Table 3.

Hierarchical Bayesian Poisson models for counts of alcohol outlets in census block groups (n = 8,877) nested in 50 cities, with random effects for cities

Variable	Model 1a: All outlets IRR [95% CI]	Model 2a: Bars IRR [95% CI]	Model 3a: Restaurants IRR [95% CI]	Model 4a: Off premise IRR [95% CI]
Area (ln) Incomea	1.523 [1.458, 1.592]	1.442 [1.350, 1.541]	1.644 [1.555, 1.737]	1.358 [1.316, 1.402]
Local	0.801 [0.781, 0.821]	0.774 [0.740, 0.811]	0.792 [0.769, 0.816]	0.835 [0.817, 0.853]
Lagged	0.854 [0.823, 0.886]	0.844 [0.791, 0.901]	0.852 [0.806, 0.898]	0.877 [0.851, 0.905]
City	1.326 [1.258, 1.399]	1.336 [1.214, 1.482]	1.494 [1.339, 1.634]	1.190 [1.111, 1.275]
Market potential
Localb	1.010 [1.006, 1.015]	1.004 [0.996, 1.011]	1.010 [1.004, 1.015]	1.011 [1.007, 1.014]
Laggedc	1.059 [1.046, 1.072]	1.042 [1.021, 1.062]	1.077 [1.062, 1.094]	1.046 [1.036, 1.056]
Cityd	1.004 [0.995, 1.013]	1.004 [0.991, 1.017]	1.003 [0.990, 1.016]	0.999 [0.990, 1.008]
Moranʼs I for CAR term Proportion of variance explained by:	0.207	0.311	0.240	0.260
City random effect	0.060 [0.040, 0.086]	0.091 [0.054, 0.136]	0.070 [0.055, 0.089]	0.117 [0.089, 0.150]
CAR random effect	0.226 [0.179, 0.273]	0.163 [0.079, 0.266]	0.419 [0.356, 0.488]	0.048 [0.016, 0.092]

Notes: Bold indicates CI does not include null value of IRR = 1.000. IRR = incidence rate ratio; CI = credible interval; CAR = conditional autoregressive.

^aPer $10,000 increase;

^bper 10,000 unit increase;

^cper 100,000 unit increase;

^dper 1,000,000 unit increase.