Hello!
I am fitting a multivariate model with shared parameters. I am new to stan and had help from this forum to edit the stan code produced by brms (https://discourse.mc-stan.org/t/fit-multivariate-non-linear-model-with-shared-parameters/36243). I was able to fit the model relatively easily with two chains, thin = 1, adapt_delta = 0.9, and 8000 iterations. The fit was also very good. However, now that my model is performing well I want to run it with four chains to have a more final version. When I increase the number of chains to 3 or 4 I get wasnings about the low ESS, very high Rhat and very low n_eff. I tried stronger priors, more iteration and higher thin. It did not change anything. More iterations did not increase n_eff of the problemeatic parameters at all.
My stan code is:
functions {
}
data {
int<lower=1> N; // total number of observations
int<lower=1> N_Nmr; // number of observations
vector[N_Nmr] Y_Nmr; // response variable
vector<lower=0>[N_Nmr] se_Nmr; // known sampling error
int<lower=1> K_Nmr_logI0; // number of population-level effects
matrix[N_Nmr, K_Nmr_logI0] X_Nmr_logI0; // population-level design matrix
int<lower=1> K_Nmr_b; // number of population-level effects
matrix[N_Nmr, K_Nmr_b] X_Nmr_b; // population-level design matrix
int<lower=1> K_Nmr_k; // number of population-level effects
matrix[N_Nmr, K_Nmr_k] X_Nmr_k; // population-level design matrix
int<lower=1> K_Nmr_int; // number of population-level effects
matrix[N_Nmr, K_Nmr_int] X_Nmr_int; // population-level design matrix
int<lower=1> K_Nmr_a; // number of population-level effects
matrix[N_Nmr, K_Nmr_a] X_Nmr_a; // population-level design matrix
// covariates for non-linear functions
vector[N_Nmr] C_Nmr_1;
vector[N_Nmr] C_Nmr_2;
vector[N_Nmr] C_Nmr_3;
vector[N_Nmr] C_Nmr_4;
vector[N_Nmr] C_Nmr_5;
vector[N_Nmr] C_Nmr_6;
// covariates for non-linear functions
vector[N_Nmr] C_sigma_Nmr_1;
int<lower=1> N_BI; // number of observations
vector[N_BI] Y_BI; // response variable
vector<lower=0>[N_BI] se_BI; // known sampling error
int<lower=1> K_BI_logI0; // number of population-level effects
matrix[N_BI, K_BI_logI0] X_BI_logI0; // population-level design matrix
int<lower=1> K_BI_b; // number of population-level effects
matrix[N_BI, K_BI_b] X_BI_b; // population-level design matrix
int<lower=1> K_BI_k; // number of population-level effects
matrix[N_BI, K_BI_k] X_BI_k; // population-level design matrix
int<lower=1> K_BI_int; // number of population-level effects
matrix[N_BI, K_BI_int] X_BI_int; // population-level design matrix
int<lower=1> K_BI_a; // number of population-level effects
matrix[N_BI, K_BI_a] X_BI_a; // population-level design matrix
// covariates for non-linear functions
vector[N_BI] C_BI_1;
vector[N_BI] C_BI_2;
vector[N_BI] C_BI_3;
vector[N_BI] C_BI_4;
vector[N_BI] C_BI_5;
vector[N_BI] C_BI_6;
// covariates for non-linear functions
vector[N_BI] C_sigma_BI_1;
int<lower=1> nresp; // number of responses
int nrescor; // number of residual correlations
// data for group-level effects of ID 1
int<lower=1> N_1; // number of grouping levels
int<lower=1> M_1; // number of coefficients per level
array[N_Nmr] int<lower=1> J_1_Nmr; // grouping indicator per observation
// group-level predictor values
vector[N_Nmr] Z_1_Nmr_k_1;
// data for group-level effects of ID 2
int<lower=1> N_2; // number of grouping levels
int<lower=1> M_2; // number of coefficients per level
array[N_BI] int<lower=1> J_2_BI; // grouping indicator per observation
int prior_only; // should the likelihood be ignored?
}
transformed data {
vector<lower=0>[N_Nmr] se2_Nmr = square(se_Nmr);
vector<lower=0>[N_BI] se2_BI = square(se_BI);
array[N] vector[nresp] Y; // response array
for (n in 1:N) {
Y[n] = transpose([Y_Nmr[n], Y_BI[n]]);
}
}
parameters {
vector<lower=0>[K_Nmr_logI0] b_Nmr_logI0; // regression coefficients
vector<lower=0,upper=1>[K_Nmr_b] b_Nmr_b; // regression coefficients
vector<lower=0>[K_Nmr_k] b_Nmr_k; // regression coefficients
vector<lower=0>[K_Nmr_int] b_Nmr_int; // regression coefficients
vector<lower=0>[K_Nmr_a] b_Nmr_a; // regression coefficients
vector<lower=0>[K_BI_int] b_BI_int; // regression coefficients
vector<lower=0>[K_BI_a] b_BI_a; // regression coefficients
cholesky_factor_corr[nresp] Lrescor; // parameters for multivariate linear models
vector<lower=0>[M_1] sd_1; // group-level standard deviations
array[M_1] vector[N_1] z_1; // standardized group-level effects
}
transformed parameters {
vector[N_1] r_1_Nmr_k_1; // actual group-level effects
real lprior = 0; // prior contributions to the log posterior
r_1_Nmr_k_1 = (sd_1[1] * (z_1[1]));
lprior += normal_lpdf(b_Nmr_logI0 | 10, 2)
- 1 * normal_lccdf(0 | 10, 2);
lprior += beta_lpdf(b_Nmr_b | 0.7 * 4,(1 - 0.7) * 4);
lprior += normal_lpdf(b_Nmr_k | 0,1)
- 1 * normal_lccdf(0 | 0, 1);
lprior += normal_lpdf(b_Nmr_int | 0, 1)
- 1 * normal_lccdf(0 | 0, 1);
lprior += normal_lpdf(b_Nmr_a | 0, 0.5)
- 1 * normal_lccdf(0 | 0, 0.5);
lprior += normal_lpdf(b_BI_int | 0, 1)
- 1 * normal_lccdf(0 | 0, 1);
lprior += normal_lpdf(b_BI_a | 0, 0.5)
- 1 * normal_lccdf(0 | 0, 0.5);
lprior += lkj_corr_cholesky_lpdf(Lrescor | 1);
lprior += exponential_lpdf(sd_1 | 3);
}
model {
// likelihood including constants
if (!prior_only) {
// initialize linear predictor term
vector[N_Nmr] nlp_Nmr_logI0 = rep_vector(0.0, N_Nmr);
// initialize linear predictor term
vector[N_Nmr] nlp_Nmr_b = rep_vector(0.0, N_Nmr);
// initialize linear predictor term
vector[N_Nmr] nlp_Nmr_k = rep_vector(0.0, N_Nmr);
// initialize linear predictor term
vector[N_Nmr] nlp_Nmr_int = rep_vector(0.0, N_Nmr);
// initialize linear predictor term
vector[N_Nmr] nlp_Nmr_a = rep_vector(0.0, N_Nmr);
// initialize non-linear predictor term
vector[N_Nmr] mu_Nmr;
// initialize non-linear predictor term
vector[N_Nmr] sigma_Nmr;
// initialize linear predictor term
vector[N_BI] nlp_BI_int = rep_vector(0.0, N_BI);
// initialize linear predictor term
vector[N_BI] nlp_BI_a = rep_vector(0.0, N_BI);
// initialize non-linear predictor term
vector[N_BI] mu_BI;
// initialize non-linear predictor term
vector[N_BI] sigma_BI;
// multivariate predictor array
array[N] vector[nresp] Mu;
array[N] vector[nresp] sigma;
// cholesky factor of residual covariance matrix
array[N] matrix[nresp, nresp] LSigma;
nlp_Nmr_logI0 += X_Nmr_logI0 * b_Nmr_logI0;
nlp_Nmr_b += X_Nmr_b * b_Nmr_b;
nlp_Nmr_k += X_Nmr_k * b_Nmr_k;
nlp_Nmr_int += X_Nmr_int * b_Nmr_int;
nlp_Nmr_a += X_Nmr_a * b_Nmr_a;
nlp_BI_int += X_BI_int * b_BI_int;
nlp_BI_a += X_BI_a * b_BI_a;
for (n in 1:N_Nmr) {
// add more terms to the linear predictor
nlp_Nmr_k[n] += r_1_Nmr_k_1[J_1_Nmr[n]] * Z_1_Nmr_k_1[n];
}
for (n in 1:N_Nmr) {
// compute non-linear predictor values
mu_Nmr[n] = ((C_Nmr_1[n] * (C_Nmr_2[n] + (inv_logit(nlp_Nmr_k[n]) * C_Nmr_3[n]))) / (exp(nlp_Nmr_logI0[n]) * C_Nmr_4[n] * (C_Nmr_5[n] ^ nlp_Nmr_b[n] + (C_Nmr_6[n] / 2) * nlp_Nmr_b[n] * (nlp_Nmr_b[n] - 1) * C_Nmr_5[n] ^ (nlp_Nmr_b[n] - 2))));
}
for (n in 1:N_Nmr) {
// compute non-linear predictor values
sigma_Nmr[n] = exp(nlp_Nmr_int[n] + C_sigma_Nmr_1[n] ^ nlp_Nmr_a[n]);
}
for (n in 1:N_BI) {
// compute non-linear predictor values
mu_BI[n] = (((C_BI_1[n] + inv_logit(nlp_Nmr_k[n]) * C_BI_2[n]) * C_BI_3[n] * C_BI_4[n]) / (exp(nlp_Nmr_logI0[n]) * C_BI_5[n] * (C_BI_4[n] ^ nlp_Nmr_b[n] + (C_BI_6[n] / 2) * nlp_Nmr_b[n] * (nlp_Nmr_b[n] - 1) * C_BI_4[n] ^ (nlp_Nmr_b[n] - 2))));
}
for (n in 1:N_BI) {
// compute non-linear predictor values
sigma_BI[n] = exp(nlp_BI_int[n] + C_sigma_BI_1[n] ^ nlp_BI_a[n]);
}
// combine univariate parameters
for (n in 1:N) {
Mu[n] = transpose([mu_Nmr[n], mu_BI[n]]);
sigma[n] = transpose([sqrt(square(sigma_Nmr[n]) + se2_Nmr[n]), sqrt(square(sigma_BI[n]) + se2_BI[n])]);
LSigma[n] = diag_pre_multiply(sigma[n], Lrescor);
}
for (n in 1:N) {
target += multi_normal_cholesky_lpdf(Y[n] | Mu[n], LSigma[n]);
}
}
// priors including constants
target += lprior;
target += std_normal_lpdf(z_1[1]);
}
generated quantities {
// residual correlations
corr_matrix[nresp] Rescor = multiply_lower_tri_self_transpose(Lrescor);
vector<lower=-1,upper=1>[nrescor] rescor;
// extract upper diagonal of correlation matrix
for (k in 1:nresp) {
for (j in 1:(k - 1)) {
rescor[choose(k - 1, 2) + j] = Rescor[j, k];
}
}
}
Nmr and BI are highly correlated. It is a problem?
The stan data:
structure(list(N_Nmr = 35L, Y_Nmr = structure(c(145L, 41L, 72L,
3173L, 2966L, 1262L, 1149L, 504L, 453L, 777L, 704L, 1923L, 1751L,
2052L, 1921L, 195L, 167L, 245L, 208L, 805L, 327L, 456L, 78L,
1747L, 936L, 934L, 326L, 1319L, 383L, 1350L, 82L, 1533L, 372L,
896L, 193L), dim = 35L), se_Nmr = structure(c(36.4795918367347,
33.9285714285714, 18.1122448979592, 336.989795918367, 336.989795918367,
167.602040816327, 167.602040816327, 87.7551020408163, 87.7551020408163,
146.428571428571, 146.428571428571, 233.163265306122, 233.163265306122,
356.632653061225, 356.632653061225, 28.8265306122449, 28.8265306122449,
38.7755102040816, 38.7755102040816, 70.9183673469388, 70.9183673469388,
43.3673469387755, 43.3673469387755, 266.326530612245, 266.326530612245,
116.326530612245, 116.326530612245, 109.948979591837, 109.948979591837,
101.530612244898, 79.0816326530612, 163.520408163265, 163.520408163265,
139.030612244898, 131.377551020408), dim = 35L), N_BI = 35L,
Y_BI = structure(c(58699.2067307692, 16338.5, 37062.72, 586326.283422458,
547110.145417652, 310087.009803921, 281911.414847162, 34735.4823529412,
31263.0941704036, 70328.0794520548, 63944.1487839771, 215919.163157895,
196235.196078432, 229360.696875, 214911.875, 26769.8888888888,
22947.037037037, 32365.8243243242, 27198.3756345178, 114220.875,
52637.9166666666, 42936.2584615384, 9754.75609756097, 75333.7133028107,
41971.8079673136, 45241.4505050505, 18686.2824207493, 126776.251643957,
44161.8114602588, 95337.7232142857, 6722.56559766764, 77728.6077844312,
21346.2576687117, 55276.7228915663, 9130.71748878923), dim = 35L),
se_BI = structure(c(14767.7455357143, 13520.5357142857, 9323.45918367347,
62271.0288660917, 62161.3406099672, 41181.6289015605, 41121.7828179307,
6048.04721888756, 6056.28260272719, 13253.5909980431, 13300.0715307582,
26180.1441102757, 26130.6905114988, 39862.3361766582, 39898.2780612245,
3957.34882842024, 3960.97883597882, 5122.45449531162, 5070.34082668601,
10062.5564868805, 11415.8871882086, 4083.40266875981, 5423.56271777003,
11484.4685186463, 11942.5277771987, 5634.66914038342, 6667.82332529554,
10567.7934076808, 12677.6660756724, 7170.14622813411, 6483.31052537633,
8291.07219235, 9383.19560953216, 8577.18373493977, 6215.39535096549
), dim = 35L), nresp = 2L, nrescor = 1, N = 35L, C_Nmr_1 = structure(c(592.2,
551.335652173913, 1720.40869551196, 5135.1, 3710.06869230388,
1904.81995681897, 1681.86864942529, 2445.9, 460.748600012,
2357.455533366, 1091.59457333333, 1240.4, 2162.041408085,
1302.2663333, 410.54, 3050.5, 2351.75561511765, 6834.90718954248,
5222.50784313725, 797.5, 847.063260001027, 696.263082154795,
1297.35043378995, 7805.1, 7483.01666657353, 12660.8274504265,
6406.01764705882, 917.4, 1138.47565652879, 1740.51025227273,
2371.19474747475, 1530.6, 4231.82828278788, 1926.86065651591,
619.783535353535), dim = 35L), C_Nmr_2 = structure(c(10662.3716311457,
1924.04403258699, 8519.96312725198, 44606.1973266835, 7148.80605247308,
40475.0499899619, 14328.9779815932, 1179.41546274407, 311.338271604938,
1011.65268657152, 343.723340046114, 30416.3327204273, 6934.1645973791,
28020.7274319236, 8795.01318623588, 15102.014475937, 2992.42688425335,
13679.0305628833, 4596.94257937868, 1431.80202918211, 321.916668837846,
1258.3342989412, 365.206573098678, 1384.29643593022, 221.813518739632,
1101.88876890077, 458.025245406228, 27277.3732597846, 6227.95201821207,
25551.6259521933, 6779.72156553717, 3858.32694159881, 849.379914193153,
3493.00224732218, 1107.93016373347), dim = 35L), C_Nmr_3 = structure(c(107809.545032839,
139852.603250838, 107809.545032839, 319346.983077122, 319346.983077122,
319346.983077122, 319346.983077122, 56377.3469017162, 142137.4817856,
142137.4817856, 142137.4817856, 438588.370047914, 438588.370047914,
438588.370047914, 1851206.799571, 19513.2105459205, 19513.2105459205,
19513.2105459205, 19513.2105459205, 320208.980098382, 320208.980098382,
320208.980098382, 320208.980098382, 37654.7145510446, 37654.7145510446,
37654.7145510446, 37654.7145510446, 355618, 330896.902438548,
330896.902438548, 330896.902438548, 156332.500004466, 60228.1080636982,
60228.1080636982, 60228.1080636982), dim = 35L), C_Nmr_4 = structure(c(0.968898826010513,
0.919258766903425, 0.952629817554708, 0.964098761243345,
0.915984845013819, 0.957674570493223, 0.900846934099921,
0.861315579722472, 0.891627183842253, 0.750831703960004,
0.900846934099921, 0.826518486768192, 0.640759038748287,
0.763040264421148, 0.774392686186511, 0.731328502676302,
0.68537658471524, 0.637465208746466, 0.68537658471524, 0.94955451815625,
0.80289108787463, 0.909417409482917, 0.794101192295099, 0.920525161523524,
0.677939358232424, 0.856408047245123, 0.76414932341953, 0.800447272830747,
0.626426585425339, 0.742450488957026, 0.620807014871961,
0.48341486108144, 0.624795727445052, 0.502013926753242, 0.620807014871961
), dim = 35L), C_Nmr_5 = structure(c(404.822115384615, 398.5,
514.76, 184.786096256684, 184.460601961447, 245.710784313725,
245.353711790393, 68.9196078431373, 69.0134529147982, 90.5123287671233,
90.829756795422, 112.282456140351, 112.070357554787, 111.77421875,
111.875, 137.281481481481, 137.407407407407, 132.105405405405,
130.761421319797, 141.889285714286, 160.972222222222, 94.1584615384615,
125.060975609756, 43.1217591887869, 44.8416751787538, 48.4383838383838,
57.3198847262248, 96.1154296011807, 115.304990757856, 70.6205357142857,
81.9825072886297, 50.7035928143713, 57.3824130879346, 61.6927710843374,
47.3094170403587), dim = 35L), C_Nmr_6 = structure(c(17205.5561081031,
7855.52631578947, 17981.9402222222, 7167.07851532402, 7083.85137352115,
4429.97998155698, 4310.38614224204, 1366.25000784314, 1255.20431299441,
563.231373668189, 586.130001516698, 5353.76039628483, 5295.71114620791,
2950.8776765502, 2976.15945805107, 5062.27618233618, 4841.68391994479,
6727.54052552553, 6431.56013674505, 19279.9067512909, 24098.3565351895,
14572.9452788462, 31025.1496333982, 505.623552253161, 431.953435227717,
464.226674912389, 321.986973397078, 26678.425812748, 53513.8419935647,
2334.9340789897, 3756.29209077115, 404.951071351273, 411.166985148681,
661.822873934763, 404.439865874843), dim = 35L), C_sigma_Nmr_1 = structure(c(592.2,
551.335652173913, 1720.40869551196, 5135.1, 3710.06869230388,
1904.81995681897, 1681.86864942529, 2445.9, 460.748600012,
2357.455533366, 1091.59457333333, 1240.4, 2162.041408085,
1302.2663333, 410.54, 3050.5, 2351.75561511765, 6834.90718954248,
5222.50784313725, 797.5, 847.063260001027, 696.263082154795,
1297.35043378995, 7805.1, 7483.01666657353, 12660.8274504265,
6406.01764705882, 917.4, 1138.47565652879, 1740.51025227273,
2371.19474747475, 1530.6, 4231.82828278788, 1926.86065651591,
619.783535353535), dim = 35L), K_Nmr_logI0 = 1L, X_Nmr_logI0 = structure(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), dim = c(35L,
1L), dimnames = list(c("1", "2", "3", "4", "5", "6", "7",
"8", "9", "10", "11", "12", "13", "14", "15", "16", "17",
"18", "19", "20", "21", "22", "23", "24", "25", "26", "27",
"28", "29", "30", "31", "32", "33", "34", "35"), "Intercept"), assign = 0L),
K_Nmr_b = 1L, X_Nmr_b = structure(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), dim = c(35L, 1L), dimnames = list(
c("1", "2", "3", "4", "5", "6", "7", "8", "9", "10",
"11", "12", "13", "14", "15", "16", "17", "18", "19",
"20", "21", "22", "23", "24", "25", "26", "27", "28",
"29", "30", "31", "32", "33", "34", "35"), "Intercept"), assign = 0L),
K_Nmr_k = 1L, X_Nmr_k = structure(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), dim = c(35L, 1L), dimnames = list(
c("1", "2", "3", "4", "5", "6", "7", "8", "9", "10",
"11", "12", "13", "14", "15", "16", "17", "18", "19",
"20", "21", "22", "23", "24", "25", "26", "27", "28",
"29", "30", "31", "32", "33", "34", "35"), "Intercept"), assign = 0L),
Z_1_Nmr_k_1 = structure(c(`1` = 1, `2` = 1, `3` = 1, `4` = 1,
`5` = 1, `6` = 1, `7` = 1, `8` = 1, `9` = 1, `10` = 1, `11` = 1,
`12` = 1, `13` = 1, `14` = 1, `15` = 1, `16` = 1, `17` = 1,
`18` = 1, `19` = 1, `20` = 1, `21` = 1, `22` = 1, `23` = 1,
`24` = 1, `25` = 1, `26` = 1, `27` = 1, `28` = 1, `29` = 1,
`30` = 1, `31` = 1, `32` = 1, `33` = 1, `34` = 1, `35` = 1
), dim = 35L, dimnames = list(c("1", "2", "3", "4", "5",
"6", "7", "8", "9", "10", "11", "12", "13", "14", "15", "16",
"17", "18", "19", "20", "21", "22", "23", "24", "25", "26",
"27", "28", "29", "30", "31", "32", "33", "34", "35"))),
K_Nmr_int = 1L, X_Nmr_int = structure(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), dim = c(35L, 1L), dimnames = list(
c("1", "2", "3", "4", "5", "6", "7", "8", "9", "10",
"11", "12", "13", "14", "15", "16", "17", "18", "19",
"20", "21", "22", "23", "24", "25", "26", "27", "28",
"29", "30", "31", "32", "33", "34", "35"), "Intercept"), assign = 0L),
K_Nmr_a = 1L, X_Nmr_a = structure(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), dim = c(35L, 1L), dimnames = list(
c("1", "2", "3", "4", "5", "6", "7", "8", "9", "10",
"11", "12", "13", "14", "15", "16", "17", "18", "19",
"20", "21", "22", "23", "24", "25", "26", "27", "28",
"29", "30", "31", "32", "33", "34", "35"), "Intercept"), assign = 0L),
J_1_Nmr = structure(c(1L, 1L, 1L, 2L, 2L, 2L, 2L, 3L, 3L,
3L, 3L, 4L, 4L, 4L, 4L, 5L, 5L, 5L, 5L, 6L, 6L, 6L, 6L, 7L,
7L, 7L, 7L, 8L, 8L, 8L, 8L, 9L, 9L, 9L, 9L), dim = 35L),
C_BI_1 = structure(c(10662.3716311457, 1924.04403258699,
8519.96312725198, 44606.1973266835, 7148.80605247308, 40475.0499899619,
14328.9779815932, 1179.41546274407, 311.338271604938, 1011.65268657152,
343.723340046114, 30416.3327204273, 6934.1645973791, 28020.7274319236,
8795.01318623588, 15102.014475937, 2992.42688425335, 13679.0305628833,
4596.94257937868, 1431.80202918211, 321.916668837846, 1258.3342989412,
365.206573098678, 1384.29643593022, 221.813518739632, 1101.88876890077,
458.025245406228, 27277.3732597846, 6227.95201821207, 25551.6259521933,
6779.72156553717, 3858.32694159881, 849.379914193153, 3493.00224732218,
1107.93016373347), dim = 35L), C_BI_2 = structure(c(107809.545032839,
139852.603250838, 107809.545032839, 319346.983077122, 319346.983077122,
319346.983077122, 319346.983077122, 56377.3469017162, 142137.4817856,
142137.4817856, 142137.4817856, 438588.370047914, 438588.370047914,
438588.370047914, 1851206.799571, 19513.2105459205, 19513.2105459205,
19513.2105459205, 19513.2105459205, 320208.980098382, 320208.980098382,
320208.980098382, 320208.980098382, 37654.7145510446, 37654.7145510446,
37654.7145510446, 37654.7145510446, 355618, 330896.902438548,
330896.902438548, 330896.902438548, 156332.500004466, 60228.1080636982,
60228.1080636982, 60228.1080636982), dim = 35L), C_BI_3 = structure(c(592.2,
551.335652173913, 1720.40869551196, 5135.1, 3710.06869230388,
1904.81995681897, 1681.86864942529, 2445.9, 460.748600012,
2357.455533366, 1091.59457333333, 1240.4, 2162.041408085,
1302.2663333, 410.54, 3050.5, 2351.75561511765, 6834.90718954248,
5222.50784313725, 797.5, 847.063260001027, 696.263082154795,
1297.35043378995, 7805.1, 7483.01666657353, 12660.8274504265,
6406.01764705882, 917.4, 1138.47565652879, 1740.51025227273,
2371.19474747475, 1530.6, 4231.82828278788, 1926.86065651591,
619.783535353535), dim = 35L), C_BI_4 = structure(c(404.822115384615,
398.5, 514.76, 184.786096256684, 184.460601961447, 245.710784313725,
245.353711790393, 68.9196078431373, 69.0134529147982, 90.5123287671233,
90.829756795422, 112.282456140351, 112.070357554787, 111.77421875,
111.875, 137.281481481481, 137.407407407407, 132.105405405405,
130.761421319797, 141.889285714286, 160.972222222222, 94.1584615384615,
125.060975609756, 43.1217591887869, 44.8416751787538, 48.4383838383838,
57.3198847262248, 96.1154296011807, 115.304990757856, 70.6205357142857,
81.9825072886297, 50.7035928143713, 57.3824130879346, 61.6927710843374,
47.3094170403587), dim = 35L), C_BI_5 = structure(c(0.968898826010513,
0.919258766903425, 0.952629817554708, 0.964098761243345,
0.915984845013819, 0.957674570493223, 0.900846934099921,
0.861315579722472, 0.891627183842253, 0.750831703960004,
0.900846934099921, 0.826518486768192, 0.640759038748287,
0.763040264421148, 0.774392686186511, 0.731328502676302,
0.68537658471524, 0.637465208746466, 0.68537658471524, 0.94955451815625,
0.80289108787463, 0.909417409482917, 0.794101192295099, 0.920525161523524,
0.677939358232424, 0.856408047245123, 0.76414932341953, 0.800447272830747,
0.626426585425339, 0.742450488957026, 0.620807014871961,
0.48341486108144, 0.624795727445052, 0.502013926753242, 0.620807014871961
), dim = 35L), C_BI_6 = structure(c(17205.5561081031, 7855.52631578947,
17981.9402222222, 7167.07851532402, 7083.85137352115, 4429.97998155698,
4310.38614224204, 1366.25000784314, 1255.20431299441, 563.231373668189,
586.130001516698, 5353.76039628483, 5295.71114620791, 2950.8776765502,
2976.15945805107, 5062.27618233618, 4841.68391994479, 6727.54052552553,
6431.56013674505, 19279.9067512909, 24098.3565351895, 14572.9452788462,
31025.1496333982, 505.623552253161, 431.953435227717, 464.226674912389,
321.986973397078, 26678.425812748, 53513.8419935647, 2334.9340789897,
3756.29209077115, 404.951071351273, 411.166985148681, 661.822873934763,
404.439865874843), dim = 35L), C_sigma_BI_1 = structure(c(592.2,
551.335652173913, 1720.40869551196, 5135.1, 3710.06869230388,
1904.81995681897, 1681.86864942529, 2445.9, 460.748600012,
2357.455533366, 1091.59457333333, 1240.4, 2162.041408085,
1302.2663333, 410.54, 3050.5, 2351.75561511765, 6834.90718954248,
5222.50784313725, 797.5, 847.063260001027, 696.263082154795,
1297.35043378995, 7805.1, 7483.01666657353, 12660.8274504265,
6406.01764705882, 917.4, 1138.47565652879, 1740.51025227273,
2371.19474747475, 1530.6, 4231.82828278788, 1926.86065651591,
619.783535353535), dim = 35L), K_BI_logI0 = 1L, X_BI_logI0 = structure(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), dim = c(35L,
1L), dimnames = list(c("1", "2", "3", "4", "5", "6", "7",
"8", "9", "10", "11", "12", "13", "14", "15", "16", "17",
"18", "19", "20", "21", "22", "23", "24", "25", "26", "27",
"28", "29", "30", "31", "32", "33", "34", "35"), "Intercept"), assign = 0L),
K_BI_b = 1L, X_BI_b = structure(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), dim = c(35L, 1L), dimnames = list(
c("1", "2", "3", "4", "5", "6", "7", "8", "9", "10",
"11", "12", "13", "14", "15", "16", "17", "18", "19",
"20", "21", "22", "23", "24", "25", "26", "27", "28",
"29", "30", "31", "32", "33", "34", "35"), "Intercept"), assign = 0L),
K_BI_k = 1L, X_BI_k = structure(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), dim = c(35L, 1L), dimnames = list(
c("1", "2", "3", "4", "5", "6", "7", "8", "9", "10",
"11", "12", "13", "14", "15", "16", "17", "18", "19",
"20", "21", "22", "23", "24", "25", "26", "27", "28",
"29", "30", "31", "32", "33", "34", "35"), "Intercept"), assign = 0L),
Z_2_BI_k_1 = structure(c(`1` = 1, `2` = 1, `3` = 1, `4` = 1,
`5` = 1, `6` = 1, `7` = 1, `8` = 1, `9` = 1, `10` = 1, `11` = 1,
`12` = 1, `13` = 1, `14` = 1, `15` = 1, `16` = 1, `17` = 1,
`18` = 1, `19` = 1, `20` = 1, `21` = 1, `22` = 1, `23` = 1,
`24` = 1, `25` = 1, `26` = 1, `27` = 1, `28` = 1, `29` = 1,
`30` = 1, `31` = 1, `32` = 1, `33` = 1, `34` = 1, `35` = 1
), dim = 35L, dimnames = list(c("1", "2", "3", "4", "5",
"6", "7", "8", "9", "10", "11", "12", "13", "14", "15", "16",
"17", "18", "19", "20", "21", "22", "23", "24", "25", "26",
"27", "28", "29", "30", "31", "32", "33", "34", "35"))),
K_BI_int = 1L, X_BI_int = structure(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), dim = c(35L, 1L), dimnames = list(
c("1", "2", "3", "4", "5", "6", "7", "8", "9", "10",
"11", "12", "13", "14", "15", "16", "17", "18", "19",
"20", "21", "22", "23", "24", "25", "26", "27", "28",
"29", "30", "31", "32", "33", "34", "35"), "Intercept"), assign = 0L),
K_BI_a = 1L, X_BI_a = structure(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), dim = c(35L, 1L), dimnames = list(
c("1", "2", "3", "4", "5", "6", "7", "8", "9", "10",
"11", "12", "13", "14", "15", "16", "17", "18", "19",
"20", "21", "22", "23", "24", "25", "26", "27", "28",
"29", "30", "31", "32", "33", "34", "35"), "Intercept"), assign = 0L),
J_2_BI = structure(c(1L, 1L, 1L, 2L, 2L, 2L, 2L, 3L, 3L,
3L, 3L, 4L, 4L, 4L, 4L, 5L, 5L, 5L, 5L, 6L, 6L, 6L, 6L, 7L,
7L, 7L, 7L, 8L, 8L, 8L, 8L, 9L, 9L, 9L, 9L), dim = 35L),
N_1 = 9L, M_1 = 1L, NC_1 = 0L, N_2 = 9L, M_2 = 1L, NC_2 = 0L,
prior_only = 0L), class = c("standata", "list"))
And the cod to fit the model:
stan_fit <- stan(file = mod_1,
data = stan_data,
warmup = 2000,
iter = 8000,
chains = 2,
cores = 2,
seed = 17,
control = list(adapt_delta = 0.9),
thin = 1)
What can I do to fix this issue? Thank you!