# Table 1 Characteristics of four different base models (no predictors). Lower deviance information criterion (DIC) represents a better trade off between model fit and complexity. Models 1 and 3 have a random intercept; models 2 and 4 follow a BYM2 structure. $$D\left (\overline \theta \right)$$, deviance of mean model parameters θ; pD, effective number of parameters
Model Distribution Parameters Hyperparameters $$D\left (\overline \theta \right)$$ pD DIC
Model 2** Poisson β0, $$\upsilon _{i}^{*}$$, $$\nu _{i}^{*}$$ τγ, φ 1362.37 124.68 1611.73
Model 4 Negative binomial β0, $$\upsilon _{i}^{*}$$, $$\nu _{i}^{*}$$ n, τγ, φ 1455.71 103.58 1662.87
2. **Model 2: yi|λiPois(λi), $$\log \left (\lambda _{i}\right)=\eta _{i}+\log \left (E_{i}\right)=\beta _{0}+\frac {1}{\sqrt {\tau _{\gamma }}}\left ({\sqrt {\varphi }\upsilon _{i}^{*}}+\sqrt {1-\varphi }\nu _{i}^{*}\right)+\log \left (E_{i}\right)$$
4. Model 4: yi|λiNegBin(n,λi), $$\log \left (\lambda _{i}\right)=\eta _{i}+\log \left (E_{i}\right)=\beta _{0}+\frac {1}{\sqrt {\tau _{\gamma }}}\left ({\sqrt {\varphi }\upsilon _{i}^{*}}+\sqrt {1-\varphi }\nu _{i}^{*}\right)+\log \left (E_{i}\right)$$
5. Symbols: yi, count of cases in Zip Code Tabulation Area (ZCTA) i; λi, expected cases in ZCTA i; Ei, number of total COVID-19 tests in ZCTA i; ηi, linear predictor for ZCTA i; β0, intercept; νi, nonspatial random-effect; $$\nu _{i}^{*}$$, scaled nonspatial random-effect; $$\upsilon _{i}^{*}$$, scaled spatial random-effect with intrinsic conditional autoregressive structure; τν, precision for nonspatial random effect, log-gamma prior; τγ, overall precision, penalized complexity (PC) prior; φ, mixing parameter, PC prior; n, overdispersion parameter, PC gamma prior