正常 CAR u[22] 的邻接矩阵必须是对称的 - WINBUGS

Question

我正在尝试为我的空间数据建立一个卷积模型，但它一直给我一个错误，提示“法线 CAR u[22] 的邻接矩阵必须是对称的”。谁能给我一个想法，我做错了什么？我认为问题与没有任何邻居的obs 42有关。

    model
{
    for (i in 1:N){
    # Poisson likelihood for observed counts
        O[i] ~ dpois(mu[i])
        log(mu[i]) <- log(E[i]) + alpha + u[i] + v[i]
        RR[i] <- exp(alpha + u[i] + v[i])
        v[i] ~ dnorm(0, tau.v)
        }
    # CAR prior distribution for random effects:
        u[1:N] ~ car.normal(adj[], weights[], num[], tau.u)
        for(k in 1:sumNumNeigh){
            weights[k] <- 1
        }
    # Other priors
        alpha ~ dflat()
        mean <- exp(alpha)
        tau.u ~ dgamma(0.5, 0.0005)
        tau.v ~ dgamma(0.5, 0.0005)
        
        sigma.u <- 1/tau.u
        sigma.v <- 1/tau.v
        ratio <- sigma.u/sigma.v
}

# Data
list(E = c(
309.644702, 1743.709601,  711.804186, 2526.881056,  318.644541,  375.876925,
3078.079354,  479.665537,  611.054281,  578.794301,  263.825542,  443.047869,
1563.163287,  706.636964,  800.620723,  271.043082,  414.554323, 1276.548784,
499.220755,  625.658895,  455.259480, 1293.033647,  970.491142,  636.352367,
636.352367,  614.983914,  560.249202,  468.749744, 1136.010294,  443.047869,
766.793038,  443.221218, 1237.341543,  418.018262,  275.975567,    3.160066,
369.597694,  314.777270,  990.528173,  645.661892, 1205.130767,  278.188792,
1449.545851,  159.055131),
    O = c(
345, 1325,  845, 2815,  705,  400, 3150,  485,  325,  405,  585,  410, 3555,  320, 1030,  310,
305,1185,  300,  710,  225,  600,  800,  335,  220,  385,  310,  165, 1190,  175,  840, 1075,
1155,  600,  225, 5,  400,  200, 1155,  850, 1215,  300, 1275,  160), 
    N = 44,
    num = c(
2, 5, 3, 4, 6, 6, 3, 4, 6, 3, 
6, 3, 6, 7, 8, 2, 3, 5, 5, 5, 
6, 9, 4, 4, 2, 9, 5, 4, 5, 4, 
7, 4, 5, 5, 7, 6, 5, 5, 4, 7, 
4, 0, 2, 1),

    adj = c(
5, 2, 
6, 5, 4, 3, 1, 
9, 4, 2, 
9, 6, 3, 2, 
11, 8, 7, 6, 2, 1, 
15, 11, 9, 5, 4, 2, 
13, 8, 5, 
13, 11, 7, 5, 
15, 14, 10, 6, 4, 3, 
14, 12, 9, 
19, 15, 13, 8, 6, 5, 
16, 14, 10, 
21, 19, 17, 11, 8, 7, 
20, 18, 16, 15, 12, 10, 9, 
24, 22, 19, 18, 14, 11, 9, 6, 
14, 12, 
23, 21, 13, 
26, 24, 20, 15, 14, 
22, 21, 15, 13, 11, 
28, 26, 25, 18, 14, 
27, 23, 22, 19, 17, 13, 
31, 29, 27, 26, 24, 23, 21, 19, 15, 
30, 27, 21, 17, 
26, 22, 18, 15, 
28, 20, 
35, 33, 32, 29, 28, 24, 22, 20, 18, 
31, 30, 23, 22, 21, 
32, 26, 25, 20, 
35, 34, 31, 26, 22, 
39, 31, 27, 23, 
40, 39, 34, 30, 29, 27, 22, 
36, 33, 28, 26, 
37, 36, 35, 32, 26, 
40, 39, 35, 31, 29, 
40, 38, 37, 34, 33, 29, 26, 
43, 41, 38, 37, 33, 32, 
38, 36, 35, 33, 26, 
41, 40, 37, 36, 35, 
40, 34, 31, 30, 
44, 41, 39, 38, 35, 34, 31, 
43, 40, 38, 36
,
41, 36, 
40
),
sumNumNeigh = 206))

# initial value
list(alpha = 0.01, tau.v = 0.01, tau.u = 0.01, u = c(
0.01, 0.01, 0.01, 0.01, 0.01, 0.01, 0.01, 0.01, 0.01, 0.01, 0.01,
0.01, 0.01, 0.01, 0.01, 0.01, 0.01, 0.01, 0.01, 0.01, 0.01, 0.01,
0.01, 0.01, 0.01, 0.01, 0.01, 0.01, 0.01, 0.01, 0.01, 0.01, 0.01,
0.01, 0.01, 0.01, 0.01, 0.01, 0.01, 0.01, 0.01, 0.01, 0.01, 0.01
),
v = c(
0.01, 0.01, 0.01, 0.01, 0.01, 0.01, 0.01, 0.01, 0.01, 0.01, 0.01,
0.01, 0.01, 0.01, 0.01, 0.01, 0.01, 0.01, 0.01, 0.01, 0.01, 0.01,
0.01, 0.01, 0.01, 0.01, 0.01, 0.01, 0.01, 0.01, 0.01, 0.01, 0.01,
0.01, 0.01, 0.01, 0.01, 0.01, 0.01, 0.01, 0.01, 0.01, 0.01,0.01
))

感谢您的宝贵时间！非常感谢。

Answer 1

u[22] 表示区域 22 有一个邻居，在 return 中没有区域 22 作为它自己的邻居，因此创建了一个非对称邻接矩阵。除了使用 winbugs 中的 'adjacency map' 工具手动检查之外，我不知道还有什么其他方法。

正常 CAR u[22] 的邻接矩阵必须是对称的 - WINBUGS

Adjacency matrix of normal CAR u[22] must be symmetric - WINBUGS

spatial

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