note: Model terms used in four models include an intercept (α); a spatially unstructured random effect term (νi); a spatially structured conditional autoregression term (υi); uncorrelated time (γj); a first-order random walk-correlated time variable (γ1j); and an interaction term for time and place (δ1j). θij represents the relative risk of area i at time j.
  3. *Model 1, convolution + uncorrelated time (time IID), e.g., \(\log ({\theta }_{ij})=\alpha +{\nu }_{i}+{\upsilon }_{i}+{\gamma }_{1j}\), where.
  4. **Model 2, convolution + 1st order random walk correlated time (time RW1), e.g., \(\log ({\theta }_{ij})=\alpha +{\nu }_{i}+{\upsilon }_{i}+{\gamma }_{1j}\).
  5. †Model 3, convolution + 1st order random walk correlated time (time RW1) + uncorrelated time (time IID), e.g., \(\log ({\theta }_{ij})=\alpha +{\nu }_{i}+{\upsilon }_{i}+{\gamma }_{1j}+{\gamma }_{j}\).
  6. ‡Model 4, convolution + 1st order random walk correlated time (time RW1) + space-time interaction term with uncorrelated prior for the interaction term, e.g., \(\log ({\theta }_{ij})=\alpha +{\nu }_{i}+{\upsilon }_{i}+{\gamma }_{1j}+{\delta }_{ij}\).
  7. #Model 5, model 4 + covariates, e.g., \(\log ({\theta }_{ij})={\rm{\alpha }}+{\sum }_{k=1}^{n}{\beta }_{k}{x}_{k}+{\nu }_{i}+{\upsilon }_{i}+{\gamma }_{1j}+{\delta }_{ij}\).
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