R语言向β-二项式混合模型添加协变量时尝试重新定义节点p[1，1]

当我尝试在碎片中的β-二项式N-混合模型上添加检测协变量时，我不断得到上述错误。根据Royle（2004）。二项式N混合模型可用于对重复计数调查产生的丰度数据建模。站点上的个体数量可由Poisson * 建模[为简单起见，我将仅坚持Poisson模型]*，使得：

Ni ~泊松（λi）
一个~一个（π，Ni）
**Ni -**是研究中心i可用的动物数量
**yit -**是在研究中心i访视t观察到的动物计数
**λi -**是研究中心i的平均动物数量
**pit -**是平均检测概率。

协变量效应可建模为：
丰度：

log（λi）= B 0 + B1 xi 1 +...+Brxir其中1...r为协变量

检测：

logit（pit）= B 0 + B1 xi 1 +...+Brxir其中1...r为协变量

假设所有动物的检出概率pit恒定。

beta二项式模型通过让检测概率**遵循随机分布而简化了该假设 *，使得
pi 't ~ β（凹坑（1-δ2）/δ2，（1-凹坑）（1-δ2）/δ2

对于0〈δ〈1
我尝试用模拟数据实现模型：
20家临床试验机构，5次访视，临床试验机构协变量=位置，2个观察协变量。

模拟数据

library(modelr)
Location<-c("A","B","C","D")
Location<-data.frame(Location=rep(Location,5))

location=Location%>%model_matrix(~Location)%>%select(-1)
set.seed(100)
y<-matrix(rpois(100,0.5),ncol=5)

# Cov1
set.seed(100)
cov1<-matrix(rnorm(100,100,5),ncol=5)

# cov 2
set.seed(100)
cov2<-matrix(rnorm(100,50,2),ncol=5)

data<-list(y=y,
           nSites=20,
           nOcc=5,
           nA=ncol(data$location),
           location=location,
           cov1=cov1,
           cov2=cov2)

如果我尝试在没有用于检测的协变量效应的情况下在rjags中估计该模型，则它工作。

nx<-"
model{
  for(i in 1:nSites) {
    # Biological model

    N[i] ~ dpois(lambda[i])
    log(lambda[i])<-alphao+inprod(alpha, location[i,])
  }

    # Observation model
    for(i in 1:nSites) {
    for(t in 1:nOcc) {
      y[i,t] ~ dbin(pit_h[i,t], N[i])
      pit_h[i,t]~ dbeta((pit[i,t]*fac),(fac*(1-pit[i,t])))

    }
  }
  # Priors
alphao ~ dnorm(5,1)
    for(i in 1:nA){
      alpha[i] ~ dnorm(2,.5)
    }

for(i in 1:nSites) {
    for(t in 1:nOcc) {
    pit[i,t]~dunif(0,1)
    }
}

sigma ~ dunif(0,1)
fac <-(1-sigma^2)/sigma^2

}"

writeLines(nx,con="mod.txt")
inits = function() list(N = apply(y,1,max,na.rm=T))
watch=c("alphao","alpha","lambda","pit")
set.seed(100)
mod<-jagsUI::jags(data,
                  parameters.to.save=watch,
                  model.file="mod.txt",n.iter=3,
                  n.chains=2)
mod

屈服

JAGS output for model 'mod.txt', generated by jagsUI.
Estimates based on 2 chains of 3 iterations,
adaptation = 100 iterations (sufficient),
burn-in = 0 iterations and thin rate = 1,
yielding 6 total samples from the joint posterior. 
MCMC ran for 0.009 minutes at time 2023-01-11 16:52:03.

              mean      sd    2.5%     50%    97.5% overlap0 f   Rhat n.eff
alphao       4.769   0.446   4.350   4.754    5.218    FALSE 1 27.188     2
alpha[1]     1.725   0.629   1.115   1.735    2.310    FALSE 1 48.915     2
alpha[2]     1.991   0.161   1.795   2.012    2.149    FALSE 1  7.456     2
alpha[3]     1.822   0.633   1.186   1.852    2.415    FALSE 1 28.072     2
lambda[1]  127.706  54.181  77.504 124.146  184.586    FALSE 1 19.433     2
lambda[2]  670.612 122.557 551.850 671.722  785.277    FALSE 1 48.321     2
lambda[3]  893.022 252.923 660.011 887.089 1138.013    FALSE 1 50.136     2
lambda[4]  739.326 137.772 604.421 735.512  877.068    FALSE 1 19.180     2
lambda[5]  127.706  54.181  77.504 124.146  184.586    FALSE 1 19.433     2
lambda[6]  670.612 122.557 551.850 671.722  785.277    FALSE 1 48.321     2
lambda[7]  893.022 252.923 660.011 887.089 1138.013    FALSE 1 50.136     2
lambda[8]  739.326 137.772 604.421 735.512  877.068    FALSE 1 19.180     2
lambda[9]  127.706  54.181  77.504 124.146  184.586    FALSE 1 19.433     2
lambda[10] 670.612 122.557 551.850 671.722  785.277    FALSE 1 48.321     2
lambda[11] 893.022 252.923 660.011 887.089 1138.013    FALSE 1 50.136     2
lambda[12] 739.326 137.772 604.421 735.512  877.068    FALSE 1 19.180     2
lambda[13] 127.706  54.181  77.504 124.146  184.586    FALSE 1 19.433     2
lambda[14] 670.612 122.557 551.850 671.722  785.277    FALSE 1 48.321     2
lambda[15] 893.022 252.923 660.011 887.089 1138.013    FALSE 1 50.136     2
lambda[16] 739.326 137.772 604.421 735.512  877.068    FALSE 1 19.180     2
lambda[17] 127.706  54.181  77.504 124.146  184.586    FALSE 1 19.433     2
lambda[18] 670.612 122.557 551.850 671.722  785.277    FALSE 1 48.321     2
lambda[19] 893.022 252.923 660.011 887.089 1138.013    FALSE 1 50.136     2
lambda[20] 739.326 137.772 604.421 735.512  877.068    FALSE 1 19.180     2
pit[1,1]     0.183   0.118   0.048   0.157    0.327    FALSE 1  0.946     6
pit[2,1]     0.267   0.238   0.036   0.218    0.576    FALSE 1  4.558     2
pit[3,1]     0.280   0.143   0.085   0.313    0.432    FALSE 1  0.929     6
pit[4,1]     0.354   0.236   0.045   0.396    0.622    FALSE 1  1.186     6
pit[5,1]     0.199   0.100   0.082   0.190    0.346    FALSE 1  1.128     6
pit[6,1]     0.130   0.076   0.037   0.118    0.233    FALSE 1  3.429     2
pit[7,1]     0.503   0.197   0.209   0.536    0.741    FALSE 1  1.120     6
pit[8,1]     0.369   0.199   0.076   0.414    0.597    FALSE 1  0.986     6
pit[9,1]     0.396   0.131   0.224   0.425    0.551    FALSE 1  1.751     4
pit[10,1]    0.281   0.141   0.122   0.271    0.468    FALSE 1  1.179     6
pit[11,1]    0.554   0.226   0.291   0.585    0.768    FALSE 1  1.031     6
pit[12,1]    0.304   0.165   0.139   0.296    0.558    FALSE 1  1.001     6
pit[13,1]    0.240   0.274   0.071   0.139    0.717    FALSE 1  1.648     4
pit[14,1]    0.199   0.111   0.074   0.197    0.332    FALSE 1  4.464     2
pit[15,1]    0.322   0.093   0.207   0.303    0.446    FALSE 1  0.849     6
pit[16,1]    0.380   0.226   0.060   0.381    0.690    FALSE 1  1.043     6
pit[17,1]    0.085   0.045   0.035   0.084    0.133    FALSE 1  1.130     6
pit[18,1]    0.193   0.109   0.066   0.217    0.335    FALSE 1  2.724     3
pit[19,1]    0.135   0.047   0.081   0.137    0.203    FALSE 1  1.110     6
pit[20,1]    0.370   0.219   0.099   0.368    0.702    FALSE 1  1.063     6
pit[1,2]     0.419   0.168   0.285   0.362    0.707    FALSE 1  1.275     6
pit[2,2]     0.535   0.287   0.250   0.502    0.869    FALSE 1  8.332     2
pit[3,2]     0.356   0.206   0.095   0.362    0.662    FALSE 1  1.030     6
pit[4,2]     0.330   0.123   0.177   0.335    0.486    FALSE 1  4.460     2
pit[5,2]     0.334   0.215   0.072   0.350    0.617    FALSE 1  1.160     6
pit[6,2]     0.032   0.026   0.005   0.023    0.072    FALSE 1  2.278     3
pit[7,2]     0.385   0.289   0.035   0.438    0.682    FALSE 1  1.426     5
pit[8,2]     0.537   0.162   0.378   0.488    0.778    FALSE 1  0.881     6
pit[9,2]     0.489   0.266   0.073   0.539    0.741    FALSE 1  1.344     5
pit[10,2]    0.194   0.182   0.024   0.180    0.414    FALSE 1  1.166     6
pit[11,2]    0.476   0.258   0.236   0.424    0.811    FALSE 1  6.065     2
pit[12,2]    0.536   0.225   0.232   0.610    0.744    FALSE 1  2.909     3
pit[13,2]    0.244   0.090   0.141   0.239    0.375    FALSE 1  3.298     2
pit[14,2]    0.432   0.175   0.257   0.403    0.660    FALSE 1  1.097     6
pit[15,2]    0.419   0.287   0.122   0.404    0.738    FALSE 1  8.309     2
pit[16,2]    0.522   0.146   0.378   0.502    0.744    FALSE 1  2.006     3
pit[17,2]    0.225   0.167   0.041   0.176    0.449    FALSE 1  3.682     2
pit[18,2]    0.264   0.079   0.164   0.265    0.356    FALSE 1  1.245     6
pit[19,2]    0.440   0.243   0.161   0.466    0.766    FALSE 1  3.425     2
pit[20,2]    0.238   0.139   0.099   0.216    0.446    FALSE 1  2.344     3
pit[1,3]     0.273   0.159   0.064   0.263    0.484    FALSE 1  1.031     6
pit[2,3]     0.332   0.115   0.200   0.327    0.497    FALSE 1  3.520     2
pit[3,3]     0.533   0.251   0.183   0.494    0.840    FALSE 1  1.101     6
pit[4,3]     0.324   0.250   0.117   0.205    0.685    FALSE 1  0.865     6
pit[5,3]     0.607   0.221   0.224   0.674    0.742    FALSE 1  1.470     5
pit[6,3]     0.298   0.113   0.160   0.293    0.461    FALSE 1  1.069     6
pit[7,3]     0.403   0.143   0.163   0.429    0.526    FALSE 1  1.613     4
pit[8,3]     0.415   0.170   0.261   0.363    0.682    FALSE 1  3.085     2
pit[9,3]     0.498   0.321   0.099   0.594    0.861    FALSE 1  3.386     2
pit[10,3]    0.258   0.222   0.055   0.185    0.611    FALSE 1  0.970     6
pit[11,3]    0.381   0.268   0.058   0.360    0.789    FALSE 1  1.756     4
pit[12,3]    0.162   0.072   0.084   0.159    0.268    FALSE 1  1.566     4
pit[13,3]    0.152   0.159   0.004   0.097    0.356    FALSE 1  2.475     3
pit[14,3]    0.057   0.042   0.010   0.060    0.099    FALSE 1  8.243     2
pit[15,3]    0.429   0.192   0.175   0.404    0.708    FALSE 1  1.080     6
pit[16,3]    0.099   0.044   0.045   0.108    0.143    FALSE 1  4.856     2
pit[17,3]    0.262   0.206   0.052   0.238    0.492    FALSE 1  9.405     2
pit[18,3]    0.400   0.153   0.177   0.416    0.573    FALSE 1  1.203     6
pit[19,3]    0.314   0.221   0.043   0.320    0.569    FALSE 1  0.955     6
pit[20,3]    0.150   0.108   0.045   0.114    0.325    FALSE 1  1.776     4
pit[1,4]     0.280   0.299   0.014   0.191    0.635    FALSE 1  5.639     2
pit[2,4]     0.329   0.317   0.113   0.225    0.877    FALSE 1  1.243     6
pit[3,4]     0.472   0.204   0.208   0.462    0.750    FALSE 1  1.074     6
pit[4,4]     0.457   0.293   0.146   0.460    0.806    FALSE 1  6.732     2
pit[5,4]     0.268   0.148   0.036   0.301    0.406    FALSE 1  0.943     6
pit[6,4]     0.251   0.213   0.047   0.193    0.561    FALSE 1  0.892     6
pit[7,4]     0.104   0.106   0.022   0.069    0.287    FALSE 1  1.347     6
pit[8,4]     0.220   0.079   0.140   0.194    0.346    FALSE 1  1.804     4
pit[9,4]     0.379   0.306   0.127   0.213    0.830    FALSE 1  2.284     3
pit[10,4]    0.482   0.209   0.164   0.582    0.660    FALSE 1  0.896     6
pit[11,4]    0.052   0.045   0.012   0.043    0.127    FALSE 1  1.629     4
pit[12,4]    0.465   0.136   0.341   0.418    0.671    FALSE 1  3.070     2
pit[13,4]    0.496   0.216   0.260   0.462    0.758    FALSE 1  2.080     3
pit[14,4]    0.365   0.194   0.176   0.301    0.642    FALSE 1  0.847     6
pit[15,4]    0.371   0.277   0.126   0.281    0.785    FALSE 1  1.523     4
pit[16,4]    0.371   0.254   0.088   0.375    0.699    FALSE 1  1.163     6
pit[17,4]    0.442   0.172   0.209   0.427    0.686    FALSE 1  1.040     6
pit[18,4]    0.527   0.300   0.141   0.629    0.804    FALSE 1  0.818     6
pit[19,4]    0.563   0.144   0.384   0.580    0.735    FALSE 1  3.056     2
pit[20,4]    0.198   0.096   0.104   0.187    0.343    FALSE 1  3.528     2
pit[1,5]     0.264   0.128   0.157   0.229    0.482    FALSE 1  1.119     6
pit[2,5]     0.397   0.102   0.229   0.419    0.496    FALSE 1  1.460     5
pit[3,5]     0.396   0.202   0.100   0.493    0.580    FALSE 1  0.888     6
pit[4,5]     0.423   0.092   0.312   0.403    0.532    FALSE 1  3.020     2
pit[5,5]     0.268   0.208   0.033   0.219    0.523    FALSE 1  3.875     2
pit[6,5]     0.330   0.158   0.172   0.326    0.514    FALSE 1  0.871     6
pit[7,5]     0.329   0.133   0.142   0.336    0.483    FALSE 1  0.905     6
 [ reached 'max' / getOption("max.print") -- omitted 14 rows ]

**WARNING** Rhat values indicate convergence failure. 
Rhat is the potential scale reduction factor (at convergence, Rhat=1). 
For each parameter, n.eff is a crude measure of effective sample size. 

overlap0 checks if 0 falls in the parameter's 95% credible interval.
f is the proportion of the posterior with the same sign as the mean;
i.e., our confidence that the parameter is positive or negative.

DIC info: (pD = var(deviance)/2) 
pD = 71.8 and DIC = 239.53 
DIC is an estimate of expected predictive error (lower is better).
>

如果我忽略pit的随机分布，它实际上是有效的，这就是我提到的恒定pit，每个人在每个教程中都在做
守则

nx <- "
model{
# Abundance
for (i in 1:nSites) {
N[i]~ dpois(lambda[i])
log(lambda[i])<-alphao+inprod(alpha, location[i,])
}

for (i in 1:nSites) {
for(t in 1:nOcc){
y[i,t]~ dbin(pit[i,t],N[i])
#pit_h[i,t]~ dbeta(1,1)
logit(pit[i,t]) <- beta0+inprod(beta, location[i,])+inprod(beta1,c(cov1[i,t],cov2[i,t]))
}
}

 # Priors
 alphao ~ dnorm(1.2824,0.302)
    for(i in 1:nA){
      alpha[i] ~ dnorm(0.284,0.570)
    }
beta0 ~ dunif(-1.67,0.61)
   for(i in 1:3){
     beta[i] ~ dnorm(-0.370,0.254)
   }
   for(i in 1:2){
     beta1[i] ~ dnorm(-0.104,0.44)
   }

# det
sigma ~ dunif(0,1)
fac <-(1-sigma^2)/sigma^2

# derived
}"
writeLines(nx,con="mod1.txt")

watch=c("alphao","alpha","lambda","beta0","beta","beta1","pit","sigma")

inits = function() list(N = apply(y,1,max,na.rm=T))
set.seed(100)
mod<-jagsUI::jags(data,
                  parameters.to.save=watch,inits=inits,
                  model.file="mod1.txt",n.iter=3,
                  n.chains=2,DIC=TRUE)

mod

屈服

JAGS output for model 'mod1.txt', generated by jagsUI.
Estimates based on 2 chains of 3 iterations,
adaptation = 100 iterations (sufficient),
burn-in = 0 iterations and thin rate = 1,
yielding 6 total samples from the joint posterior. 
MCMC ran for 0.006 minutes at time 2023-01-11 17:02:18.

              mean     sd    2.5%     50%   97.5% overlap0   f   Rhat n.eff
alphao       4.405  0.098   4.247   4.448   4.489    FALSE 1.0  2.264     3
alpha[1]     0.705  0.311   0.386   0.702   1.052    FALSE 1.0  8.735     2
alpha[2]     1.568  0.229   1.346   1.550   1.829    FALSE 1.0 10.655     2
alpha[3]     1.300  0.086   1.167   1.333   1.380    FALSE 1.0  2.526     3
lambda[1]   82.166  7.700  69.933  85.482  89.069    FALSE 1.0  2.337     3
lambda[2]  169.553 39.141 128.321 171.241 207.988    FALSE 1.0 12.838     2
lambda[3]  396.653 61.786 337.056 388.711 467.843    FALSE 1.0  9.972     2
lambda[4]  302.649 41.450 260.019 302.933 343.100    FALSE 1.0 19.472     2
lambda[5]   82.166  7.700  69.933  85.482  89.069    FALSE 1.0  2.337     3
lambda[6]  169.553 39.141 128.321 171.241 207.988    FALSE 1.0 12.838     2
lambda[7]  396.653 61.786 337.056 388.711 467.843    FALSE 1.0  9.972     2
lambda[8]  302.649 41.450 260.019 302.933 343.100    FALSE 1.0 19.472     2
lambda[9]   82.166  7.700  69.933  85.482  89.069    FALSE 1.0  2.337     3
lambda[10] 169.553 39.141 128.321 171.241 207.988    FALSE 1.0 12.838     2
lambda[11] 396.653 61.786 337.056 388.711 467.843    FALSE 1.0  9.972     2
lambda[12] 302.649 41.450 260.019 302.933 343.100    FALSE 1.0 19.472     2
lambda[13]  82.166  7.700  69.933  85.482  89.069    FALSE 1.0  2.337     3
lambda[14] 169.553 39.141 128.321 171.241 207.988    FALSE 1.0 12.838     2
lambda[15] 396.653 61.786 337.056 388.711 467.843    FALSE 1.0  9.972     2
lambda[16] 302.649 41.450 260.019 302.933 343.100    FALSE 1.0 19.472     2
lambda[17]  82.166  7.700  69.933  85.482  89.069    FALSE 1.0  2.337     3
lambda[18] 169.553 39.141 128.321 171.241 207.988    FALSE 1.0 12.838     2
lambda[19] 396.653 61.786 337.056 388.711 467.843    FALSE 1.0  9.972     2
lambda[20] 302.649 41.450 260.019 302.933 343.100    FALSE 1.0 19.472     2
beta0        0.598  0.010   0.583   0.598   0.609    FALSE 1.0  2.973     2
beta[1]     -0.669  0.138  -0.825  -0.663  -0.526    FALSE 1.0 10.339     2
beta[2]      0.071  0.148  -0.087   0.075   0.217     TRUE 0.5 14.514     2
beta[3]     -0.260  0.079  -0.348  -0.261  -0.178    FALSE 1.0  9.102     2
beta1[1]    -0.027  0.136  -0.154  -0.027   0.101     TRUE 0.5 73.857     2
beta1[2]    -0.241  0.272  -0.498  -0.241   0.014     TRUE 0.5 73.668     2
pit[1,1]     0.000  0.000   0.000   0.000   0.000    FALSE 1.0 14.106     1
pit[2,1]     0.000  0.000   0.000   0.000   0.000    FALSE 1.0 34.146     1
pit[3,1]     0.000  0.000   0.000   0.000   0.000    FALSE 1.0 48.475     1
pit[4,1]     0.000  0.000   0.000   0.000   0.000    FALSE 1.0 19.522     1
pit[5,1]     0.000  0.000   0.000   0.000   0.000    FALSE 1.0  4.367     1
pit[6,1]     0.000  0.000   0.000   0.000   0.000    FALSE 1.0 29.277     1
pit[7,1]     0.000  0.000   0.000   0.000   0.000    FALSE 1.0 51.736     1
pit[8,1]     0.000  0.000   0.000   0.000   0.000    FALSE 1.0 17.004     1
pit[9,1]     0.000  0.000   0.000   0.000   0.000    FALSE 1.0 19.399     1
pit[10,1]    0.000  0.000   0.000   0.000   0.000    FALSE 1.0 45.000     1
pit[11,1]    0.000  0.000   0.000   0.000   0.000    FALSE 1.0 46.585     1
pit[12,1]    0.000  0.000   0.000   0.000   0.000    FALSE 1.0  5.782     1
pit[13,1]    0.000  0.000   0.000   0.000   0.000    FALSE 1.0  9.274     1
pit[14,1]    0.000  0.000   0.000   0.000   0.000    FALSE 1.0 17.662     1
pit[15,1]    0.000  0.000   0.000   0.000   0.000    FALSE 1.0 46.144     1
pit[16,1]    0.000  0.000   0.000   0.000   0.000    FALSE 1.0  3.164     1
pit[17,1]    0.000  0.000   0.000   0.000   0.000    FALSE 1.0 12.268     1
pit[18,1]    0.000  0.000   0.000   0.000   0.000    FALSE 1.0 24.030     1
pit[19,1]    0.000  0.000   0.000   0.000   0.000    FALSE 1.0 52.667     1
pit[20,1]    0.000  0.000   0.000   0.000   0.000    FALSE 1.0 31.711     1
pit[1,2]     0.000  0.000   0.000   0.000   0.000    FALSE 1.0 13.064     1
pit[2,2]     0.000  0.000   0.000   0.000   0.000    FALSE 1.0 16.990     1
pit[3,2]     0.000  0.000   0.000   0.000   0.000    FALSE 1.0 44.056     1
pit[4,2]     0.000  0.000   0.000   0.000   0.000    FALSE 1.0 17.895     1
pit[5,2]     0.000  0.000   0.000   0.000   0.000    FALSE 1.0 19.220     1
pit[6,2]     0.000  0.000   0.000   0.000   0.000    FALSE 1.0 46.416     1
pit[7,2]     0.000  0.000   0.000   0.000   0.000    FALSE 1.0 52.210     1
pit[8,2]     0.000  0.000   0.000   0.000   0.000    FALSE 1.0  8.495     1
pit[9,2]     0.000  0.000   0.000   0.000   0.000    FALSE 1.0 24.812     1
pit[10,2]    0.000  0.000   0.000   0.000   0.000    FALSE 1.0 31.174     1
pit[11,2]    0.000  0.000   0.000   0.000   0.000    FALSE 1.0 48.592     1
pit[12,2]    0.000  0.000   0.000   0.000   0.000    FALSE 1.0 28.506     1
pit[13,2]    0.000  0.000   0.000   0.000   0.000    FALSE 1.0  8.271     1
pit[14,2]    0.000  0.000   0.000   0.000   0.000    FALSE 1.0 39.914     1
pit[15,2]    0.000  0.000   0.000   0.000   0.000    FALSE 1.0 52.118     1
pit[16,2]    0.000  0.000   0.000   0.000   0.000    FALSE 1.0  1.402     1
pit[17,2]    0.000  0.000   0.000   0.000   0.000    FALSE 1.0  3.396     1
pit[18,2]    0.000  0.000   0.000   0.000   0.000    FALSE 1.0 26.605     1
pit[19,2]    0.000  0.000   0.000   0.000   0.000    FALSE 1.0 20.285     1
pit[20,2]    0.000  0.000   0.000   0.000   0.000    FALSE 1.0 20.645     1
pit[1,3]     0.000  0.000   0.000   0.000   0.000    FALSE 1.0  7.704     1
pit[2,3]     0.000  0.000   0.000   0.000   0.000    FALSE 1.0  0.944     1
pit[3,3]     0.000  0.000   0.000   0.000   0.000    FALSE 1.0 52.881     1
pit[4,3]     0.000  0.000   0.000   0.000   0.000    FALSE 1.0 15.553     1
pit[5,3]     0.000  0.000   0.000   0.000   0.000    FALSE 1.0 14.434     1
pit[6,3]     0.000  0.000   0.000   0.000   0.000    FALSE 1.0  2.484     1
pit[7,3]     0.000  0.000   0.000   0.000   0.000    FALSE 1.0 50.668     1
pit[8,3]     0.000  0.000   0.000   0.000   0.000    FALSE 1.0 24.700     1
pit[9,3]     0.000  0.000   0.000   0.000   0.000    FALSE 1.0  5.467     1
pit[10,3]    0.000  0.000   0.000   0.000   0.000    FALSE 1.0 58.360     1
pit[11,3]    0.000  0.000   0.000   0.000   0.000    FALSE 1.0 51.129     1
pit[12,3]    0.000  0.000   0.000   0.000   0.000    FALSE 1.0 31.265     1
pit[13,3]    0.000  0.000   0.000   0.000   0.000    FALSE 1.0  3.455     1
pit[14,3]    0.000  0.000   0.000   0.000   0.000    FALSE 1.0  9.752     1
pit[15,3]    0.000  0.000   0.000   0.000   0.000    FALSE 1.0 52.242     1
pit[16,3]    0.000  0.000   0.000   0.000   0.000    FALSE 1.0 20.779     1
pit[17,3]    0.000  0.000   0.000   0.000   0.000    FALSE 1.0 28.627     1
pit[18,3]    0.000  0.000   0.000   0.000   0.000    FALSE 1.0  8.427     1
pit[19,3]    0.000  0.000   0.000   0.000   0.000    FALSE 1.0  5.913     1
pit[20,3]    0.000  0.000   0.000   0.000   0.000    FALSE 1.0 15.146     1
pit[1,4]     0.000  0.000   0.000   0.000   0.000    FALSE 1.0 10.232     1
pit[2,4]     0.000  0.000   0.000   0.000   0.000    FALSE 1.0 38.961     1
pit[3,4]     0.000  0.000   0.000   0.000   0.000    FALSE 1.0 50.758     1
pit[4,4]     0.000  0.000   0.000   0.000   0.000    FALSE 1.0 32.788     1
pit[5,4]     0.000  0.000   0.000   0.000   0.000    FALSE 1.0  4.176     1
pit[6,4]     0.000  0.000   0.000   0.000   0.000    FALSE 1.0 50.633     1
pit[7,4]     0.000  0.000   0.000   0.000   0.000    FALSE 1.0 35.684     1
pit[8,4]     0.000  0.000   0.000   0.000   0.000    FALSE 1.0  7.917     1
pit[9,4]     0.000  0.000   0.000   0.000   0.000    FALSE 1.0  7.211     1
pit[10,4]    0.000  0.000   0.000   0.000   0.000    FALSE 1.0 39.496     1
pit[11,4]    0.000  0.000   0.000   0.000   0.000    FALSE 1.0 40.445     1
pit[12,4]    0.000  0.000   0.000   0.000   0.000    FALSE 1.0 19.869     1
pit[13,4]    0.000  0.000   0.000   0.000   0.000    FALSE 1.0 24.888     1
pit[14,4]    0.000  0.000   0.000   0.000   0.000    FALSE 1.0  4.988     1
pit[15,4]    0.000  0.000   0.000   0.000   0.000    FALSE 1.0 52.557     1
pit[16,4]    0.000  0.000   0.000   0.000   0.000    FALSE 1.0  4.046     1
pit[17,4]    0.000  0.000   0.000   0.000   0.000    FALSE 1.0 23.680     1
pit[18,4]    0.000  0.000   0.000   0.000   0.000    FALSE 1.0 30.557     1
pit[19,4]    0.000  0.000   0.000   0.000   0.000    FALSE 1.0 22.686     1
pit[20,4]    0.000  0.000   0.000   0.000   0.000    FALSE 1.0 35.248     1
pit[1,5]     0.000  0.000   0.000   0.000   0.000    FALSE 1.0  6.609     1
 [ reached 'max' / getOption("max.print") -- omitted 21 rows ]

**WARNING** Rhat values indicate convergence failure. 
Rhat is the potential scale reduction factor (at convergence, Rhat=1). 
For each parameter, n.eff is a crude measure of effective sample size. 

overlap0 checks if 0 falls in the parameter's 95% credible interval.
f is the proportion of the posterior with the same sign as the mean;
i.e., our confidence that the parameter is positive or negative.

DIC info: (pD = var(deviance)/2) 
pD = 19.7 and DIC = 1249.054 
DIC is an estimate of expected predictive error (lower is better).

但是如果我同时包含了检测的协变量效应和检测概率的随机分布，事情就变糟了。* 见下面的代码 *

nx <- "
model{
# Abundance
for (i in 1:nSites) {
N[i]~ dpois(lambda[i])
log(lambda[i])<-alphao+inprod(alpha, location[i,])
}

for (i in 1:nSites) {
for(t in 1:nOcc){
y[i,t]~ dbin(pit[i,t],N[i])
pit[i,t]~ dbeta(1,1)
logit(pit[i,t]) <- beta0+inprod(beta, location[i,])+inprod(beta1,c(cov1[i,t],cov2[i,t]))
}
}

 # Priors
 alphao ~ dnorm(1.2824,0.302)
    for(i in 1:nA){
      alpha[i] ~ dnorm(0.284,0.570)
    }
beta0 ~ dunif(-1.67,0.61)
   for(i in 1:3){
     beta[i] ~ dnorm(-0.370,0.254)
   }
   for(i in 1:2){
     beta1[i] ~ dnorm(-0.104,0.44)
   }

# det
sigma ~ dunif(0,1)
fac <-(1-sigma^2)/sigma^2

# derived
}"
writeLines(nx,con="mod1.txt")

watch=c("alphao","alpha","lambda","beta0","beta","beta1","pit","sigma")

inits = function() list(N = apply(y,1,max,na.rm=T))
set.seed(100)
mod<-jagsUI::jags(data,
                  parameters.to.save=watch,inits=inits,
                  model.file="mod1.txt",n.iter=3,
                  n.chains=2,DIC=TRUE)

mod

这就是错误。

Error in jags.model(file = model.file, data = data, inits = inits, n.chains = n.chains,  : 
  RUNTIME ERROR:
Compilation error on line 12.
Attempt to redefine node pit[1,1]

我明白它在告诉我;pit[i,t]~ dbeta(1,1)正在被logit(pit[i,t])<-beta0+inprod(beta1, location[i,])+inprod(beta2,c(cov1[i,t],cov2[i,t]))覆盖，但是应该如何准确地实现这个模型。here这个模型是在没有检测协变量的情况下实现的。这不是我要找的。

注意：我编辑了我的问题，以匹配我编写的公式中的参数

出现此错误是因为未正确指定检测模型。此处有两个进程正在尝试确定pit[i,t]，第一个是pit[i,t]~ dbeta(1,1)
那么
logit(pit[i,t])<-beta0+inprod(beta1, location[i,])+inprod(beta2,c(cov1[i,j],cov2[i,j]))
因此，当第二进程试图设置pit[i,t]的值时，它发现另一进程已经这样做了，因此产生了这个错误。
在写代码的时候我忘记了，pi't是一个随机值，服从贝塔分布，我应该估算贝塔二项分布的参数，生成随机pi't，但我在这里选择了随机值。
以下是正确的实现

nx <- "
model{
# Abundance
for (i in 1:nSites) {
N[i]~ dpois(lambda[i])
log(lambda[i])<-alphao+inprod(alpha, location[i,])
}

for (i in 1:nSites) {
for(t in 1:nOcc){
y[i,t]~ dbin(pit_h[i,t],N[i])
pit_h[i,t]~ dbeta((pit[i,t]*fac),(fac*(1-pit[i,t])))
logit(pit[i,t]) <- beta0+inprod(beta, location[i,])+inprod(beta1,c(cov1[i,t],cov2[i,t]))
}
}

 # Priors
 alphao ~ dnorm(1.2824,0.302)
    for(i in 1:nA){
      alpha[i] ~ dnorm(0.284,0.570)
    }
beta0 ~ dunif(-1.67,0.61)
   for(i in 1:3){
     beta[i] ~ dnorm(-0.370,0.254)
   }
   for(i in 1:2){
     beta1[i] ~ dnorm(-0.104,0.44)
   }

# det
sigma ~ dunif(0,1)
fac <-(1-sigma^2)/sigma^2

# derived
}"
writeLines(nx,con="mod1.txt")

watch=c("alphao","alpha","lambda","beta0","beta","beta1","pit","sigma")

inits = function() list(N = apply(y,1,max,na.rm=T))
set.seed(100)
mod<-jagsUI::jags(data,
                  parameters.to.save=watch,inits=inits,
                  model.file="mod1.txt",n.iter=3,
                  n.chains=2,DIC=TRUE)

mod

屈服

JAGS output for model 'mod1.txt', generated by jagsUI.
Estimates based on 2 chains of 3 iterations,
adaptation = 100 iterations (sufficient),
burn-in = 0 iterations and thin rate = 1,
yielding 6 total samples from the joint posterior. 
MCMC ran for 0.051 minutes at time 2023-01-11 17:53:55.

             mean     sd   2.5%    50%  97.5% overlap0   f   Rhat n.eff
alphao      2.114  0.887  1.205  2.127  2.970    FALSE 1.0 19.132     2
alpha[1]   -0.181  0.774 -0.929 -0.232  0.674     TRUE 0.5 13.424     2
alpha[2]   -0.792  0.437 -1.211 -0.821 -0.284    FALSE 1.0 10.708     2
alpha[3]   -0.123  0.391 -0.537 -0.114  0.306     TRUE 0.5 10.409     2
lambda[1]  11.143  8.192  3.338 10.511 19.499    FALSE 1.0 16.476     2
lambda[2]   6.989  1.152  5.440  7.218  8.436    FALSE 1.0  2.041     3
lambda[3]   4.078  1.757  2.388  3.947  5.864    FALSE 1.0 18.172     2
lambda[4]  12.868 11.770  2.060 11.100 26.299    FALSE 1.0 10.437     2
lambda[5]  11.143  8.192  3.338 10.511 19.499    FALSE 1.0 16.476     2
lambda[6]   6.989  1.152  5.440  7.218  8.436    FALSE 1.0  2.041     3
lambda[7]   4.078  1.757  2.388  3.947  5.864    FALSE 1.0 18.172     2
lambda[8]  12.868 11.770  2.060 11.100 26.299    FALSE 1.0 10.437     2
lambda[9]  11.143  8.192  3.338 10.511 19.499    FALSE 1.0 16.476     2
lambda[10]  6.989  1.152  5.440  7.218  8.436    FALSE 1.0  2.041     3
lambda[11]  4.078  1.757  2.388  3.947  5.864    FALSE 1.0 18.172     2
lambda[12] 12.868 11.770  2.060 11.100 26.299    FALSE 1.0 10.437     2
lambda[13] 11.143  8.192  3.338 10.511 19.499    FALSE 1.0 16.476     2
lambda[14]  6.989  1.152  5.440  7.218  8.436    FALSE 1.0  2.041     3
lambda[15]  4.078  1.757  2.388  3.947  5.864    FALSE 1.0 18.172     2
lambda[16] 12.868 11.770  2.060 11.100 26.299    FALSE 1.0 10.437     2
lambda[17] 11.143  8.192  3.338 10.511 19.499    FALSE 1.0 16.476     2
lambda[18]  6.989  1.152  5.440  7.218  8.436    FALSE 1.0  2.041     3
lambda[19]  4.078  1.757  2.388  3.947  5.864    FALSE 1.0 18.172     2
lambda[20] 12.868 11.770  2.060 11.100 26.299    FALSE 1.0 10.437     2
beta0      -0.162  0.447 -0.600 -0.186  0.325     TRUE 0.5 14.944     2
beta[1]     0.924  0.693  0.243  0.892  1.644    FALSE 1.0 14.009     2
beta[2]     2.147  0.133  1.987  2.152  2.288    FALSE 1.0  7.489     2
beta[3]     1.047  0.911  0.072  1.073  1.920    FALSE 1.0 17.258     2
beta1[1]   -0.088  0.008 -0.096 -0.088 -0.080    FALSE 1.0 42.539     2
beta1[2]    0.121  0.022  0.100  0.121  0.142    FALSE 1.0 55.542     2
pit[1,1]    0.067  0.041  0.029  0.061  0.114    FALSE 1.0 10.366     2
pit[2,1]    0.117  0.015  0.098  0.122  0.131    FALSE 1.0  0.923     6
pit[3,1]    0.341  0.181  0.169  0.324  0.538    FALSE 1.0 13.526     2
pit[4,1]    0.195  0.183  0.025  0.187  0.379    FALSE 1.0 29.881     2
pit[5,1]    0.060  0.037  0.026  0.054  0.102    FALSE 1.0 10.199     2
pit[6,1]    0.114  0.014  0.095  0.118  0.127    FALSE 1.0  0.926     6
pit[7,1]    0.360  0.186  0.184  0.345  0.563    FALSE 1.0 13.999     2
pit[8,1]    0.200  0.187  0.026  0.191  0.387    FALSE 1.0 30.322     2
pit[9,1]    0.071  0.043  0.031  0.064  0.120    FALSE 1.0 10.459     2
pit[10,1]   0.128  0.016  0.107  0.133  0.142    FALSE 1.0  0.915     6
pit[11,1]   0.334  0.179  0.164  0.318  0.530    FALSE 1.0 13.373     2
pit[12,1]   0.216  0.201  0.029  0.207  0.415    FALSE 1.0 31.999     2
pit[13,1]   0.063  0.039  0.028  0.058  0.108    FALSE 1.0 10.284     2
pit[14,1]   0.105  0.013  0.088  0.110  0.118    FALSE 1.0  0.933     6
pit[15,1]   0.333  0.178  0.163  0.316  0.529    FALSE 1.0 13.343     2
pit[16,1]   0.219  0.203  0.030  0.211  0.421    FALSE 1.0 32.359     2
pit[17,1]   0.065  0.040  0.029  0.060  0.112    FALSE 1.0 10.335     2
pit[18,1]   0.110  0.014  0.091  0.114  0.123    FALSE 1.0  0.929     6
pit[19,1]   0.374  0.189  0.194  0.358  0.578    FALSE 1.0 14.324     2
pit[20,1]   0.161  0.153  0.019  0.153  0.316    FALSE 1.0 26.658     2
pit[1,2]    0.066  0.040  0.029  0.060  0.113    FALSE 1.0 10.349     2
pit[2,2]    0.105  0.013  0.087  0.109  0.118    FALSE 1.0  0.934     6
pit[3,2]    0.327  0.177  0.160  0.311  0.522    FALSE 1.0 13.219     2
pit[4,2]    0.198  0.186  0.026  0.190  0.384    FALSE 1.0 30.170     2
pit[5,2]    0.070  0.043  0.031  0.064  0.120    FALSE 1.0 10.455     2
pit[6,2]    0.130  0.016  0.109  0.135  0.144    FALSE 1.0  0.914     6
pit[7,2]    0.366  0.187  0.188  0.350  0.569    FALSE 1.0 14.133     2
pit[8,2]    0.212  0.198  0.028  0.204  0.409    FALSE 1.0 31.621     2
pit[9,2]    0.075  0.046  0.034  0.069  0.127    FALSE 1.0 10.557     2
pit[10,2]   0.115  0.014  0.096  0.120  0.128    FALSE 1.0  0.925     6
pit[11,2]   0.341  0.181  0.169  0.325  0.539    FALSE 1.0 13.537     2
pit[12,2]   0.174  0.165  0.021  0.165  0.340    FALSE 1.0 27.825     2
pit[13,2]   0.062  0.038  0.027  0.057  0.107    FALSE 1.0 10.267     2
pit[14,2]   0.122  0.015  0.102  0.128  0.136    FALSE 1.0  0.919     6
pit[15,2]   0.365  0.187  0.187  0.349  0.568    FALSE 1.0 14.103     2
pit[16,2]   0.225  0.208  0.031  0.216  0.431    FALSE 1.0 32.922     2
pit[17,2]   0.059  0.036  0.026  0.054  0.101    FALSE 1.0 10.182     2
pit[18,2]   0.112  0.014  0.093  0.116  0.125    FALSE 1.0  0.928     6
pit[19,2]   0.297  0.167  0.139  0.280  0.483    FALSE 1.0 12.542     2
pit[20,2]   0.193  0.182  0.025  0.185  0.375    FALSE 1.0 29.672     2
pit[1,3]    0.062  0.038  0.027  0.056  0.106    FALSE 1.0 10.257     2
pit[2,3]    0.094  0.012  0.077  0.098  0.105    FALSE 1.0  0.944     6
pit[3,3]    0.409  0.195  0.223  0.395  0.619    FALSE 1.0 15.215     2
pit[4,3]    0.202  0.189  0.026  0.194  0.391    FALSE 1.0 30.561     2
pit[5,3]    0.067  0.041  0.030  0.061  0.114    FALSE 1.0 10.372     2
pit[6,3]    0.095  0.012  0.079  0.099  0.107    FALSE 1.0  0.943     6
pit[7,3]    0.352  0.184  0.177  0.336  0.552    FALSE 1.0 13.790     2
pit[8,3]    0.185  0.174  0.023  0.176  0.359    FALSE 1.0 28.825     2
pit[9,3]    0.060  0.037  0.026  0.055  0.104    FALSE 1.0 10.218     2
pit[10,3]   0.165  0.019  0.140  0.172  0.182    FALSE 1.0  0.893     6
pit[11,3]   0.355  0.184  0.180  0.339  0.556    FALSE 1.0 13.870     2
pit[12,3]   0.267  0.241  0.042  0.260  0.504    FALSE 1.0 37.848     2
pit[13,3]   0.059  0.036  0.026  0.054  0.101    FALSE 1.0 10.183     2
pit[14,3]   0.086  0.011  0.071  0.089  0.097    FALSE 1.0  0.953     6
pit[15,3]   0.430  0.198  0.241  0.416  0.641    FALSE 1.0 15.755     2
pit[16,3]   0.193  0.181  0.025  0.184  0.374    FALSE 1.0 29.647     2
pit[17,3]   0.078  0.047  0.035  0.072  0.133    FALSE 1.0 10.632     2
pit[18,3]   0.087  0.012  0.072  0.090  0.098    FALSE 1.0  0.952     6
pit[19,3]   0.286  0.163  0.131  0.269  0.467    FALSE 1.0 12.293     2
pit[20,3]   0.242  0.221  0.035  0.233  0.460    FALSE 1.0 34.824     2
pit[1,4]    0.064  0.039  0.028  0.058  0.109    FALSE 1.0 10.300     2
pit[2,4]    0.122  0.015  0.102  0.127  0.135    FALSE 1.0  0.920     6
pit[3,4]    0.352  0.184  0.178  0.336  0.553    FALSE 1.0 13.805     2
pit[4,4]    0.155  0.148  0.018  0.147  0.305    FALSE 1.0 26.121     2
pit[5,4]    0.059  0.037  0.026  0.054  0.102    FALSE 1.0 10.196     2
pit[6,4]    0.136  0.016  0.114  0.142  0.151    FALSE 1.0  0.910     6
pit[7,4]    0.313  0.173  0.150  0.296  0.504    FALSE 1.0 12.894     2
pit[8,4]    0.213  0.198  0.029  0.205  0.410    FALSE 1.0 31.703     2
pit[9,4]    0.062  0.038  0.027  0.056  0.106    FALSE 1.0 10.249     2
pit[10,4]   0.122  0.015  0.102  0.127  0.136    FALSE 1.0  0.920     6
pit[11,4]   0.320  0.175  0.155  0.304  0.513    FALSE 1.0 13.056     2
pit[12,4]   0.248  0.226  0.037  0.240  0.471    FALSE 1.0 35.556     2
pit[13,4]   0.075  0.046  0.034  0.069  0.128    FALSE 1.0 10.559     2
pit[14,4]   0.090  0.012  0.074  0.093  0.101    FALSE 1.0  0.948     6
pit[15,4]   0.421  0.197  0.233  0.407  0.632    FALSE 1.0 15.524     2
pit[16,4]   0.218  0.203  0.030  0.210  0.419    FALSE 1.0 32.238     2
pit[17,4]   0.074  0.045  0.033  0.068  0.126    FALSE 1.0 10.536     2
pit[18,4]   0.115  0.014  0.095  0.119  0.128    FALSE 1.0  0.925     6
pit[19,4]   0.299  0.168  0.140  0.283  0.486    FALSE 1.0 12.588     2
pit[20,4]   0.277  0.249  0.044  0.270  0.520    FALSE 1.0 39.039     2
pit[1,5]    0.052  0.032  0.022  0.047  0.089    FALSE 1.0 10.005     2
 [ reached 'max' / getOption("max.print") -- omitted 21 rows ]

**WARNING** Rhat values indicate convergence failure. 
Rhat is the potential scale reduction factor (at convergence, Rhat=1). 
For each parameter, n.eff is a crude measure of effective sample size. 

overlap0 checks if 0 falls in the parameter's 95% credible interval.
f is the proportion of the posterior with the same sign as the mean;
i.e., our confidence that the parameter is positive or negative.

DIC info: (pD = var(deviance)/2) 
pD = 32.5 and DIC = 215.949 
DIC is an estimate of expected predictive error (lower is better).
>

R语言向β-二项式混合模型添加协变量时尝试重新定义节点p[1，1]

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R语言 向β-二项式混合模型添加协变量时尝试重新定义节点p[1，1]

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R语言向β-二项式混合模型添加协变量时尝试重新定义节点p[1，1]