Table 4.

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 1b: All outlets IRR [95% CI]	Model 2b: Bars IRR [95% CI]	Model 3b: Restaurants IRR [95% CI]	Model 4b: Off premise IRR [95% CI]
Area (ln)	1.495 [1.430, 1.561]	1.443 [1.351, 1.540]	1.538 [1.454, 1.631]	1.358 [1.316, 1.402]
Incomea
Local	0.819 [0.799, 0.840]	0.773 [0.737, 0.810]	0.792 [0.768, 0.819]	0.861 [0.843, 0.880]
Lagged	0.833 [0.799, 0.867]	0.804 [0.749, 0.865]	0.807 [0.759, 0.853]	0.892 [0.861, 0.923]
City	1.360 [1.274, 1.452]	1.422 [1.244, 1.670]	1.493 [1.373, 1.629]	1.238 [1.132, 1.348]
Population
Localb	2.281 [1.755, 2.962]	1.257 [0.809, 1.928]	2.145 [1.542, 2.986]	2.124 [1.722, 2.633]
Laggedb	1.508 [1.404, 1.616]	1.306 [1.162, 1.476]	1.670 [1.528, 1.827]	1.344 [1.272, 1.420]
Cityc	1.039 [1.001, 1.086]	1.042 [0.967, 1.130]	1.051 [1.006, 1.099]	1.017 [0.971, 1.069]
Whited
Local	0.980 [0.933, 1.034]	1.039 [0.958, 1.129]	1.001 [0.934, 1.067]	0.977 [0.937, 1.021]
Lagged	1.077 [0.993, 1.157]	1.221 [1.081, 1.378]	1.035 [0.939, 1.152]	1.097 [1.035, 1.161]
City	0.962 [0.854, 1.053]	0.893 [0.733, 1.127]	0.915 [0.822, 1.039]	1.026 [0.911, 1.159]
Blackd
Local	0.972 [0.909, 1.048]	0.993 [0.876, 1.124]	0.949 [0.858, 1.051]	0.993 [0.935, 1.057]
Lagged	0.821 [0.738, 0.906]	0.838 [0.709, 0.995]	0.673 [0.579, 0.775]	0.913 [0.843, 0.985]
City	1.111 [0.908, 1.324]	1.306 [0.928, 1.931]	1.098 [0.903, 1.360]	1.177 [0.948, 1.453]
Hispanicd
Local	1.033 [0.990, 1.080]	1.059 [0.988, 1.136]	0.976 [0.922, 1.033]	1.063 [1.025, 1.105]
Lagged	0.915 [0.851, 0.981]	1.057 [0.950, 1.170]	0.835 [0.769, 0.916]	0.985 [0.935, 1.036]
City	1.049 [0.940, 1.147]	0.948 [0.782, 1.205]	1.052 [0.941, 1.189]	1.073 [0.949, 1.210]
Moranʼs I for CAR term Proportion of variance explained by:	0.206	0.275	0.214	0.270
City random effect	0.054 [0.035, 0.079]	0.119 [0.074, 0.177]	0.033 [0.018, 0.052]	0.104 [0.076, 0.138]
CAR random effect	0.195 [0.149, 0.242]	0.046 [0.002, 0.179]	0.320 [0.258, 0.383]	0.011 [0.000, 0.054]

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 10% increase.