No worries!
In the meantime, I did some further digging, and I am wondering if the kernel
in the integrate_1d
version of the model is set up correctly. I added some print statements to see what the parameters of the two lognormal distributions, the value of the integral, and the response time are. Here’s what I found for the integrate_1d
version of the model (it’s an excerpt of the print-output):
mu1 , sigma1 , mu2 , sigma2 , value, rt[n]
Chain 1 -0.308038 , 4.40524 , 0.623202 , 0.216137 , 1.67579e-06 , 9.04837
Chain 1 -0.308038 , 4.40524 , 0.623202 , 0.216137 , 4.80961e-13 , 9.04837
Chain 1 -0.308038 , 4.40524 , 0.623202 , 0.216137 , 4.2959e-23 , 9.04837
Chain 1 -0.308038 , 4.40524 , 0.623202 , 0.216137 , 6.03236e-11 , 9.04837
Chain 1 -0.308038 , 4.40524 , 0.623202 , 0.216137 , 0 , 9.04837
Chain 1 -0.308038 , 4.40524 , 0.623202 , 0.216137 , 9.92889e-11 , 9.04837
Chain 1 -0.308038 , 4.40524 , 0.623202 , 0.216137 , 0 , 9.04837
Chain 1 -0.308038 , 4.40524 , 0.623202 , 0.216137 , 0 , 9.04837
Chain 1 -0.308038 , 4.40524 , 0.623202 , 0.216137 , 0 , 9.04837
Chain 1 -0.308038 , 4.40524 , 0.623202 , 0.216137 , 0 , 9.04837
Chain 1 -0.308038 , 4.40524 , 0.623202 , 0.216137 , 0 , 9.04837
Chain 1 -0.308038 , 4.40524 , 0.623202 , 0.216137 , 0 , 9.04837
Chain 1 -0.308038 , 4.40524 , 0.623202 , 0.216137 , 0 , 9.04837
Chain 1 -0.308038 , 4.40524 , 0.623202 , 0.216137 , 1.09195e-11 , 9.04837
Chain 1 -0.308038 , 4.40524 , 0.623202 , 0.216137 , 0.00719056 , 9.04837
Chain 1 -0.308038 , 4.40524 , 0.623202 , 0.216137 , 2.77921e-12 , 9.04837
Chain 1 -0.308038 , 4.40524 , 0.623202 , 0.216137 , 5.14692e-122 , 9.04837
Chain 1 -0.308038 , 4.40524 , 0.623202 , 0.216137 , 8.40563e-10 , 9.04837
Chain 1 -0.308038 , 4.40524 , 0.623202 , 0.216137 , 0 , 9.04837
Chain 1 -0.308038 , 4.40524 , 0.623202 , 0.216137 , 0 , 9.04837
Chain 1 -0.308038 , 4.40524 , 0.623202 , 0.216137 , 0 , 9.04837
Chain 1 -0.308038 , 4.40524 , 0.623202 , 0.216137 , 0 , 9.04837
Chain 1 -0.308038 , 4.40524 , 0.623202 , 0.216137 , 0 , 9.04837
Chain 1 -0.308038 , 4.40524 , 0.623202 , 0.216137 , 0 , 9.04837
Chain 1 -0.308038 , 4.40524 , 0.623202 , 0.216137 , 0 , 9.04837
Chain 1 -0.308038 , 4.40524 , 0.623202 , 0.216137 , 1.56489e-09 , 9.04837
Chain 1 -0.308038 , 4.40524 , 0.623202 , 0.216137 , 0.00136742 , 9.04837
Chain 1 -0.308038 , 4.40524 , 0.623202 , 0.216137 , 8.7948e-13 , 9.04837
Chain 1 -0.308038 , 4.40524 , 0.623202 , 0.216137 , 1.09369e-07 , 9.04837
Chain 1 -0.308038 , 4.40524 , 0.623202 , 0.216137 , 8.51028e-13 , 9.04837
Chain 1 -0.308038 , 4.40524 , 0.623202 , 0.216137 , 6.20755e-57 , 9.04837
Chain 1 -0.308038 , 4.40524 , 0.623202 , 0.216137 , 1.22079e-11 , 9.04837
Chain 1 -0.308038 , 4.40524 , 0.623202 , 0.216137 , 8.6849e-240 , 9.04837
Chain 1 -0.308038 , 4.40524 , 0.623202 , 0.216137 , 2.77081e-10 , 9.04837
Chain 1 -0.308038 , 4.40524 , 0.623202 , 0.216137 , 0 , 9.04837
Chain 1 -0.308038 , 4.40524 , 0.623202 , 0.216137 , 8.83661e-10 , 9.04837
Chain 1 -0.308038 , 4.40524 , 0.623202 , 0.216137 , 0 , 9.04837
Chain 1 -0.308038 , 4.40524 , 0.623202 , 0.216137 , 0 , 9.04837
Chain 1 -0.308038 , 4.40524 , 0.623202 , 0.216137 , 0 , 9.04837
Chain 1 -0.308038 , 4.40524 , 0.623202 , 0.216137 , 0 , 9.04837
Chain 1 -0.308038 , 4.40524 , 0.623202 , 0.216137 , 0 , 9.04837
Chain 1 -0.308038 , 4.40524 , 0.623202 , 0.216137 , 0 , 9.04837
Chain 1 -0.308038 , 4.40524 , 0.623202 , 0.216137 , 0 , 9.04837
Chain 1 -0.308038 , 4.40524 , 0.623202 , 0.216137 , 0 , 9.04837
Chain 1 -0.308038 , 4.40524 , 0.623202 , 0.216137 , 0 , 9.04837
Chain 1 -0.308038 , 4.40524 , 0.623202 , 0.216137 , 0 , 9.04837
Chain 1 -0.308038 , 4.40524 , 0.623202 , 0.216137 , 0 , 9.04837
Chain 1 -0.308038 , 4.40524 , 0.623202 , 0.216137 , 0 , 9.04837
Chain 1 -0.308038 , 4.40524 , 0.623202 , 0.216137 , 0 , 9.04837
Chain 1 -0.308038 , 4.40524 , 0.623202 , 0.216137 , 4.35777e-08 , 9.04837
Chain 1 -0.308038 , 4.40524 , 0.623202 , 0.216137 , 6.26381e-05 , 9.04837
As can be seen, it 0 all the time, and the integral (not shown) is very small. Moreover, it does not match the integral of the R-function, or the exposed stan-function.
As a comparison, the output for the integrate_ode_rk45
version:
mu1 , sigma1 , mu2 , sigma2 , value , rt[n]
2.1114 , 0.289429 , 0.61694 , 0.197171 , [0] , 8.24347
2.1114 , 0.289429 , 0.61694 , 0.197171 , [4.57871e-114] , 8.24347
2.1114 , 0.289429 , 0.61694 , 0.197171 , [1.20465e-94] , 8.24347
2.1114 , 0.289429 , 0.61694 , 0.197171 , [2.91694e-55] , 8.24347
2.1114 , 0.289429 , 0.61694 , 0.197171 , [1.1389e-51] , 8.24347
2.1114 , 0.289429 , 0.61694 , 0.197171 , [8.40904e-48] , 8.24347
2.1114 , 0.289429 , 0.61694 , 0.197171 , [8.40904e-48] , 8.24347
2.1114 , 0.289429 , 0.61694 , 0.197171 , [1.91545e-29] , 8.24347
2.1114 , 0.289429 , 0.61694 , 0.197171 , [2.2267e-24] , 8.24347
2.1114 , 0.289429 , 0.61694 , 0.197171 , [1.08777e-11] , 8.24347
2.1114 , 0.289429 , 0.61694 , 0.197171 , [1.8199e-10] , 8.24347
2.1114 , 0.289429 , 0.61694 , 0.197171 , [3.65875e-09] , 8.24347
2.1114 , 0.289429 , 0.61694 , 0.197171 , [3.65875e-09] , 8.24347
2.1114 , 0.289429 , 0.61694 , 0.197171 , [3.8977e-05] , 8.24347
2.1114 , 0.289429 , 0.61694 , 0.197171 , [0.00057898] , 8.24347
2.1114 , 0.289429 , 0.61694 , 0.197171 , [0.125052] , 8.24347
2.1114 , 0.289429 , 0.61694 , 0.197171 , [0.153581] , 8.24347
2.1114 , 0.289429 , 0.61694 , 0.197171 , [0.166528] , 8.24347
2.1114 , 0.289429 , 0.61694 , 0.197171 , [0.166528] , 8.24347
2.1114 , 0.289429 , 0.61694 , 0.197171 , [4.21655e-08] , 8.24347
2.1114 , 0.289429 , 0.61694 , 0.197171 , [1.25028e-07] , 8.24347
2.1114 , 0.289429 , 0.61694 , 0.197171 , [9.98243e-06] , 8.24347
2.1114 , 0.289429 , 0.61694 , 0.197171 , [1.87166e-05] , 8.24347
2.1114 , 0.289429 , 0.61694 , 0.197171 , [3.8977e-05] , 8.24347
2.1114 , 0.289429 , 0.61694 , 0.197171 , [3.8977e-05] , 8.24347
2.1114 , 0.289429 , 0.61694 , 0.197171 , [3.11154e-08] , 8.24347
2.1114 , 0.289429 , 0.61694 , 0.197171 , [8.1785e-08] , 8.24347
2.1114 , 0.289429 , 0.61694 , 0.197171 , [4.45558e-06] , 8.24347
2.1114 , 0.289429 , 0.61694 , 0.197171 , [8.0317e-06] , 8.24347
2.1114 , 0.289429 , 0.61694 , 0.197171 , [1.60671e-05] , 8.24347
2.1114 , 0.289429 , 0.61694 , 0.197171 , [1.60671e-05] , 8.24347
2.1114 , 0.289429 , 0.61694 , 0.197171 , [5.45134e-05] , 8.24347
2.1114 , 0.289429 , 0.61694 , 0.197171 , [9.49629e-05] , 8.24347
2.1114 , 0.289429 , 0.61694 , 0.197171 , [0.000956631] , 8.24347
2.1114 , 0.289429 , 0.61694 , 0.197171 , [0.00134517] , 8.24347
2.1114 , 0.289429 , 0.61694 , 0.197171 , [0.00200791] , 8.24347
2.1114 , 0.289429 , 0.61694 , 0.197171 , [0.00200791] , 8.24347
2.1114 , 0.289429 , 0.61694 , 0.197171 , [0.00386584] , 8.24347
2.1114 , 0.289429 , 0.61694 , 0.197171 , [0.00520896] , 8.24347
2.1114 , 0.289429 , 0.61694 , 0.197171 , [0.0179617] , 8.24347
2.1114 , 0.289429 , 0.61694 , 0.197171 , [0.0215265] , 8.24347
2.1114 , 0.289429 , 0.61694 , 0.197171 , [0.0266011] , 8.24347
2.1114 , 0.289429 , 0.61694 , 0.197171 , [0.0266011] , 8.24347
2.1114 , 0.289429 , 0.61694 , 0.197171 , [0.00285658] , 8.24347
2.1114 , 0.289429 , 0.61694 , 0.197171 , [0.00337873] , 8.24347
2.1114 , 0.289429 , 0.61694 , 0.197171 , [0.00723843] , 8.24347
2.1114 , 0.289429 , 0.61694 , 0.197171 , [0.00818435] , 8.24347
2.1114 , 0.289429 , 0.61694 , 0.197171 , [0.00949476] , 8.24347
2.1114 , 0.289429 , 0.61694 , 0.197171 , [0.00949476] , 8.24347
2.1114 , 0.289429 , 0.61694 , 0.197171 , [0.0127254] , 8.24347
2.1114 , 0.289429 , 0.61694 , 0.197171 , [0.0146093] , 8.24347
2.1114 , 0.289429 , 0.61694 , 0.197171 , [0.0269781] , 8.24347
2.1114 , 0.289429 , 0.61694 , 0.197171 , [0.0297124] , 8.24347
2.1114 , 0.289429 , 0.61694 , 0.197171 , [0.033358] , 8.24347
2.1114 , 0.289429 , 0.61694 , 0.197171 , [0.033358] , 8.24347
2.1114 , 0.289429 , 0.61694 , 0.197171 , [0.0418711] , 8.24347
2.1114 , 0.289429 , 0.61694 , 0.197171 , [0.0465173] , 8.24347
2.1114 , 0.289429 , 0.61694 , 0.197171 , [0.072892] , 8.24347
2.1114 , 0.289429 , 0.61694 , 0.197171 , [0.0779737] , 8.24347
2.1114 , 0.289429 , 0.61694 , 0.197171 , [0.0844121] , 8.24347
2.1114 , 0.289429 , 0.61694 , 0.197171 , [0.0844121] , 8.24347
2.1114 , 0.289429 , 0.61694 , 0.197171 , [0.0398428] , 8.24347
2.1114 , 0.289429 , 0.61694 , 0.197171 , [0.0433225] , 8.24347
2.1114 , 0.289429 , 0.61694 , 0.197171 , [0.0627921] , 8.24347
2.1114 , 0.289429 , 0.61694 , 0.197171 , [0.0665531] , 8.24347
2.1114 , 0.289429 , 0.61694 , 0.197171 , [0.0713496] , 8.24347
2.1114 , 0.289429 , 0.61694 , 0.197171 , [0.0713496] , 8.24347
2.1114 , 0.289429 , 0.61694 , 0.197171 , [0.0807985] , 8.24347
2.1114 , 0.289429 , 0.61694 , 0.197171 , [0.0855973] , 8.24347
2.1114 , 0.289429 , 0.61694 , 0.197171 , [0.109534] , 8.24347
2.1114 , 0.289429 , 0.61694 , 0.197171 , [0.113656] , 8.24347
2.1114 , 0.289429 , 0.61694 , 0.197171 , [0.118699] , 8.24347
2.1114 , 0.289429 , 0.61694 , 0.197171 , [0.118699] , 8.24347
2.1114 , 0.289429 , 0.61694 , 0.197171 , [0.128151] , 8.24347
2.1114 , 0.289429 , 0.61694 , 0.197171 , [0.132606] , 8.24347
2.1114 , 0.289429 , 0.61694 , 0.197171 , [0.151361] , 8.24347
2.1114 , 0.289429 , 0.61694 , 0.197171 , [0.153982] , 8.24347
2.1114 , 0.289429 , 0.61694 , 0.197171 , [0.156924] , 8.24347
2.1114 , 0.289429 , 0.61694 , 0.197171 , [0.156924] , 8.24347
2.1114 , 0.289429 , 0.61694 , 0.197171 , [0.161704] , 8.24347
2.1114 , 0.289429 , 0.61694 , 0.197171 , [0.163485] , 8.24347
2.1114 , 0.289429 , 0.61694 , 0.197171 , [0.166306] , 8.24347
2.1114 , 0.289429 , 0.61694 , 0.197171 , [0.165784] , 8.24347
2.1114 , 0.289429 , 0.61694 , 0.197171 , [0.164728] , 8.24347
2.1114 , 0.289429 , 0.61694 , 0.197171 , [0.164728] , 8.24347
2.1114 , 0.289429 , 0.61694 , 0.197171 , [0.161289] , 8.24347
2.1114 , 0.289429 , 0.61694 , 0.197171 , [0.162982] , 8.24347
2.1114 , 0.289429 , 0.61694 , 0.197171 , [0.166522] , 8.24347
2.1114 , 0.289429 , 0.61694 , 0.197171 , [0.166314] , 8.24347
2.1114 , 0.289429 , 0.61694 , 0.197171 , [0.165717] , 8.24347
2.1114 , 0.289429 , 0.61694 , 0.197171 , [0.165717] , 8.24347
2.1114 , 0.289429 , 0.61694 , 0.197171 , [0.163739] , 8.24347
2.1114 , 0.289429 , 0.61694 , 0.197171 , [0.162339] , 8.24347
2.1114 , 0.289429 , 0.61694 , 0.197171 , [0.151784] , 8.24347
2.1114 , 0.289429 , 0.61694 , 0.197171 , [0.149378] , 8.24347
2.1114 , 0.289429 , 0.61694 , 0.197171 , [0.146186] , 8.24347
2.1114 , 0.289429 , 0.61694 , 0.197171 , [0.146186] , 8.24347
2.1114 , 0.289429 , 0.61694 , 0.197171 , [0.138538] , 8.24347
2.1114 , 0.289429 , 0.61694 , 0.197171 , [0.134452] , 8.24347
2.1114 , 0.289429 , 0.61694 , 0.197171 , [0.112487] , 8.24347
2.1114 , 0.289429 , 0.61694 , 0.197171 , [0.108463] , 8.24347
2.1114 , 0.289429 , 0.61694 , 0.197171 , [0.103439] , 8.24347
2.1114 , 0.289429 , 0.61694 , 0.197171 , [0.103439] , 8.24347
2.1114 , 0.289429 , 0.61694 , 0.197171 , [0.0941432] , 8.24347
2.1114 , 0.289429 , 0.61694 , 0.197171 , [0.0895825] , 8.24347
2.1114 , 0.289429 , 0.61694 , 0.197171 , [0.0682218] , 8.24347
2.1114 , 0.289429 , 0.61694 , 0.197171 , [0.0647387] , 8.24347
2.1114 , 0.289429 , 0.61694 , 0.197171 , [0.0605371] , 8.24347
2.1114 , 0.289429 , 0.61694 , 0.197171 , [0.0605371] , 8.24347
2.1114 , 0.289429 , 0.61694 , 0.197171 , [0.0534174] , 8.24347
2.1114 , 0.289429 , 0.61694 , 0.197171 , [0.0500765] , 8.24347
2.1114 , 0.289429 , 0.61694 , 0.197171 , [0.0355719] , 8.24347
2.1114 , 0.289429 , 0.61694 , 0.197171 , [0.0333679] , 8.24347
2.1114 , 0.289429 , 0.61694 , 0.197171 , [0.0307647] , 8.24347
2.1114 , 0.289429 , 0.61694 , 0.197171 , [0.0307647] , 8.24347
2.1114 , 0.289429 , 0.61694 , 0.197171 , [0.0250924] , 8.24347
2.1114 , 0.289429 , 0.61694 , 0.197171 , [0.0225947] , 8.24347
2.1114 , 0.289429 , 0.61694 , 0.197171 , [0.0130143] , 8.24347
2.1114 , 0.289429 , 0.61694 , 0.197171 , [0.0117456] , 8.24347
2.1114 , 0.289429 , 0.61694 , 0.197171 , [0.0103136] , 8.24347
2.1114 , 0.289429 , 0.61694 , 0.197171 , [0.0103136] , 8.24347
2.1114 , 0.289429 , 0.61694 , 0.197171 , [0.00802044] , 8.24347
2.1114 , 0.289429 , 0.61694 , 0.197171 , [0.0070551] , 8.24347
2.1114 , 0.289429 , 0.61694 , 0.197171 , [0.00362924] , 8.24347
2.1114 , 0.289429 , 0.61694 , 0.197171 , [0.00321222] , 8.24347
2.1114 , 0.289429 , 0.61694 , 0.197171 , [0.00275335] , 8.24347
2.1114 , 0.289429 , 0.61694 , 0.197171 , [0.00275335] , 8.24347
2.1114 , 0.289429 , 0.61694 , 0.197171 , [0.00202028] , 8.24347
2.1114 , 0.289429 , 0.61694 , 0.197171 , [0.00172641] , 8.24347
2.1114 , 0.289429 , 0.61694 , 0.197171 , [0.000769043] , 8.24347
2.1114 , 0.289429 , 0.61694 , 0.197171 , [0.000663547] , 8.24347
2.1114 , 0.289429 , 0.61694 , 0.197171 , [0.000550939] , 8.24347
2.1114 , 0.289429 , 0.61694 , 0.197171 , [0.000550939] , 8.24347
2.1114 , 0.289429 , 0.61694 , 0.197171 , [0.000329682] , 8.24347
2.1114 , 0.289429 , 0.61694 , 0.197171 , [0.000253892] , 8.24347
2.1114 , 0.289429 , 0.61694 , 0.197171 , [6.59106e-05] , 8.24347
2.1114 , 0.289429 , 0.61694 , 0.197171 , [5.14903e-05] , 8.24347
2.1114 , 0.289429 , 0.61694 , 0.197171 , [3.77056e-05] , 8.24347
2.1114 , 0.289429 , 0.61694 , 0.197171 , [3.77056e-05] , 8.24347
2.1114 , 0.289429 , 0.61694 , 0.197171 , [1.99253e-05] , 8.24347
2.1114 , 0.289429 , 0.61694 , 0.197171 , [1.44138e-05] , 8.24347
2.1114 , 0.289429 , 0.61694 , 0.197171 , [2.71958e-06] , 8.24347
2.1114 , 0.289429 , 0.61694 , 0.197171 , [2.0046e-06] , 8.24347
2.1114 , 0.289429 , 0.61694 , 0.197171 , [1.36407e-06] , 8.24347
2.1114 , 0.289429 , 0.61694 , 0.197171 , [1.36407e-06] , 8.24347
2.1114 , 0.289429 , 0.61694 , 0.197171 , [5.21191e-07] , 8.24347
2.1114 , 0.289429 , 0.61694 , 0.197171 , [3.19072e-07] , 8.24347
2.1114 , 0.289429 , 0.61694 , 0.197171 , [2.47419e-08] , 8.24347
2.1114 , 0.289429 , 0.61694 , 0.197171 , [1.54021e-08] , 8.24347
2.1114 , 0.289429 , 0.61694 , 0.197171 , [8.44038e-09] , 8.24347
2.1114 , 0.289429 , 0.61694 , 0.197171 , [8.44038e-09] , 8.24347
2.1114 , 0.289429 , 0.61694 , 0.197171 , [1.04504e-09] , 8.24347
2.1114 , 0.289429 , 0.61694 , 0.197171 , [3.49609e-10] , 8.24347
2.1114 , 0.289429 , 0.61694 , 0.197171 , [7.51767e-13] , 8.24347
2.1114 , 0.289429 , 0.61694 , 0.197171 , [2.16789e-13] , 8.24347
2.1114 , 0.289429 , 0.61694 , 0.197171 , [4.20522e-14] , 8.24347
2.1114 , 0.289429 , 0.61694 , 0.197171 , [4.20522e-14] , 8.24347
2.1114 , 0.289429 , 0.61694 , 0.197171 , [4.20522e-14] , 8.24347
2.1114 , 0.289429 , 0.61694 , 0.197171 , [1.17796e-16] , 8.24347
2.1114 , 0.289429 , 0.61694 , 0.197171 , [3.30553e-18] , 8.24347
2.1114 , 0.289429 , 0.61694 , 0.197171 , [3.8154e-35] , 8.24347
2.1114 , 0.289429 , 0.61694 , 0.197171 , [3.24338e-45] , 8.24347
2.1114 , 0.289429 , 0.61694 , 0.197171 , [0] , 8.24347
2.1114 , 0.289429 , 0.61694 , 0.197171 , [0] , 8.24347
The integral (not shown) does match the R-function, and the exposed stan-function. I am still not sure how to properly interpret this, and how this might be related to the error messages. I managed to run the integrate_ode_rk45
version of the model for I=2 items and J=10 test takers for 200 iterations (but only once I installed the Rstan-developer version), although I am still getting the
Informational Message: The current Metropolis proposal is about to be rejected because of the following issue:
Chain 1 Exception: Exception: Exception: lognormal_lpdf: Random variable is -8.88178e-16, but must be nonnegative!.
error message sporadically during warmup and during sampling.