MODEL 0 is non-spatial only with gamma random effects and no covariate

model
{
  for (i in 1 : N) {
      Y[i]  ~ dpois(mu[i])
      mu[i] <- E[i]*exp(beta0)*theta[i] 
      RR[i] <- exp(beta0)*theta[i]
      theta[i] ~ dgamma(alpha,alpha)
  } 
# 
  alpha ~ dgamma(1,1)
  beta0 ~ dflat()  
# Functions of interest:
  sigma.theta <- sqrt(1/alpha)   # standard deviation of non-spatial
  base <- exp(beta0)
}

DATA 0

list(N = 56,  
Y   = c(    9,   39,   11,    9,   15,    8,   26,    7,    6,   20,
                13,    5,    3,    8,   17,    9,    2,    7,    9,    7,
                16,   31,   11,    7,   19,   15,    7,   10,   16,   11,
                 5,    3,    7,    8,   11,    9,   11,    8,    6,    4,
                10,    8,    2,    6,   19,    3,    2,    3,   28,    6,
                 1,    1,    1,    1,    0,    0),
E = c( 1.4, 8.7, 3.0, 2.5, 4.3, 2.4, 8.1, 2.3, 2.0, 6.6,
            4.4, 1.8, 1.1, 3.3, 7.8, 4.6, 1.1, 4.2, 5.5, 4.4,
           10.5,22.7, 8.8, 5.6,15.5,12.5, 6.0, 9.0,14.4,10.2,
            4.8, 2.9, 7.0, 8.5,12.3,10.1,12.7, 9.4, 7.2, 5.3,
           18.8,15.8, 4.3,14.6,50.7, 8.2, 5.6, 9.3,88.7,19.6,
            3.4, 3.6, 5.7, 7.0, 4.2, 1.8))

INIT 0
list(alpha = 1, beta0 = 0, 
theta=c(1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,
    1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1))

OUTPUT:
	 node	 mean	 sd	 MC error	2.5%	median	97.5%	start	sample
	RR[1]	4.07	1.297	0.01877	1.959	3.92	7.001	4000	6001
	RR[2]	4.105	0.6469	0.008642	2.938	4.068	5.48	4000	6001
	RR[3]	3.006	0.858	0.01159	1.607	2.915	4.937	4000	6001
	RR[4]	2.875	0.8995	0.01019	1.391	2.773	4.886	4000	6001
	RR[5]	3.016	0.7406	0.01114	1.754	2.955	4.668	4000	6001
	RR[6]	2.68	0.8865	0.01325	1.227	2.568	4.696	4000	6001
	RR[7]	2.975	0.5666	0.008305	1.994	2.929	4.236	4000	6001
	RR[8]	2.476	0.8492	0.01224	1.082	2.379	4.412	4000	6001
	RR[9]	2.398	0.8863	0.01208	0.9793	2.306	4.445	4000	6001
	RR[10]	2.763	0.5932	0.007403	1.715	2.716	4.053	4000	6001
	RR[11]	2.615	0.6887	0.008123	1.432	2.565	4.119	4000	6001
	RR[12]	2.242	0.8778	0.01361	0.859	2.133	4.297	4000	6001
	RR[13]	2.03	0.9582	0.01481	0.6056	1.872	4.299	4000	6001
	RR[14]	2.143	0.6804	0.007334	1.037	2.065	3.688	4000	6001
	RR[15]	2.083	0.4764	0.005953	1.261	2.041	3.077	4000	6001
	RR[16]	1.839	0.556	0.006439	0.9382	1.783	3.086	4000	6001
	RR[17]	1.626	0.8399	0.01122	0.4277	1.488	3.598	4000	6001
	RR[18]	1.612	0.5461	0.007131	0.7327	1.547	2.85	4000	6001
	RR[19]	1.599	0.4912	0.007916	0.7854	1.546	2.674	4000	6001
	RR[20]	1.555	0.5271	0.007354	0.7136	1.495	2.748	4000	6001
	RR[21]	1.505	0.3596	0.004303	0.8876	1.476	2.302	4000	6001
	RR[22]	1.372	0.2355	0.003404	0.9517	1.356	1.869	4000	6001
	RR[23]	1.28	0.3608	0.004843	0.6784	1.246	2.084	4000	6001
	RR[24]	1.286	0.4385	0.005744	0.5745	1.237	2.251	4000	6001
	RR[25]	1.242	0.2713	0.003548	0.7714	1.219	1.828	4000	6001
	RR[26]	1.228	0.2975	0.004119	0.7142	1.208	1.88	4000	6001
	RR[27]	1.201	0.4039	0.005305	0.556	1.15	2.128	4000	6001
	RR[28]	1.146	0.3335	0.004086	0.5753	1.118	1.878	4000	6001
	RR[29]	1.131	0.2697	0.003386	0.6715	1.11	1.716	4000	6001
	RR[30]	1.112	0.3124	0.004678	0.5936	1.082	1.806	4000	6001
	RR[31]	1.115	0.4328	0.005919	0.4502	1.055	2.102	4000	6001
	RR[32]	1.154	0.5397	0.008106	0.3577	1.067	2.43	4000	6001
	RR[33]	1.064	0.3632	0.004776	0.4821	1.019	1.902	4000	6001
	RR[34]	1.0	0.323	0.003728	0.4689	0.9648	1.725	4000	6001
	RR[35]	0.9489	0.2669	0.003294	0.4941	0.924	1.526	4000	6001
	RR[36]	0.9589	0.2931	0.003769	0.4695	0.9254	1.624	4000	6001
	RR[37]	0.9252	0.2575	0.003131	0.488	0.8995	1.502	4000	6001
	RR[38]	0.9181	0.2942	0.003855	0.446	0.889	1.58	4000	6001
	RR[39]	0.9248	0.335	0.004034	0.3926	0.8853	1.694	4000	6001
	RR[40]	0.8836	0.3698	0.004262	0.3132	0.8298	1.721	4000	6001
	RR[41]	0.5866	0.1686	0.002154	0.3017	0.5714	0.9754	4000	6001
	RR[42]	0.5729	0.1846	0.002617	0.2709	0.5513	0.9862	4000	6001
	RR[43]	0.6791	0.3494	0.004313	0.1686	0.6266	1.509	4000	6001
	RR[44]	0.4904	0.1786	0.002317	0.1994	0.4702	0.8849	4000	6001
	RR[45]	0.4027	0.08775	0.001215	0.2512	0.3959	0.5925	4000	6001
	RR[46]	0.5066	0.2299	0.002959	0.1598	0.4747	1.034	4000	6001
	RR[47]	0.5487	0.2774	0.003792	0.1449	0.505	1.195	4000	6001
	RR[48]	0.4498	0.2039	0.002677	0.1369	0.4188	0.924	4000	6001
	RR[49]	0.3321	0.06051	7.884E-4	0.2261	0.3286	0.4612	4000	6001
	RR[50]	0.3685	0.1334	0.001624	0.1603	0.3522	0.6725	4000	6001
	RR[51]	0.6	0.3539	0.004243	0.1112	0.5327	1.45	4000	6001
	RR[52]	0.5702	0.3425	0.005197	0.1034	0.5017	1.4	4000	6001
	RR[53]	0.4021	0.2446	0.00316	0.07137	0.3546	0.9934	4000	6001
	RR[54]	0.3327	0.2042	0.002271	0.05706	0.2924	0.8143	4000	6001
	RR[55]	0.3259	0.2533	0.003452	0.02491	0.2646	0.9605	4000	6001
	RR[56]	0.5814	0.4538	0.006368	0.04737	0.4723	1.745	4000	6001
	alpha	1.79	0.3985	0.007926	1.129	1.753	2.682	4001	6000
	beta0	0.3567	0.1188	0.005916	0.1315	0.353	0.5966	4000	6001