# Why hierarchical model get a lot of warnings

I want to construct hierarchical ordered logit model. I use several ways but get a lot of warnings. I use induced dirichlet prior for threshold and reduce sum to speed up. My stan code like this.

``````functions {
real partial_sum(
int[] slice_y,
int start, int end,
matrix x1,matrix x2, vector[] thresh,
vector beta1, vector[] beta2, int[] g
)
{
real lp = 0;
for(i in start:end)
lp += ordered_logistic_lpmf(slice_y[i-start+1] |x1[i]*beta1+x2[i]*beta2[g[i]]  , thresh[g[i]]);
return lp;
}
real induced_dirichlet_lpdf(vector c, vector alpha, real phi) {
int K = num_elements(c) + 1;
vector[K - 1] sigma = inv_logit(phi - c);
vector[K] p;
matrix[K, K] J = rep_matrix(0, K, K);
// Induced ordinal probabilities
p[1] = 1 - sigma[1];
for (k in 2:(K - 1))
p[k] = sigma[k - 1] - sigma[k];
p[K] = sigma[K - 1];
// Baseline column of Jacobian
for (k in 1:K) J[k, 1] = 1;
// Diagonal entries of Jacobian
for (k in 2:K) {
real rho = sigma[k - 1] * (1 - sigma[k - 1]);
J[k, k] = - rho;
J[k - 1, k] = rho;
}
return   dirichlet_lpdf(p | alpha)
+ log_determinant(J);
}
}

data {
int<lower=1> N;             // Number of observations
int<lower=1> K;             // Number of ordinal categories
int<lower=1> D;             //Number of covariates
int<lower=1> DN;          //Number of  covariates to estimate use time-varying beta
array[N] int<lower=1, upper=K> y; // Observed ordinals
matrix[N,D-DN] x1;
matrix[N,DN] x2;
int g[N];                   //time indicator
int<lower=1> P;        //P different time
}
parameters {
vector[D-DN] beta1;
vector[DN] beta2[P];     //time varying beta
ordered[K - 1] thresh[P];    //time varying threshold
real<lower=0> sigma;

vector<lower=0,upper=15>[DN] Omega;
}

model {
vector[DN] Zero= rep_vector(0,DN);
beta1~ normal(0,10);
beta2[1] ~normal(0,10);
//tau ~ cauchy(0,2.5);
//Omega ~ lkj_corr(2);
thresh[1] ~ induced_dirichlet(rep_vector(1, K), 0);
for (i in 1: (P-1)){
(thresh[i+1] - thresh[i]) ~ normal(0,sigma);
//(beta2[i+1]-beta2[i]) ~ normal(0,omega[i]);
(beta2[i+1]-beta2[i]) ~ normal(Zero,Omega);
}
target += reduce_sum(partial_sum, y, 1, x1,x2, thresh, beta1,beta2, g);
}

``````

I have got the warnings like this:

``````Warning messages:
1: There were 152 divergent transitions after warmup. See
https://mc-stan.org/misc/warnings.html#divergent-transitions-after-warmup
to find out why this is a problem and how to eliminate them.
2: Examine the pairs() plot to diagnose sampling problems

3: Bulk Effective Samples Size (ESS) is too low, indicating posterior means and medians may be unreliable.
Running the chains for more iterations may help. See
https://mc-stan.org/misc/warnings.html#bulk-ess
4: Tail Effective Samples Size (ESS) is too low, indicating posterior variances and tail quantiles may be unreliable.
Running the chains for more iterations may help. See
https://mc-stan.org/misc/warnings.html#tail-ess
``````

And my estimate result is

``````               mean se_mean    sd    2.5%     25%     50%     75%   97.5% n_eff Rhat
beta1[1]     -17.71    0.20  9.61  -36.27  -24.02  -17.88  -11.39    1.90  2418 1.00
beta1[2]      -4.67    0.18  9.95  -23.83  -11.40   -4.60    2.07   15.01  2919 1.00
beta1[3]     -19.19    0.24  9.22  -36.77  -25.41  -19.40  -13.25   -0.33  1427 1.00
beta1[4]      -0.56    0.02  0.44   -1.53   -0.83   -0.54   -0.24    0.21   824 1.00
beta2[1,1]     7.89    0.17  5.44   -3.72    4.40    8.47   11.79   17.12  1016 1.00
beta2[1,2]    -3.45    0.03  1.44   -6.06   -4.47   -3.54   -2.51   -0.47  2296 1.00
beta2[1,3]    -0.28    0.00  0.10   -0.46   -0.34   -0.28   -0.22   -0.07  2083 1.00
beta2[1,4]     2.73    0.01  0.25    2.29    2.55    2.71    2.88    3.25  1564 1.00
beta2[1,5]     2.17    0.03  0.83    0.96    1.49    2.05    2.72    3.99   815 1.01
beta2[1,6]     1.33    0.01  0.52    0.35    0.99    1.30    1.64    2.43  2979 1.00
beta2[1,7]    -0.13    0.01  0.28   -0.66   -0.31   -0.14    0.03    0.50  2876 1.00
beta2[2,1]    12.75    0.08  4.64    3.59    9.82   12.51   15.34   23.07  3000 1.00
beta2[2,2]    -5.68    0.05  1.84   -9.82   -6.78   -5.39   -4.39   -2.67  1286 1.00
beta2[2,3]    -0.30    0.00  0.11   -0.54   -0.36   -0.30   -0.24   -0.09  2335 1.00
beta2[2,4]     2.62    0.00  0.20    2.24    2.49    2.61    2.74    3.06  1898 1.00
beta2[2,5]     1.56    0.01  0.51    0.61    1.23    1.52    1.88    2.64  2063 1.00
beta2[2,6]     0.82    0.01  0.49   -0.23    0.50    0.87    1.17    1.67  1735 1.00
beta2[2,7]    -0.24    0.01  0.30   -0.95   -0.39   -0.22   -0.07    0.32  2532 1.00
beta2[3,1]    14.35    0.08  3.71    7.68   11.81   14.12   16.58   22.22  2279 1.00
beta2[3,2]    -3.61    0.02  1.07   -5.56   -4.39   -3.64   -2.90   -1.40  1852 1.00
beta2[3,3]    -0.30    0.00  0.07   -0.43   -0.34   -0.30   -0.25   -0.16  2156 1.00
beta2[3,4]     2.61    0.00  0.15    2.33    2.51    2.61    2.71    2.93  2004 1.00
beta2[3,5]     1.19    0.01  0.31    0.55    0.99    1.20    1.39    1.78  1862 1.00
beta2[3,6]     1.45    0.01  0.34    0.84    1.22    1.42    1.68    2.16  2620 1.00
beta2[3,7]    -0.15    0.00  0.21   -0.53   -0.29   -0.16   -0.02    0.30  2377 1.00
beta2[4,1]    12.17    0.07  3.79    4.77    9.72   12.11   14.64   19.68  3236 1.00
beta2[4,2]    -6.45    0.06  1.72  -10.21   -7.59   -6.28   -5.16   -3.69   851 1.00
beta2[4,3]    -0.30    0.00  0.09   -0.47   -0.35   -0.30   -0.25   -0.10  2597 1.00
beta2[4,4]     2.69    0.01  0.20    2.36    2.54    2.66    2.81    3.16  1135 1.00
beta2[4,5]     1.33    0.01  0.34    0.66    1.12    1.30    1.53    2.06  2198 1.00
beta2[4,6]     0.86    0.01  0.37    0.11    0.61    0.89    1.13    1.51  1726 1.00
beta2[4,7]    -0.17    0.00  0.23   -0.59   -0.33   -0.19   -0.04    0.34  2767 1.00
beta2[5,1]    12.68    0.08  3.48    5.81   10.41   12.62   14.93   19.54  1941 1.00
beta2[5,2]    -4.76    0.02  0.90   -6.56   -5.37   -4.76   -4.15   -3.01  3032 1.00
beta2[5,3]    -0.32    0.00  0.07   -0.46   -0.37   -0.32   -0.28   -0.20  2368 1.00
beta2[5,4]     2.41    0.00  0.16    2.10    2.30    2.41    2.51    2.72  1462 1.00
beta2[5,5]     1.17    0.01  0.27    0.62    0.98    1.18    1.35    1.67  1938 1.00
beta2[5,6]     1.44    0.01  0.28    0.93    1.25    1.43    1.63    2.00  1908 1.00
beta2[5,7]    -0.35    0.00  0.20   -0.77   -0.48   -0.34   -0.22    0.00  2124 1.00
thresh[1,1]   -1.91    0.03  1.21   -4.33   -2.72   -1.86   -1.09    0.39  1695 1.00
thresh[1,2]    1.03    0.04  1.28   -1.57    0.16    1.03    1.91    3.46  1148 1.00
thresh[1,3]    4.45    0.04  1.38    1.68    3.54    4.44    5.40    7.17  1094 1.00
thresh[1,4]    7.26    0.04  1.41    4.42    6.35    7.26    8.25    9.89  1142 1.00
thresh[2,1]   -2.03    0.03  1.39   -4.98   -2.93   -1.95   -1.11    0.50  1747 1.00
thresh[2,2]    1.79    0.03  1.22   -0.62    0.96    1.80    2.59    4.16  1798 1.00
thresh[2,3]    5.72    0.03  1.22    3.42    4.89    5.69    6.52    8.16  1718 1.00
thresh[2,4]    8.30    0.03  1.25    5.91    7.43    8.30    9.12   10.80  1696 1.00
thresh[3,1]   -1.75    0.04  1.30   -4.28   -2.63   -1.75   -0.92    0.80  1324 1.01
thresh[3,2]    2.75    0.03  1.22    0.46    1.91    2.72    3.53    5.20  1262 1.01
thresh[3,3]    6.07    0.03  1.23    3.79    5.21    6.05    6.88    8.62  1359 1.01
thresh[3,4]    8.55    0.03  1.26    6.20    7.68    8.53    9.36   11.14  1376 1.00
thresh[4,1]   -2.42    0.04  1.52   -5.54   -3.37   -2.36   -1.44    0.50  1622 1.00
thresh[4,2]    2.71    0.04  1.37    0.30    1.76    2.63    3.51    5.61  1189 1.01
thresh[4,3]    6.92    0.05  1.45    4.40    5.93    6.82    7.81    9.95  1034 1.01
thresh[4,4]    9.19    0.05  1.47    6.66    8.19    9.10   10.07   12.27  1051 1.01
thresh[5,1]   -2.88    0.04  1.72   -6.66   -3.82   -2.78   -1.76    0.21  1704 1.00
thresh[5,2]    3.50    0.06  1.69    0.68    2.36    3.31    4.48    7.29   778 1.01
thresh[5,3]    7.42    0.06  1.75    4.51    6.22    7.23    8.47   11.43   758 1.01
thresh[5,4]   10.01    0.07  1.83    6.97    8.74    9.79   11.08   14.14   734 1.01
sigma          1.05    0.03  0.73    0.17    0.54    0.88    1.36    2.89   566 1.01
Omega[1]       5.65    0.16  3.87    0.33    2.46    4.99    8.27   14.10   621 1.00
Omega[2]       3.73    0.10  2.90    0.19    1.50    3.10    5.15   11.28   890 1.00
Omega[3]       0.11    0.00  0.14    0.00    0.03    0.07    0.14    0.48   921 1.00
Omega[4]       0.35    0.01  0.32    0.02    0.15    0.27    0.45    1.15  1350 1.00
Omega[5]       0.83    0.03  0.83    0.03    0.28    0.61    1.12    2.96   738 1.01
Omega[6]       1.08    0.03  1.02    0.06    0.42    0.82    1.42    3.81  1313 1.00
Omega[7]       0.39    0.02  0.57    0.02    0.12    0.25    0.48    1.53   859 1.00
lp__        -920.76    0.60 10.95 -940.60 -928.41 -921.10 -914.03 -896.96   330 1.01

``````

I don’t know why I can get these errors. And if my model has some errors to cause the identification problem?

I use a random walk may get a true results…
so I would not estimate the `sigma` and `Omega`.
But I still not understand why cause this problem.

The Stan team has some great suggestions in the warning messages and linked document on warnings. I’ve estimated some similar models and everything looks ok to me from a quick review. My suggestion would be looking at your priors and adapt_delta. How many samples are you running? 152 divergent transitions is a bit high, but it may be possible to (at least) reduce it by increasing adapt_delta.

my prior is:

``````  beta1~ normal(0,10);
beta2[1] ~normal(0,10);
thresh[1] ~ induced_dirichlet(rep_vector(1, K), 0);
``````

for `sigma` and `Omega` I use the default uniform prior, which is the hierarchical prior of :

``````for (i in 1: (P-1)){
(thresh[i+1] - thresh[i]) ~ normal(0,sigma);
(beta2[i+1]-beta2[i]) ~ normal(Zero,Omega);
}
``````

If I set sigma and Omega to 1(that may be a strong assumption), that would not have any errors.

And the adapt_delta is default 0.95.
I use `adapt_delta=0.999` but still get the errors.

And I find my model has a strong setting that

``````thresh[P] ~ normal(thresh[1] , sqrt([P-1] * sigma^2) )
...
``````

If it can causes the unidentify problems?

I consider use non-centered parameterization.
but `thresh` is an ordered vector. I don’t know how to tranformed it in block.

Noncentered parameterization is not feasible for `thresh` due to the constraints but might work for `beta2`.

Either way, I see `Omega` and `sigma` have no priors and their relationship to the observed data is also quite indirect. That could make them difficult to estimate. You should try and see if the divergencies disappear with

``````transformed parameters {
real sigma = 1.0;
vector[DN] Omega = rep_vector(1.0, DN);
}
``````

Non-centering `beta2` would look like this:

``````parameters {
vector[DN] beta2_raw[P];
vector[DN] Omega;
}
transformed parameters {
vector[DN] beta2[P];
beta2[1] = 10*beta2_raw[1];
for (i in 1:P) {
beta2[i] = beta2[i-1] + Omega .* beta2_raw[i];
}
}
model {
//Omega ~ prior()
for (i in 1:P) {
beta2_raw[i] ~ std_normal();
}
}
``````

or with a full covariance matrix

``````parameters {
vector[DN] beta2_raw[P];
vector[DN] Omega;
cholesky_factor_corr[DN] L_Omega;
}
transformed parameters {
vector[DN] beta2[P];
beta2[1] = 10*beta2_raw[1];
for (i in 1:P) {
beta2[i] = beta2[i-1] + Omega .* (L_Omega*beta2_raw[i]);
}
}
model {
//Omega ~ prior()
L_Omega ~ lkj_corr_cholesky(2.0);
for (i in 1:P) {
beta2_raw[i] ~ std_normal();
}
}
``````

Hi nhuurre,

If I set

Everything is OK! No errors and running quickly.
I try to use the NCP in `beta2`, But still get the errors like before. Maybe I have some problem in my dataset? I upload it And upload my R code. Hope it can be useful!
new_brmdata.csv (5.1 MB)
tv_iv_ncp_ologit.stan (2.0 KB)

``````library(rstan)
rstan_options(auto_write = TRUE)
options(mc.cores=parallel::detectCores())
SEED<- 16001
g<-factor(data\$kk, labels = 1:26)
data\$y<- as.numeric(data\$y)
data\$Industry<-as.factor(data\$Industry)
data\$Industry = relevel(data\$Industry, ref = "Z")
mf <- model.frame(y ~ x3+x10+x7+Assets+SOE+islist+CRA_F+Industry+Gdpcum01+rf+M2_ratio+PMI, data = data)
y <- mf\$y
x <- model.matrix(y ~ x3+x10+x7+Assets+SOE+islist+CRA_F+Industry+Gdpcum01+rf+M2_ratio+PMI, data = mf)[,-1]
N<- nrow(data)
D<- ncol(x)
K<-5
x1=x[,20:23]
x2 = x[,-20:-23]

g=as.numeric(g)
P=26
DN=19
dat<-list(N=N,D=D,K=K,y=y,x=x,x1=x1,x2=x2,g=g,P=P,DN=DN)
fit<- stan("tv_iv_ncp_ologit.stan",data=dat,control = list(adapt_delta = 0.999,max_treedepth=12))

``````

Then you should experiment with narrow priors, like

``````Omega ~ lognormal(0, 0.1);
``````

Hi nhuurre, I’m really curious about this block that why use ` beta2[1] = 10*beta2_raw[1]`?It may increases the running time.
If I can use the ` beta2[1] = beta2_raw[1]`?
thanks~

``````beta2[1] ~ normal(0,10);
``````

and I reparametrized it as

``````beta2_raw[1] ~ normal(0,1);
beta2[1] = 10*beta2_raw[1];
``````

That probably didn’t make much difference. It’s the `beta2[2:]` ones that needed reparametrization most.
So yes, you can use `beta2[1] = beta2_raw[1]` here.

``````  beta21 ~normal(0,10);
``````

So you should use

``````  beta2[1] = beta21;
``````

if you want to keep the original prior.

thanks~nhuurre, your suggestions really help me!
And The NCP really increase the running time. The former code spent me about 3h. The NCP
model may cost 24h(I have not get the result). If there are some methods to improve the speed?

Yikes!
Keep in mind that increasing `max_treedepth` and `adapt_delta` always increases runtime. If NCP helps it’s because NCP allows lowering `adapt_delta` without causing divergent transitions.

Yeah! I definitely forget that I really increase the `max_treedepth`and `alpha_delta`. Expecting the result can converge

Hi nhuurre,
I get the result, and there are two warnings:

``````Warning messages:
1: Bulk Effective Samples Size (ESS) is too low, indicating posterior means and medians may be unreliable.
Running the chains for more iterations may help. See
https://mc-stan.org/misc/warnings.html#bulk-ess
2: Tail Effective Samples Size (ESS) is too low, indicating posterior variances and tail quantiles may be unreliable.
Running the chains for more iterations may help. See
https://mc-stan.org/misc/warnings.html#tail-ess
``````

If I can ignore these warnings because no divergent here.
And I find that my `beta1` and `thresh` parameters have lower n_eff compared with other parameters.

``````
mean se_mean    sd      2.5%       25%       50%       75%     97.5% n_eff Rhat
beta1[1]         -4.74    0.08  2.14     -9.07     -6.16     -4.72     -3.29     -0.57   724 1.00
beta1[2]        -11.12    0.25  7.24    -25.52    -15.85    -11.05     -6.28      2.76   858 1.00
beta1[3]        -10.78    0.25  3.98    -19.27    -13.29    -10.59     -8.00     -3.61   251 1.01
beta1[4]          0.04    0.00  0.07     -0.09     -0.01      0.04      0.09      0.18   953 1.00
beta21[1]        15.30    0.06  3.36      8.04     13.19     15.46     17.58     21.45  3367 1.00
beta21[2]        -3.76    0.01  0.51     -4.69     -4.09     -3.80     -3.47     -2.64  2173 1.00
beta21[3]        -0.20    0.00  0.06     -0.32     -0.24     -0.20     -0.16     -0.08  3185 1.00
beta21[4]         2.68    0.00  0.07      2.55      2.64      2.67      2.71      2.82  1464 1.00
beta21[5]         1.77    0.00  0.22      1.30      1.63      1.78      1.90      2.22  2662 1.00
beta21[6]         1.17    0.01  0.35      0.46      0.94      1.18      1.41      1.84  3960 1.00
beta21[7]         0.00    0.00  0.26     -0.50     -0.19     -0.01      0.18      0.53  3692 1.00
beta21[8]         0.11    0.01  0.27     -0.49     -0.03      0.13      0.28      0.62  2731 1.00
beta21[9]         0.81    0.00  0.21      0.44      0.68      0.79      0.90      1.33  2366 1.00
beta21[10]       -0.41    0.00  0.24     -0.93     -0.53     -0.41     -0.29      0.11  2723 1.00
beta21[11]       -0.77    0.00  0.18     -1.22     -0.86     -0.73     -0.64     -0.49  1970 1.00
beta21[12]        0.60    0.01  0.24      0.04      0.45      0.63      0.77      1.00  2137 1.00
beta21[13]        0.40    0.02  0.98     -1.35     -0.08      0.31      0.78      2.78  2348 1.00
beta21[14]       -0.19    0.00  0.22     -0.70     -0.31     -0.17     -0.06      0.22  2784 1.00
beta21[15]        0.71    0.02  0.71     -0.43      0.28      0.58      1.04      2.43  1879 1.00
beta21[16]        1.78    0.02  0.96     -0.49      1.40      1.80      2.22      3.64  1738 1.00
beta21[17]        0.52    0.01  0.74     -1.12      0.09      0.57      0.99      1.90  3187 1.00
beta21[18]       -0.12    0.00  0.16     -0.47     -0.21     -0.12     -0.02      0.17  3060 1.00
beta21[19]        0.08    0.01  0.42     -0.85     -0.16      0.13      0.34      0.84  2546 1.00
thresh[1,1]       4.09    0.06  0.90      2.23      3.52      4.15      4.68      5.76   256 1.01
thresh[1,2]       8.00    0.06  0.89      6.12      7.42      8.05      8.61      9.63   236 1.01
thresh[1,3]      11.63    0.06  0.90      9.73     11.05     11.68     12.23     13.27   240 1.01
thresh[1,4]      14.39    0.06  0.89     12.53     13.83     14.44     15.00     16.07   244 1.01
thresh[2,1]       4.05    0.06  0.87      2.28      3.49      4.10      4.63      5.66   244 1.01
thresh[2,2]       8.15    0.06  0.85      6.36      7.60      8.19      8.73      9.72   233 1.01
thresh[2,3]      11.87    0.06  0.84     10.12     11.33     11.90     12.45     13.42   234 1.01
thresh[2,4]      14.50    0.06  0.86     12.72     13.96     14.55     15.08     16.13   236 1.01
thresh[3,1]       4.01    0.06  0.85      2.27      3.47      4.05      4.59      5.56   232 1.01
thresh[3,2]       8.39    0.05  0.80      6.74      7.86      8.42      8.93      9.86   224 1.01
thresh[3,3]      12.02    0.05  0.82     10.31     11.48     12.06     12.58     13.50   224 1.01
thresh[3,4]      14.57    0.05  0.84     12.84     14.04     14.62     15.14     16.11   232 1.01
thresh[4,1]       3.92    0.06  0.84      2.20      3.38      3.97      4.49      5.48   224 1.01
thresh[4,2]       8.17    0.05  0.79      6.55      7.67      8.23      8.70      9.65   224 1.01
thresh[4,3]      12.29    0.05  0.79     10.69     11.79     12.33     12.84     13.76   220 1.01
thresh[4,4]      14.76    0.05  0.81     13.13     14.25     14.81     15.32     16.25   233 1.01
thresh[5,1]       3.85    0.06  0.82      2.16      3.34      3.91      4.41      5.35   220 1.01
thresh[5,2]       8.11    0.05  0.75      6.60      7.63      8.15      8.61      9.50   219 1.01
thresh[5,3]      12.38    0.05  0.76     10.86     11.89     12.42     12.90     13.77   221 1.01
thresh[5,4]      15.19    0.05  0.77     13.64     14.71     15.23     15.72     16.62   226 1.01
thresh[6,1]       3.97    0.05  0.79      2.34      3.47      4.02      4.51      5.43   212 1.01
thresh[6,2]       7.86    0.05  0.74      6.32      7.38      7.90      8.36      9.25   222 1.01
thresh[6,3]      12.42    0.05  0.75     10.88     11.94     12.47     12.94     13.80   218 1.01
thresh[6,4]      15.41    0.05  0.75     13.92     14.93     15.44     15.92     16.81   226 1.01
thresh[7,1]       4.12    0.05  0.76      2.52      3.65      4.15      4.63      5.49   208 1.01
thresh[7,2]       7.73    0.05  0.73      6.24      7.27      7.77      8.23      9.10   218 1.01
thresh[7,3]      12.68    0.05  0.74     11.19     12.21     12.72     13.17     14.05   218 1.01
thresh[7,4]      15.37    0.05  0.75     13.87     14.89     15.41     15.88     16.78   227 1.01
thresh[8,1]       4.09    0.05  0.76      2.50      3.61      4.13      4.61      5.46   214 1.01
thresh[8,2]       7.71    0.05  0.73      6.22      7.23      7.74      8.20      9.07   216 1.01
thresh[8,3]      12.99    0.05  0.73     11.52     12.52     13.01     13.48     14.34   226 1.01
thresh[8,4]      15.39    0.05  0.75     13.88     14.90     15.44     15.90     16.82   236 1.01
thresh[9,1]       4.17    0.05  0.74      2.60      3.70      4.22      4.66      5.51   217 1.01
thresh[9,2]       7.65    0.05  0.71      6.20      7.19      7.68      8.13      8.95   215 1.01
thresh[9,3]      13.05    0.05  0.71     11.61     12.60     13.09     13.52     14.37   223 1.01
thresh[9,4]      15.72    0.05  0.73     14.24     15.26     15.75     16.21     17.05   230 1.01
thresh[10,1]      4.38    0.05  0.73      2.87      3.92      4.43      4.88      5.75   219 1.01
thresh[10,2]      7.63    0.05  0.70      6.20      7.19      7.68      8.11      8.94   223 1.01
thresh[10,3]     13.01    0.05  0.71     11.59     12.54     13.05     13.48     14.31   223 1.01
thresh[10,4]     15.73    0.05  0.72     14.31     15.28     15.76     16.21     17.08   228 1.01
thresh[11,1]      4.51    0.05  0.71      3.03      4.05      4.56      4.99      5.84   210 1.01
thresh[11,2]      7.66    0.05  0.67      6.29      7.23      7.69      8.11      8.93   214 1.01
thresh[11,3]     13.01    0.05  0.68     11.64     12.57     13.06     13.47     14.28   221 1.01
thresh[11,4]     15.90    0.05  0.70     14.51     15.46     15.94     16.37     17.22   224 1.01
thresh[12,1]      4.78    0.05  0.69      3.38      4.34      4.81      5.25      6.07   205 1.01
thresh[12,2]      7.49    0.05  0.66      6.11      7.08      7.53      7.93      8.73   217 1.01
thresh[12,3]     13.00    0.04  0.66     11.65     12.58     13.03     13.45     14.23   219 1.01
thresh[12,4]     15.92    0.04  0.67     14.52     15.49     15.96     16.37     17.16   222 1.01
thresh[13,1]      4.91    0.05  0.67      3.50      4.47      4.94      5.37      6.16   203 1.01
thresh[13,2]      7.43    0.05  0.66      6.05      7.00      7.46      7.87      8.68   211 1.01
thresh[13,3]     12.85    0.05  0.67     11.46     12.43     12.89     13.30     14.12   213 1.01
thresh[13,4]     15.82    0.05  0.67     14.44     15.38     15.87     16.27     17.08   214 1.01
thresh[14,1]      5.04    0.05  0.66      3.68      4.62      5.07      5.50      6.29   213 1.01
thresh[14,2]      7.50    0.04  0.64      6.17      7.10      7.53      7.93      8.71   213 1.01
thresh[14,3]     12.88    0.04  0.65     11.55     12.47     12.92     13.32     14.10   214 1.01
thresh[14,4]     15.78    0.04  0.66     14.42     15.35     15.82     16.21     17.03   215 1.01
thresh[15,1]      5.10    0.04  0.64      3.79      4.69      5.13      5.54      6.34   218 1.01
thresh[15,2]      7.61    0.04  0.61      6.34      7.22      7.63      8.04      8.78   216 1.01
thresh[15,3]     12.84    0.04  0.63     11.56     12.43     12.87     13.25     14.01   216 1.01
thresh[15,4]     15.89    0.04  0.63     14.57     15.48     15.94     16.30     17.08   222 1.01
thresh[16,1]      5.24    0.04  0.63      3.92      4.84      5.27      5.65      6.43   221 1.01
thresh[16,2]      7.51    0.04  0.61      6.26      7.13      7.54      7.92      8.68   220 1.01
thresh[16,3]     12.78    0.04  0.60     11.54     12.39     12.80     13.19     13.94   217 1.01
thresh[16,4]     15.92    0.04  0.61     14.68     15.54     15.95     16.33     17.10   219 1.01
thresh[17,1]      5.29    0.04  0.62      4.02      4.89      5.31      5.71      6.46   219 1.01
thresh[17,2]      7.78    0.04  0.59      6.56      7.40      7.80      8.18      8.90   221 1.01
thresh[17,3]     12.57    0.04  0.59     11.34     12.18     12.59     12.96     13.72   212 1.01
thresh[17,4]     15.99    0.04  0.60     14.76     15.61     16.00     16.38     17.14   216 1.01
thresh[18,1]      5.36    0.04  0.62      4.08      4.96      5.38      5.77      6.54   229 1.01
thresh[18,2]      7.70    0.04  0.59      6.52      7.32      7.72      8.10      8.84   222 1.01
thresh[18,3]     12.71    0.04  0.57     11.53     12.33     12.73     13.09     13.81   216 1.01
thresh[18,4]     15.95    0.04  0.59     14.75     15.58     15.97     16.35     17.11   218 1.01
thresh[19,1]      5.19    0.04  0.62      3.89      4.80      5.20      5.60      6.39   217 1.01
thresh[19,2]      7.73    0.04  0.58      6.55      7.36      7.75      8.12      8.82   224 1.01
thresh[19,3]     12.88    0.04  0.58     11.71     12.50     12.90     13.26     13.99   215 1.01
thresh[19,4]     16.25    0.04  0.59     15.07     15.87     16.28     16.65     17.38   224 1.01
thresh[20,1]      5.12    0.04  0.63      3.78      4.73      5.14      5.54      6.32   219 1.01
thresh[20,2]      7.61    0.04  0.58      6.45      7.23      7.63      8.00      8.69   232 1.01
thresh[20,3]     13.04    0.04  0.58     11.89     12.67     13.07     13.43     14.16   222 1.01
thresh[20,4]     16.38    0.04  0.59     15.19     16.01     16.40     16.77     17.50   237 1.01
thresh[21,1]      4.98    0.04  0.64      3.64      4.58      5.00      5.40      6.20   222 1.01
thresh[21,2]      7.64    0.04  0.57      6.49      7.27      7.66      8.02      8.72   247 1.01
thresh[21,3]     13.35    0.04  0.56     12.20     12.99     13.37     13.73     14.43   235 1.01
thresh[21,4]     16.67    0.04  0.57     15.53     16.31     16.70     17.05     17.79   247 1.01
thresh[22,1]      4.92    0.04  0.66      3.52      4.50      4.95      5.35      6.20   223 1.01
thresh[22,2]      7.57    0.04  0.57      6.41      7.19      7.59      7.94      8.66   262 1.01
thresh[22,3]     13.53    0.03  0.56     12.42     13.16     13.55     13.90     14.61   258 1.01
thresh[22,4]     16.82    0.03  0.57     15.66     16.44     16.85     17.20     17.95   266 1.01
thresh[23,1]      4.84    0.04  0.68      3.43      4.42      4.87      5.29      6.15   228 1.01
thresh[23,2]      7.59    0.04  0.57      6.44      7.22      7.62      7.98      8.69   264 1.01
thresh[23,3]     13.65    0.03  0.55     12.51     13.29     13.67     14.03     14.72   260 1.01
thresh[23,4]     16.98    0.03  0.57     15.83     16.60     17.00     17.36     18.09   275 1.01
thresh[24,1]      4.73    0.05  0.71      3.23      4.29      4.76      5.20      6.11   242 1.01
thresh[24,2]      7.73    0.04  0.58      6.54      7.36      7.74      8.13      8.86   277 1.01
thresh[24,3]     13.58    0.04  0.58     12.41     13.21     13.60     13.97     14.73   268 1.01
thresh[24,4]     17.04    0.04  0.59     15.84     16.65     17.06     17.44     18.19   286 1.01
thresh[25,1]      4.65    0.05  0.73      3.11      4.20      4.67      5.14      6.10   254 1.01
thresh[25,2]      7.97    0.03  0.59      6.76      7.59      7.98      8.37      9.11   292 1.01
thresh[25,3]     13.85    0.03  0.59     12.68     13.48     13.87     14.25     14.99   285 1.01
thresh[25,4]     16.85    0.04  0.60     15.64     16.44     16.87     17.24     18.00   290 1.01
thresh[26,1]      4.63    0.05  0.77      3.01      4.13      4.65      5.15      6.09   272 1.01
thresh[26,2]      8.04    0.04  0.62      6.81      7.63      8.05      8.45      9.22   308 1.01
thresh[26,3]     13.93    0.04  0.61     12.71     13.52     13.95     14.34     15.09   294 1.01
thresh[26,4]     16.77    0.04  0.62     15.53     16.35     16.80     17.20     17.96   303 1.01
sigma             0.25    0.00  0.04      0.17      0.22      0.25      0.28      0.34   614 1.01
yita[1,1]         0.53    0.01  0.94     -1.35     -0.09      0.54      1.17      2.34  5745 1.00
yita[1,2]        -0.45    0.02  0.97     -2.39     -1.11     -0.45      0.21      1.43  4024 1.00
yita[1,3]        -0.18    0.01  0.98     -2.11     -0.83     -0.20      0.48      1.71  6901 1.00
yita[1,4]        -0.38    0.02  1.01     -2.46     -1.05     -0.36      0.31      1.58  4251 1.00
yita[1,5]        -0.47    0.02  0.99     -2.36     -1.15     -0.47      0.23      1.46  4360 1.00
yita[1,6]         0.06    0.01  0.92     -1.77     -0.55      0.05      0.69      1.81  4913 1.00
...
``````

And I considered if there are some identification problems?