lab:projects:02robust_growth_curve_modeling_using_student-t_distribution:a_working_simulation_example [ Zhiyong Johnny Zhang ND homepage]

Analyze data as student-t data

	mean	sd	MC_error	val2.5pc	median	val97.5pc	start	sample
Inv_Sig_e2	0.9794	0.05691	0.002632	0.8701	0.9795	1.093	500	2511
Inv_cov[11]	1.135	0.227	0.02002	0.7734	1.103	1.663	500	2511
Inv_cov[12]	0.3232	0.102	0.006981	0.119	0.3222	0.5242	500	2511
Inv_cov[21]	0.3232	0.102	0.006981	0.119	0.3222	0.5242	500	2511
Inv_cov[22]	0.934	0.07862	0.001955	0.7884	0.9314	1.091	500	2511
bL[1]	4.818	0.09665	0.006631	4.636	4.815	5.01	500	2511
bS[1]	2.06	0.06768	0.002447	1.92	2.061	2.194	500	2511

#WinBUGS codes generated by BAUW: http://bauw.psychstat.org
#USE WITH CAUTION!

Model{
  # Model specification for linear growth curve model
  for (i in 1:N){
    LS[i,1:2]~dmnorm(muLS[i,1:2], Inv_cov[1:2,1:2])
    muLS[i,1]<-bL[1]
    muLS[i,2]<-bS[1]
    for (t in 1:5){
      y[i, t] ~ dt(muY[i,t], Inv_Sig_e2, 4)
      muY[i,t]<-LS[i,1]+LS[i,2]*t
    }
  }

  #Priors for model parameter
  for (i in 1:1){
    bL[i] ~ dnorm(0, 1.0E-6)
    bS[i] ~ dnorm(0, 1.0E-6)
  }
  Inv_cov[1:2,1:2]~dwish(R[1:2,1:2], 2)
  R[1,1]<-1
  R[2,2]<-1
  R[2,1]<-R[1,2]
  R[1,2]<-0
  Inv_Sig_e2 ~ dgamma(.001, .001)
  Sig_e2 <- 1/Inv_Sig_e2
  Cov[1:2,1:2]<-inverse(Inv_cov[1:2,1:2])
  Sig_L2 <- Cov[1,1]
  Sig_S2 <- Cov[2,2]
  Cov_LS <- Cov[1,2]
  rho_LS <- Cov[1,2]/sqrt(Cov[1,1]*Cov[2,2])
}

# The (naive) starting values for model parameters.
list(bL=c(5), bS = c(2), Inv_Sig_e2 = 1, Inv_cov= structure(.Data = c(1,0,0,1),.Dim=c(2,2)),LS = structure(.Data = c(
4.566,1.296,5.097,1.591,5.169,
0.2067,4.221,1.752,7.714,0.05158,
4.08,0.8305,6.492,2.576,2.957,
2.289,4.33,2.634,5.698,0.9366,
3.032,2.831,3.752,3.166,4.13,
2.936,4.758,3.296,5.104,1.947,
5.585,0.3074,2.933,1.625,3.385,
2.499,4.996,1.862,4.851,3.503,
4.011,3.282,3.771,1.866,7.545,
0.7209,4.677,3.086,4.66,1.711,
5.522,0.8198,5.294,2.812,4.001,
0.9769,5.26,2.406,5.248,1.716,
4.763,1.472,3.802,1.811,5.598,
1.175,3.664,3.627,5.227,1.966,
4.348,2.246,5.761,1.038,4.725,
0.9613,7.291,1.845,4.503,1.986,
5.549,1.017,4.482,3.032,4.835,
2.42,4.757,1.839,3.154,3.117,
5.096,3.68,6.292,1.698,4.133,
2.911,6.694,1.267,2.638,2.96,
5.153,2.161,4.265,1.439,6.239,
0.5326,4.424,3.33,8.357,1.119,
5.076,3.825,3.696,3.836,6.229,
2.629,4.735,1.436,4.355,4.295,
4.083,0.587,4.017,2.176,3.932,
2.548,5.382,3.254,7.278,-1.7,
5.075,2.704,3.276,2.462,3.789,
2.759,4.188,1.682,5.856,-0.02246,
5.626,2.911,5.25,0.6643,3.518,
0.6248,5.568,-0.3362,5.113,1.026,
5.483,3.262,4.109,-0.224,5.263,
1.267,4.328,3.363,3.826,2.93,
5.072,3.007,5.006,0.1496,5.6,
3.097,3.43,2.453,3.853,1.895,
5.529,5.122,4.729,0.5532,5.483,
1.195,5.297,2.667,7.458,-0.3812,
4.517,3.327,6.143,1.963,4.166,
1.747,6.654,1.149,5.48,2.751,
4.676,3.682,4.741,0.9135,6.634,
0.9691,3.015,3.719,5.544,0.3026,
8.473,-0.05376,5.445,0.3776,5.872,
2.752,5.374,1.754,4.358,1.564,
3.614,1.932,3.819,2.293,5.234,
2.287,5.715,0.8591,4.266,1.628,
4.407,1.63,6.875,1.901,6.601,
1.814,5.26,3.401,6.045,1.512,
6.384,1.931,4.397,2.575,5.621,
2.068,3.955,2.035,3.963,4.335,
3.606,2.753,5.423,3.229,3.365,
3.694,3.162,2.068,3.245,1.526,
5.707,2.17,6.89,1.269,6.366,
1.796,5.205,2.657,2.983,2.237,
3.839,1.395,4.987,1.982,3.602,
1.472,6.281,1.734,5.184,0.6604,
5.378,0.5802,4.991,0.9695,5.066,
1.348,5.603,2.043,5.809,2.801,
5.842,2.676,3.675,3.962,3.662,
3.824,5.224,0.6743,4.469,2.333,
6.069,0.7096,4.616,-0.3334,5.343,
2.654,6.237,0.7163,4.499,2.653,
5.281,1.838,5.133,0.2718,4.094,
2.853,5.302,1.162,6.507,2.464,
5.323,2.076,5.524,1.388,4.234,
1.791,5.422,1.293,4.803,1.833,
5.437,2.918,6.329,1.807,3.844,
2.078,4.942,1.421,4.532,2.335,
4.09,3.212,4.584,1.893,4.075,
2.785,4.994,2.086,7.62,0.5028,
6.183,1.687,4.81,1.701,4.524,
2.823,4.52,1.151,4.888,2.011,
5.29,0.6222,3.902,3.948,4.576,
3.595,3.173,1.963,6.568,1.8,
4.766,4.369,5.271,2.561,2.708,
3.804,3.051,3.742,5.848,3.619,
4.575,2.68,4.086,2.482,4.773,
1.855,4.998,0.3159,5.192,1.249,
4.623,2.551,5.218,1.702,5.596,
1.383,8.594,-0.873,3.893,3.145,
5.6,2.44,2.998,2.888,4.313,
2.296,5.155,0.7865,5.493,1.181,
2.937,3.038,4.175,2.596,5.03,
0.1572,3.831,2.44,4.101,4.121,
3.439,3.192,3.721,1.967,5.265,
1.435,7.236,-0.2765,4.912,2.113,
2.975,4.473,4.462,3.098,6.984,
1.585,4.883,3.923,6.182,2.541,
5.125,4.306,5.548,1.39,3.717,
2.873,4.944,1.392,5.838,1.452,
4.414,1.325,4.637,1.496,6.23,
1.862,7.584,2.173,4.429,1.053,
3.849,4.382,6.643,1.903,5.058,
1.959,5.117,1.555,2.459,2.857,
5.061,4.801,3.284,2.263,6.385,
0.6228,5.92,1.156,3.589,2.291,
4.59,0.9942,4.94,2.276,4.362,
2.559,4.001,1.483,5.137,2.422,
6.083,1.122,4.837,0.7332,3.471,
2.692,3.333,1.38,5.112,3.04,
4.956,3.464,3.974,0.3202,5.573,
0.663,5.527,1.23,7.411,-0.7974,
5.998,2.797,6.369,1.766,4.378,
0.8029,3.94,3.282,2.703,2.085,
4.728,2.277,6.481,0.5644,4.386,
1.66,4.666,2.983,5.682,-0.1715,
3.265,3.664,3.934,3.127,5.824,
1.332,4.981,1.84,4.306,2.155,
4.282,1.269,6.326,3.538,4.848,
2.82,4.157,3.037,7.543,1.356,
5.415,1.109,3.575,2.992,6.756,
1.863,3.931,3.358,2.441,3.141,
3.26,1.156,5.415,0.1014,5.434,
4.087,4.757,0.9659,5.034,1.92,
5.907,1.306,3.807,2.066,4.787,
2.371,5.426,2.611,5.231,2.609,
4.228,1.401,5.619,0.6223,4.014,
1.677,4.832,2.845,4.735,3.127,
3.778,3.568,6.182,-0.02521,2.452,
4.343,5.177,2.523,3.454,2.347,
6.209,2.281,3.053,2.934,5.425,
2.055,3.311,4.488,4.457,3.744),
.Dim = c(300,2)))

# Please put your data here. Remeber you can convert your data by BAUW--Convert Data. :)
list(N=300,

y = structure(.Data = c(
5.434,6.667,9.555,9.774,8.141,
6.031,9.47,8.635,12.03,13.33,
4.388,5.667,6.048,7.182,5.825,
7.696,7.657,7.235,13.66,13.95,
6.763,6.758,9.775,9.979,9.139,
5.388,7.156,6.545,7.241,7.986,
9.913,12.75,13.99,17.48,15.57,
4.457,8.631,9.998,12.95,15.71,
10.78,9.27,10.28,18.82,17.15,
5.851,7.179,9.009,9.739,10.41,
7.267,9.782,11.46,16.16,17.98,
7.062,10.26,13.08,15.88,19.96,
5.28,10.33,12.66,15.06,18.82,
8.238,10.49,15.67,13.88,21.3,
8.211,8.457,9.681,12.83,14.86,
7.032,5.918,6.141,5.725,7.737,
4.502,4.673,6.797,9.571,11.42,
5.346,6.334,10.96,11.18,13.32,
7.327,9.246,8.09,11.0,13.72,
8.312,11.22,14.16,21.47,21.87,
7.561,8.409,16.16,19.37,20.62,
6.398,7.642,9.167,11.01,12.26,
8.197,7.792,9.609,9.222,13.0,
6.475,10.13,14.86,17.08,20.62,
6.518,13.3,10.87,12.87,12.74,
4.8,4.236,7.493,8.459,8.67,
8.294,10.87,14.88,15.09,18.64,
4.955,6.128,8.075,7.82,8.608,
8.83,12.34,13.19,16.03,18.8,
10.04,9.023,9.447,12.78,14.41,
-24.34,5.734,8.996,12.1,12.09,
5.237,7.455,8.778,10.16,13.19,
6.836,10.12,9.678,11.0,10.07,
6.129,12.67,14.28,17.8,21.36,
6.873,8.877,10.08,14.91,15.32,
6.897,8.645,8.155,11.67,16.04,
5.242,7.948,9.34,6.176,10.17,
5.867,5.296,7.69,8.587,11.1,
10.32,11.15,12.86,14.5,15.71,
6.092,7.549,10.65,10.15,14.42,
6.437,9.938,8.223,10.25,12.8,
8.851,10.88,14.62,15.65,19.21,
5.78,10.9,11.17,17.78,17.1,
7.626,11.15,10.92,12.74,17.14,
5.077,10.14,8.602,18.68,18.6,
10.28,12.74,16.09,21.09,21.87,
8.132,11.75,11.93,10.52,15.0,
4.784,9.41,10.95,14.35,19.41,
5.098,10.41,11.77,11.07,11.23,
3.681,6.731,12.31,15.98,16.5,
4.656,8.072,12.01,13.01,16.22,
5.526,7.743,10.1,9.762,11.08,
8.501,8.554,9.194,7.784,10.77,
8.816,11.4,16.14,18.19,23.55,
5.883,9.943,10.81,11.47,12.73,
9.612,10.21,16.01,20.61,23.51,
9.509,10.77,15.08,17.02,22.13,
9.213,10.69,14.47,18.04,19.01,
5.157,7.923,7.131,9.302,12.41,
9.781,12.61,15.93,20.92,25.0,
4.803,5.907,6.863,5.865,6.197,
7.346,10.09,10.4,14.55,15.09,
6.725,10.25,12.0,13.91,14.71,
10.44,10.65,13.8,19.52,22.26,
5.968,3.309,1.568,0.2516,0.1415,
4.673,10.31,14.23,15.65,16.5,
6.411,8.871,10.33,13.7,16.38,
6.634,9.475,13.84,14.62,17.73,
5.316,8.731,9.563,10.23,11.96,
4.682,3.747,3.121,5.813,5.657,
8.405,10.61,14.22,15.12,19.34,
5.413,3.841,5.177,7.947,8.173,
4.855,4.056,4.441,5.631,9.194,
3.873,7.993,5.764,4.727,1.546,
5.951,7.452,8.943,8.472,10.3,
9.364,13.85,14.13,17.16,21.13,
3.568,5.008,4.208,2.201,2.549,
2.506,8.606,9.179,10.47,10.94,
6.344,8.923,16.07,17.2,23.8,
7.278,10.83,12.02,14.46,19.86,
10.23,9.773,15.0,17.81,18.78,
4.633,6.487,5.389,6.911,3.369,
8.313,11.64,14.52,17.68,21.59,
6.772,4.514,11.26,13.64,14.54,
5.864,6.61,7.421,11.08,12.04,
11.97,16.87,23.24,25.97,30.85,
-0.5038,4.44,4.22,6.721,7.38,
6.895,8.83,9.489,9.843,13.0,
6.465,10.77,11.66,14.46,18.55,
6.786,5.029,6.812,6.548,5.732,
5.149,10.8,16.43,18.8,21.16,
11.16,10.13,12.67,14.52,16.22,
5.936,7.817,8.495,11.34,13.41,
7.996,7.868,8.386,9.717,12.55,
8.164,10.55,10.91,16.22,19.63,
7.101,12.95,15.79,19.48,23.44,
5.681,5.933,5.652,8.134,9.741,
9.843,8.478,10.4,9.713,12.11,
7.08,12.07,13.46,16.58,20.57,
4.86,5.75,6.042,7.756,7.575,
7.606,7.478,9.364,7.974,8.443,
5.821,4.091,6.345,5.65,6.517,
9.533,15.47,14.35,17.7,19.74,
7.027,9.603,10.15,13.86,15.88,
5.381,7.223,7.76,10.78,10.56,
7.076,7.102,10.03,11.96,13.96,
2.82,8.425,10.58,12.48,16.25,
7.635,10.25,12.55,15.47,18.3,
6.139,7.936,8.559,10.13,11.75,
5.944,7.622,7.68,12.14,11.6,
6.227,8.782,6.851,11.54,11.28,
7.478,10.48,14.38,14.15,17.43,
7.579,9.177,12.32,15.73,16.2,
8.949,12.31,15.46,19.42,22.36,
7.438,9.246,11.24,12.1,15.6,
6.016,9.548,12.03,14.71,15.81,
5.553,8.987,12.16,15.23,16.85,
5.745,9.478,11.86,13.47,15.23,
2.34,6.687,9.96,10.91,11.8,
9.228,12.75,16.27,21.87,25.32,
7.269,9.609,12.39,14.01,15.96,
7.854,11.73,14.32,15.9,19.84,
9.874,9.001,15.56,16.94,24.02,
4.125,6.003,8.816,12.77,13.34,
5.34,7.042,5.239,10.05,10.52,
8.706,8.111,11.41,12.81,17.63,
7.381,9.335,11.17,13.08,13.41,
8.069,10.97,11.04,13.64,18.91,
6.873,8.726,14.4,16.95,16.84,
1.507,8.334,10.86,11.39,12.86,
3.916,6.754,-4.17,10.71,8.455,
8.119,7.972,11.12,11.56,16.59,
6.8,5.647,8.667,9.273,12.48,
7.471,8.88,12.64,14.1,14.83,
5.876,9.407,6.248,8.864,7.71,
2.832,6.472,9.658,7.678,8.599,
5.55,7.267,5.662,6.33,9.457,
7.009,7.084,5.089,10.99,12.44,
7.434,11.18,12.83,14.06,14.32,
9.934,11.44,13.04,17.48,20.45,
8.497,10.06,14.94,16.2,19.88,
7.185,11.53,17.84,20.28,23.17,
5.919,12.17,16.17,16.21,22.54,
2.448,6.455,10.18,8.362,9.384,
6.235,8.462,10.79,12.18,16.95,
6.352,8.181,9.213,8.034,10.25,
2.528,3.022,5.37,3.118,2.576,
8.712,10.74,14.13,16.2,17.79,
6.809,8.895,10.3,9.686,8.94,
6.772,11.86,13.09,12.84,17.77,
7.698,6.951,9.389,11.73,12.73,
5.356,5.389,6.481,6.061,5.376,
6.781,11.51,13.48,17.17,19.35,
6.555,7.473,8.024,10.53,11.92,
10.99,11.04,14.81,16.94,21.18,
5.117,11.69,10.0,14.13,19.68,
8.911,9.806,9.551,10.05,12.9,
5.736,9.307,10.54,14.28,12.85,
8.198,9.182,9.134,11.14,11.58,
6.646,8.469,10.06,11.14,14.05,
7.1,11.33,14.35,17.35,19.08,
6.422,8.741,11.81,13.36,13.83,
4.895,8.199,9.752,11.63,14.05,
7.992,8.197,9.102,11.31,13.81,
6.947,10.99,14.49,12.22,13.84,
7.657,11.41,15.33,17.01,20.3,
7.358,8.334,10.49,10.9,15.71,
6.263,8.972,12.22,16.55,19.1,
6.096,10.49,12.11,10.3,16.28,
7.869,6.923,8.674,8.931,10.41,
8.518,8.2,10.23,16.18,13.47,
4.797,7.408,8.641,11.4,11.84,
8.714,9.693,12.21,15.25,20.65,
5.422,5.882,7.475,12.47,10.4,
7.396,9.947,11.17,13.76,13.46,
5.534,6.94,7.093,8.603,9.94,
9.473,9.452,16.18,19.46,22.55,
7.274,12.06,15.95,18.4,24.71,
5.006,8.394,8.229,11.01,13.45,
8.301,9.131,13.06,13.05,14.92,
6.933,13.12,15.4,22.77,27.63,
7.733,10.95,14.95,16.71,17.51,
4.47,10.03,13.38,18.11,22.31,
7.032,9.203,15.19,16.56,24.07,
10.76,14.43,19.01,19.14,24.53,
9.229,10.17,14.37,13.85,19.83,
5.513,4.403,14.26,15.59,16.8,
7.328,11.57,11.69,11.57,13.53,
5.106,6.43,5.393,6.543,4.928,
6.95,7.191,11.69,10.59,10.55,
3.387,9.406,11.83,14.42,17.95,
5.401,8.521,7.748,12.3,13.83,
6.988,7.986,8.281,10.35,10.6,
6.593,7.007,7.834,6.37,1.273,
7.387,7.677,11.48,17.18,18.62,
6.541,9.619,13.69,16.3,16.9,
3.309,6.234,12.53,15.27,17.6,
5.742,5.249,11.37,12.68,16.93,
6.748,7.126,7.033,7.74,10.33,
7.179,7.816,9.063,10.1,11.9,
6.404,10.95,10.41,13.13,16.84,
5.672,10.12,14.67,13.62,17.58,
4.771,6.432,6.369,5.669,7.253,
7.145,7.742,10.8,13.81,15.49,
8.415,13.01,16.21,20.89,25.69,
7.593,7.019,13.28,17.3,17.55,
6.861,9.019,8.923,12.65,14.2,
7.225,8.06,8.523,12.96,11.23,
5.838,5.307,3.137,5.966,5.733,
6.698,6.683,9.619,12.97,15.29,
8.003,9.819,16.31,20.78,26.22,
7.36,12.18,12.93,17.32,18.24,
8.476,11.13,13.83,15.22,14.67,
9.214,16.88,16.93,19.53,24.77,
7.873,10.17,13.86,17.95,18.31,
9.825,13.19,17.9,21.87,27.02,
6.503,8.272,10.38,11.32,12.3,
5.713,9.24,12.5,19.91,17.91,
5.669,8.369,10.28,9.336,11.01,
3.304,8.64,10.39,10.37,10.68,
6.711,8.024,10.46,10.57,10.36,
6.061,7.026,8.748,10.24,12.29,
9.735,7.702,13.02,14.52,14.68,
10.65,13.16,15.36,15.04,18.04,
4.662,6.66,6.267,6.982,9.401,
8.676,11.88,17.85,18.89,26.64,
6.097,9.547,10.87,13.3,15.76,
7.416,7.924,12.76,14.42,15.27,
7.699,8.195,8.15,12.82,12.43,
4.947,9.174,12.94,11.82,17.08,
10.11,14.72,21.19,24.82,30.36,
6.302,10.62,9.888,12.43,15.85,
8.102,14.87,8.236,8.541,9.303,
7.164,8.132,10.78,7.605,10.83,
4.26,6.816,13.92,12.01,11.7,
6.859,6.343,6.755,8.088,10.43,
4.805,9.792,15.83,15.22,15.48,
7.461,8.11,10.43,14.63,17.16,
4.439,6.938,8.087,10.56,11.83,
7.752,10.35,13.16,13.6,16.53,
7.643,8.692,6.851,11.25,12.38,
4.561,4.756,6.962,7.052,6.557,
5.119,8.035,10.99,13.78,14.84,
4.156,4.583,5.151,7.597,10.54,
8.037,11.46,15.22,17.49,24.09,
8.413,10.13,15.37,18.96,20.91,
10.42,6.146,2.242,6.541,7.009,
6.362,6.485,6.432,8.463,5.419,
7.497,8.186,11.13,11.84,11.11,
4.435,5.679,3.287,3.384,3.693,
6.438,11.33,14.83,18.87,21.76,
9.431,9.189,12.45,13.52,15.47,
4.991,7.784,6.671,7.192,8.837,
7.683,11.1,12.71,16.06,21.32,
5.288,8.055,10.34,11.47,13.86,
6.203,10.63,11.5,14.02,18.17,
6.897,7.86,7.677,9.414,7.718,
6.469,9.631,8.004,9.888,11.34,
6.438,10.21,13.33,17.89,18.96,
6.056,3.898,3.166,3.9,4.645,
7.503,9.75,14.11,17.82,19.17,
6.194,11.45,12.82,16.52,21.22,
6.879,9.928,10.37,11.0,12.54,
7.443,8.96,9.996,13.68,14.86,
6.192,8.718,8.559,12.6,14.62,
6.088,5.052,7.752,10.2,11.4,
8.152,14.4,18.46,19.96,22.65,
8.109,9.924,13.25,17.64,18.15,
7.536,12.1,12.87,14.86,19.17,
9.759,11.25,12.94,12.83,12.37,
7.341,8.644,9.471,10.69,10.78,
5.97,9.22,17.21,14.53,19.52,
8.119,11.73,11.69,14.67,15.29,
6.454,9.521,14.22,12.03,22.81,
5.253,9.432,13.26,15.8,17.29,
3.705,5.557,5.319,7.501,9.769,
7.096,5.311,5.793,5.8,5.531,
10.22,13.97,17.35,22.68,25.27,
6.687,7.265,7.91,9.513,10.88,
13.13,9.24,9.359,13.87,13.82,
5.972,7.768,12.21,11.02,11.9,
7.134,8.354,10.06,11.95,12.4,
6.82,6.696,14.41,13.21,16.61,
7.555,11.64,16.3,15.55,21.29,
9.202,7.785,12.23,13.55,17.08,
4.475,6.7,10.15,9.942,12.39,
5.155,5.567,5.345,8.752,10.74,
5.857,5.629,8.206,11.02,13.58,
7.167,11.53,15.18,15.47,18.14,
9.319,10.68,10.02,15.57,20.26,
8.728,11.06,13.76,19.58,21.99,
6.615,7.67,7.097,6.957,4.936,
7.253,10.58,16.1,19.4,24.19,
8.58,10.34,12.5,16.89,16.55,
5.01,9.503,8.964,12.74,15.53,
8.166,10.9,13.07,15.5,19.23,
5.981,8.438,15.96,14.03,15.88,
7.429,9.48,11.02,17.24,15.78,
4.993,12.18,18.07,22.74,24.87,
8.184,10.81,14.27,19.0,24.19),
.Dim = c(300,5)))

Analyze data as normal data

	mean	sd	MC_error	val2.5pc	median	val97.5pc	start	sample
Inv_Sig_e2	0.4418	0.0211	6.238E-4	0.4023	0.4417	0.4843	1	3000
Inv_cov[11]	0.4185	0.06218	0.002842	0.3147	0.413	0.5594	1	3000
Inv_cov[12]	0.2506	0.04959	0.001316	0.16	0.2484	0.3522	1	3000
Inv_cov[21]	0.2506	0.04959	0.001316	0.16	0.2484	0.3522	1	3000
Inv_cov[22]	0.9232	0.07715	0.001403	0.777	0.9201	1.08	1	3000
bL[1]	4.714	0.136	0.004562	4.446	4.714	4.988	1	3000
bS[1]	2.083	0.0722	0.001907	1.941	2.083	2.227	1	3000

#WinBUGS codes generated by BAUW: http://bauw.psychstat.org
#USE WITH CAUTION!

Model{
  # Model specification for linear growth curve model
  for (i in 1:N){
    LS[i,1:2]~dmnorm(muLS[i,1:2], Inv_cov[1:2,1:2])
    muLS[i,1]<-bL[1]
    muLS[i,2]<-bS[1]
    for (t in 1:5){
      y[i, t] ~ dnorm(muY[i,t], Inv_Sig_e2)
      muY[i,t]<-LS[i,1]+LS[i,2]*t
    }
  }

  #Priors for model parameter
  for (i in 1:1){
    bL[i] ~ dnorm(0, 1.0E-6)
    bS[i] ~ dnorm(0, 1.0E-6)
  }
  Inv_cov[1:2,1:2]~dwish(R[1:2,1:2], 2)
  R[1,1]<-1
  R[2,2]<-1
  R[2,1]<-R[1,2]
  R[1,2]<-0
  Inv_Sig_e2 ~ dgamma(.001, .001)
  Sig_e2 <- 1/Inv_Sig_e2
  Cov[1:2,1:2]<-inverse(Inv_cov[1:2,1:2])
  Sig_L2 <- Cov[1,1]
  Sig_S2 <- Cov[2,2]
  Cov_LS <- Cov[1,2]
  rho_LS <- Cov[1,2]/sqrt(Cov[1,1]*Cov[2,2])
}

# The (naive) starting values for model parameters.
list(bL=c(5), bS = c(2), Inv_Sig_e2 = 1, Inv_cov= structure(.Data = c(1,0,0,1),.Dim=c(2,2)),LS = structure(.Data = c(
4.566,1.296,5.097,1.591,5.169,
0.2067,4.221,1.752,7.714,0.05158,
4.08,0.8305,6.492,2.576,2.957,
2.289,4.33,2.634,5.698,0.9366,
3.032,2.831,3.752,3.166,4.13,
2.936,4.758,3.296,5.104,1.947,
5.585,0.3074,2.933,1.625,3.385,
2.499,4.996,1.862,4.851,3.503,
4.011,3.282,3.771,1.866,7.545,
0.7209,4.677,3.086,4.66,1.711,
5.522,0.8198,5.294,2.812,4.001,
0.9769,5.26,2.406,5.248,1.716,
4.763,1.472,3.802,1.811,5.598,
1.175,3.664,3.627,5.227,1.966,
4.348,2.246,5.761,1.038,4.725,
0.9613,7.291,1.845,4.503,1.986,
5.549,1.017,4.482,3.032,4.835,
2.42,4.757,1.839,3.154,3.117,
5.096,3.68,6.292,1.698,4.133,
2.911,6.694,1.267,2.638,2.96,
5.153,2.161,4.265,1.439,6.239,
0.5326,4.424,3.33,8.357,1.119,
5.076,3.825,3.696,3.836,6.229,
2.629,4.735,1.436,4.355,4.295,
4.083,0.587,4.017,2.176,3.932,
2.548,5.382,3.254,7.278,-1.7,
5.075,2.704,3.276,2.462,3.789,
2.759,4.188,1.682,5.856,-0.02246,
5.626,2.911,5.25,0.6643,3.518,
0.6248,5.568,-0.3362,5.113,1.026,
5.483,3.262,4.109,-0.224,5.263,
1.267,4.328,3.363,3.826,2.93,
5.072,3.007,5.006,0.1496,5.6,
3.097,3.43,2.453,3.853,1.895,
5.529,5.122,4.729,0.5532,5.483,
1.195,5.297,2.667,7.458,-0.3812,
4.517,3.327,6.143,1.963,4.166,
1.747,6.654,1.149,5.48,2.751,
4.676,3.682,4.741,0.9135,6.634,
0.9691,3.015,3.719,5.544,0.3026,
8.473,-0.05376,5.445,0.3776,5.872,
2.752,5.374,1.754,4.358,1.564,
3.614,1.932,3.819,2.293,5.234,
2.287,5.715,0.8591,4.266,1.628,
4.407,1.63,6.875,1.901,6.601,
1.814,5.26,3.401,6.045,1.512,
6.384,1.931,4.397,2.575,5.621,
2.068,3.955,2.035,3.963,4.335,
3.606,2.753,5.423,3.229,3.365,
3.694,3.162,2.068,3.245,1.526,
5.707,2.17,6.89,1.269,6.366,
1.796,5.205,2.657,2.983,2.237,
3.839,1.395,4.987,1.982,3.602,
1.472,6.281,1.734,5.184,0.6604,
5.378,0.5802,4.991,0.9695,5.066,
1.348,5.603,2.043,5.809,2.801,
5.842,2.676,3.675,3.962,3.662,
3.824,5.224,0.6743,4.469,2.333,
6.069,0.7096,4.616,-0.3334,5.343,
2.654,6.237,0.7163,4.499,2.653,
5.281,1.838,5.133,0.2718,4.094,
2.853,5.302,1.162,6.507,2.464,
5.323,2.076,5.524,1.388,4.234,
1.791,5.422,1.293,4.803,1.833,
5.437,2.918,6.329,1.807,3.844,
2.078,4.942,1.421,4.532,2.335,
4.09,3.212,4.584,1.893,4.075,
2.785,4.994,2.086,7.62,0.5028,
6.183,1.687,4.81,1.701,4.524,
2.823,4.52,1.151,4.888,2.011,
5.29,0.6222,3.902,3.948,4.576,
3.595,3.173,1.963,6.568,1.8,
4.766,4.369,5.271,2.561,2.708,
3.804,3.051,3.742,5.848,3.619,
4.575,2.68,4.086,2.482,4.773,
1.855,4.998,0.3159,5.192,1.249,
4.623,2.551,5.218,1.702,5.596,
1.383,8.594,-0.873,3.893,3.145,
5.6,2.44,2.998,2.888,4.313,
2.296,5.155,0.7865,5.493,1.181,
2.937,3.038,4.175,2.596,5.03,
0.1572,3.831,2.44,4.101,4.121,
3.439,3.192,3.721,1.967,5.265,
1.435,7.236,-0.2765,4.912,2.113,
2.975,4.473,4.462,3.098,6.984,
1.585,4.883,3.923,6.182,2.541,
5.125,4.306,5.548,1.39,3.717,
2.873,4.944,1.392,5.838,1.452,
4.414,1.325,4.637,1.496,6.23,
1.862,7.584,2.173,4.429,1.053,
3.849,4.382,6.643,1.903,5.058,
1.959,5.117,1.555,2.459,2.857,
5.061,4.801,3.284,2.263,6.385,
0.6228,5.92,1.156,3.589,2.291,
4.59,0.9942,4.94,2.276,4.362,
2.559,4.001,1.483,5.137,2.422,
6.083,1.122,4.837,0.7332,3.471,
2.692,3.333,1.38,5.112,3.04,
4.956,3.464,3.974,0.3202,5.573,
0.663,5.527,1.23,7.411,-0.7974,
5.998,2.797,6.369,1.766,4.378,
0.8029,3.94,3.282,2.703,2.085,
4.728,2.277,6.481,0.5644,4.386,
1.66,4.666,2.983,5.682,-0.1715,
3.265,3.664,3.934,3.127,5.824,
1.332,4.981,1.84,4.306,2.155,
4.282,1.269,6.326,3.538,4.848,
2.82,4.157,3.037,7.543,1.356,
5.415,1.109,3.575,2.992,6.756,
1.863,3.931,3.358,2.441,3.141,
3.26,1.156,5.415,0.1014,5.434,
4.087,4.757,0.9659,5.034,1.92,
5.907,1.306,3.807,2.066,4.787,
2.371,5.426,2.611,5.231,2.609,
4.228,1.401,5.619,0.6223,4.014,
1.677,4.832,2.845,4.735,3.127,
3.778,3.568,6.182,-0.02521,2.452,
4.343,5.177,2.523,3.454,2.347,
6.209,2.281,3.053,2.934,5.425,
2.055,3.311,4.488,4.457,3.744),
.Dim = c(300,2)))

# Please put your data here. Remeber you can convert your data by BAUW--Convert Data. :)
list(N=300,

y = structure(.Data = c(
5.434,6.667,9.555,9.774,8.141,
6.031,9.47,8.635,12.03,13.33,
4.388,5.667,6.048,7.182,5.825,
7.696,7.657,7.235,13.66,13.95,
6.763,6.758,9.775,9.979,9.139,
5.388,7.156,6.545,7.241,7.986,
9.913,12.75,13.99,17.48,15.57,
4.457,8.631,9.998,12.95,15.71,
10.78,9.27,10.28,18.82,17.15,
5.851,7.179,9.009,9.739,10.41,
7.267,9.782,11.46,16.16,17.98,
7.062,10.26,13.08,15.88,19.96,
5.28,10.33,12.66,15.06,18.82,
8.238,10.49,15.67,13.88,21.3,
8.211,8.457,9.681,12.83,14.86,
7.032,5.918,6.141,5.725,7.737,
4.502,4.673,6.797,9.571,11.42,
5.346,6.334,10.96,11.18,13.32,
7.327,9.246,8.09,11.0,13.72,
8.312,11.22,14.16,21.47,21.87,
7.561,8.409,16.16,19.37,20.62,
6.398,7.642,9.167,11.01,12.26,
8.197,7.792,9.609,9.222,13.0,
6.475,10.13,14.86,17.08,20.62,
6.518,13.3,10.87,12.87,12.74,
4.8,4.236,7.493,8.459,8.67,
8.294,10.87,14.88,15.09,18.64,
4.955,6.128,8.075,7.82,8.608,
8.83,12.34,13.19,16.03,18.8,
10.04,9.023,9.447,12.78,14.41,
-24.34,5.734,8.996,12.1,12.09,
5.237,7.455,8.778,10.16,13.19,
6.836,10.12,9.678,11.0,10.07,
6.129,12.67,14.28,17.8,21.36,
6.873,8.877,10.08,14.91,15.32,
6.897,8.645,8.155,11.67,16.04,
5.242,7.948,9.34,6.176,10.17,
5.867,5.296,7.69,8.587,11.1,
10.32,11.15,12.86,14.5,15.71,
6.092,7.549,10.65,10.15,14.42,
6.437,9.938,8.223,10.25,12.8,
8.851,10.88,14.62,15.65,19.21,
5.78,10.9,11.17,17.78,17.1,
7.626,11.15,10.92,12.74,17.14,
5.077,10.14,8.602,18.68,18.6,
10.28,12.74,16.09,21.09,21.87,
8.132,11.75,11.93,10.52,15.0,
4.784,9.41,10.95,14.35,19.41,
5.098,10.41,11.77,11.07,11.23,
3.681,6.731,12.31,15.98,16.5,
4.656,8.072,12.01,13.01,16.22,
5.526,7.743,10.1,9.762,11.08,
8.501,8.554,9.194,7.784,10.77,
8.816,11.4,16.14,18.19,23.55,
5.883,9.943,10.81,11.47,12.73,
9.612,10.21,16.01,20.61,23.51,
9.509,10.77,15.08,17.02,22.13,
9.213,10.69,14.47,18.04,19.01,
5.157,7.923,7.131,9.302,12.41,
9.781,12.61,15.93,20.92,25.0,
4.803,5.907,6.863,5.865,6.197,
7.346,10.09,10.4,14.55,15.09,
6.725,10.25,12.0,13.91,14.71,
10.44,10.65,13.8,19.52,22.26,
5.968,3.309,1.568,0.2516,0.1415,
4.673,10.31,14.23,15.65,16.5,
6.411,8.871,10.33,13.7,16.38,
6.634,9.475,13.84,14.62,17.73,
5.316,8.731,9.563,10.23,11.96,
4.682,3.747,3.121,5.813,5.657,
8.405,10.61,14.22,15.12,19.34,
5.413,3.841,5.177,7.947,8.173,
4.855,4.056,4.441,5.631,9.194,
3.873,7.993,5.764,4.727,1.546,
5.951,7.452,8.943,8.472,10.3,
9.364,13.85,14.13,17.16,21.13,
3.568,5.008,4.208,2.201,2.549,
2.506,8.606,9.179,10.47,10.94,
6.344,8.923,16.07,17.2,23.8,
7.278,10.83,12.02,14.46,19.86,
10.23,9.773,15.0,17.81,18.78,
4.633,6.487,5.389,6.911,3.369,
8.313,11.64,14.52,17.68,21.59,
6.772,4.514,11.26,13.64,14.54,
5.864,6.61,7.421,11.08,12.04,
11.97,16.87,23.24,25.97,30.85,
-0.5038,4.44,4.22,6.721,7.38,
6.895,8.83,9.489,9.843,13.0,
6.465,10.77,11.66,14.46,18.55,
6.786,5.029,6.812,6.548,5.732,
5.149,10.8,16.43,18.8,21.16,
11.16,10.13,12.67,14.52,16.22,
5.936,7.817,8.495,11.34,13.41,
7.996,7.868,8.386,9.717,12.55,
8.164,10.55,10.91,16.22,19.63,
7.101,12.95,15.79,19.48,23.44,
5.681,5.933,5.652,8.134,9.741,
9.843,8.478,10.4,9.713,12.11,
7.08,12.07,13.46,16.58,20.57,
4.86,5.75,6.042,7.756,7.575,
7.606,7.478,9.364,7.974,8.443,
5.821,4.091,6.345,5.65,6.517,
9.533,15.47,14.35,17.7,19.74,
7.027,9.603,10.15,13.86,15.88,
5.381,7.223,7.76,10.78,10.56,
7.076,7.102,10.03,11.96,13.96,
2.82,8.425,10.58,12.48,16.25,
7.635,10.25,12.55,15.47,18.3,
6.139,7.936,8.559,10.13,11.75,
5.944,7.622,7.68,12.14,11.6,
6.227,8.782,6.851,11.54,11.28,
7.478,10.48,14.38,14.15,17.43,
7.579,9.177,12.32,15.73,16.2,
8.949,12.31,15.46,19.42,22.36,
7.438,9.246,11.24,12.1,15.6,
6.016,9.548,12.03,14.71,15.81,
5.553,8.987,12.16,15.23,16.85,
5.745,9.478,11.86,13.47,15.23,
2.34,6.687,9.96,10.91,11.8,
9.228,12.75,16.27,21.87,25.32,
7.269,9.609,12.39,14.01,15.96,
7.854,11.73,14.32,15.9,19.84,
9.874,9.001,15.56,16.94,24.02,
4.125,6.003,8.816,12.77,13.34,
5.34,7.042,5.239,10.05,10.52,
8.706,8.111,11.41,12.81,17.63,
7.381,9.335,11.17,13.08,13.41,
8.069,10.97,11.04,13.64,18.91,
6.873,8.726,14.4,16.95,16.84,
1.507,8.334,10.86,11.39,12.86,
3.916,6.754,-4.17,10.71,8.455,
8.119,7.972,11.12,11.56,16.59,
6.8,5.647,8.667,9.273,12.48,
7.471,8.88,12.64,14.1,14.83,
5.876,9.407,6.248,8.864,7.71,
2.832,6.472,9.658,7.678,8.599,
5.55,7.267,5.662,6.33,9.457,
7.009,7.084,5.089,10.99,12.44,
7.434,11.18,12.83,14.06,14.32,
9.934,11.44,13.04,17.48,20.45,
8.497,10.06,14.94,16.2,19.88,
7.185,11.53,17.84,20.28,23.17,
5.919,12.17,16.17,16.21,22.54,
2.448,6.455,10.18,8.362,9.384,
6.235,8.462,10.79,12.18,16.95,
6.352,8.181,9.213,8.034,10.25,
2.528,3.022,5.37,3.118,2.576,
8.712,10.74,14.13,16.2,17.79,
6.809,8.895,10.3,9.686,8.94,
6.772,11.86,13.09,12.84,17.77,
7.698,6.951,9.389,11.73,12.73,
5.356,5.389,6.481,6.061,5.376,
6.781,11.51,13.48,17.17,19.35,
6.555,7.473,8.024,10.53,11.92,
10.99,11.04,14.81,16.94,21.18,
5.117,11.69,10.0,14.13,19.68,
8.911,9.806,9.551,10.05,12.9,
5.736,9.307,10.54,14.28,12.85,
8.198,9.182,9.134,11.14,11.58,
6.646,8.469,10.06,11.14,14.05,
7.1,11.33,14.35,17.35,19.08,
6.422,8.741,11.81,13.36,13.83,
4.895,8.199,9.752,11.63,14.05,
7.992,8.197,9.102,11.31,13.81,
6.947,10.99,14.49,12.22,13.84,
7.657,11.41,15.33,17.01,20.3,
7.358,8.334,10.49,10.9,15.71,
6.263,8.972,12.22,16.55,19.1,
6.096,10.49,12.11,10.3,16.28,
7.869,6.923,8.674,8.931,10.41,
8.518,8.2,10.23,16.18,13.47,
4.797,7.408,8.641,11.4,11.84,
8.714,9.693,12.21,15.25,20.65,
5.422,5.882,7.475,12.47,10.4,
7.396,9.947,11.17,13.76,13.46,
5.534,6.94,7.093,8.603,9.94,
9.473,9.452,16.18,19.46,22.55,
7.274,12.06,15.95,18.4,24.71,
5.006,8.394,8.229,11.01,13.45,
8.301,9.131,13.06,13.05,14.92,
6.933,13.12,15.4,22.77,27.63,
7.733,10.95,14.95,16.71,17.51,
4.47,10.03,13.38,18.11,22.31,
7.032,9.203,15.19,16.56,24.07,
10.76,14.43,19.01,19.14,24.53,
9.229,10.17,14.37,13.85,19.83,
5.513,4.403,14.26,15.59,16.8,
7.328,11.57,11.69,11.57,13.53,
5.106,6.43,5.393,6.543,4.928,
6.95,7.191,11.69,10.59,10.55,
3.387,9.406,11.83,14.42,17.95,
5.401,8.521,7.748,12.3,13.83,
6.988,7.986,8.281,10.35,10.6,
6.593,7.007,7.834,6.37,1.273,
7.387,7.677,11.48,17.18,18.62,
6.541,9.619,13.69,16.3,16.9,
3.309,6.234,12.53,15.27,17.6,
5.742,5.249,11.37,12.68,16.93,
6.748,7.126,7.033,7.74,10.33,
7.179,7.816,9.063,10.1,11.9,
6.404,10.95,10.41,13.13,16.84,
5.672,10.12,14.67,13.62,17.58,
4.771,6.432,6.369,5.669,7.253,
7.145,7.742,10.8,13.81,15.49,
8.415,13.01,16.21,20.89,25.69,
7.593,7.019,13.28,17.3,17.55,
6.861,9.019,8.923,12.65,14.2,
7.225,8.06,8.523,12.96,11.23,
5.838,5.307,3.137,5.966,5.733,
6.698,6.683,9.619,12.97,15.29,
8.003,9.819,16.31,20.78,26.22,
7.36,12.18,12.93,17.32,18.24,
8.476,11.13,13.83,15.22,14.67,
9.214,16.88,16.93,19.53,24.77,
7.873,10.17,13.86,17.95,18.31,
9.825,13.19,17.9,21.87,27.02,
6.503,8.272,10.38,11.32,12.3,
5.713,9.24,12.5,19.91,17.91,
5.669,8.369,10.28,9.336,11.01,
3.304,8.64,10.39,10.37,10.68,
6.711,8.024,10.46,10.57,10.36,
6.061,7.026,8.748,10.24,12.29,
9.735,7.702,13.02,14.52,14.68,
10.65,13.16,15.36,15.04,18.04,
4.662,6.66,6.267,6.982,9.401,
8.676,11.88,17.85,18.89,26.64,
6.097,9.547,10.87,13.3,15.76,
7.416,7.924,12.76,14.42,15.27,
7.699,8.195,8.15,12.82,12.43,
4.947,9.174,12.94,11.82,17.08,
10.11,14.72,21.19,24.82,30.36,
6.302,10.62,9.888,12.43,15.85,
8.102,14.87,8.236,8.541,9.303,
7.164,8.132,10.78,7.605,10.83,
4.26,6.816,13.92,12.01,11.7,
6.859,6.343,6.755,8.088,10.43,
4.805,9.792,15.83,15.22,15.48,
7.461,8.11,10.43,14.63,17.16,
4.439,6.938,8.087,10.56,11.83,
7.752,10.35,13.16,13.6,16.53,
7.643,8.692,6.851,11.25,12.38,
4.561,4.756,6.962,7.052,6.557,
5.119,8.035,10.99,13.78,14.84,
4.156,4.583,5.151,7.597,10.54,
8.037,11.46,15.22,17.49,24.09,
8.413,10.13,15.37,18.96,20.91,
10.42,6.146,2.242,6.541,7.009,
6.362,6.485,6.432,8.463,5.419,
7.497,8.186,11.13,11.84,11.11,
4.435,5.679,3.287,3.384,3.693,
6.438,11.33,14.83,18.87,21.76,
9.431,9.189,12.45,13.52,15.47,
4.991,7.784,6.671,7.192,8.837,
7.683,11.1,12.71,16.06,21.32,
5.288,8.055,10.34,11.47,13.86,
6.203,10.63,11.5,14.02,18.17,
6.897,7.86,7.677,9.414,7.718,
6.469,9.631,8.004,9.888,11.34,
6.438,10.21,13.33,17.89,18.96,
6.056,3.898,3.166,3.9,4.645,
7.503,9.75,14.11,17.82,19.17,
6.194,11.45,12.82,16.52,21.22,
6.879,9.928,10.37,11.0,12.54,
7.443,8.96,9.996,13.68,14.86,
6.192,8.718,8.559,12.6,14.62,
6.088,5.052,7.752,10.2,11.4,
8.152,14.4,18.46,19.96,22.65,
8.109,9.924,13.25,17.64,18.15,
7.536,12.1,12.87,14.86,19.17,
9.759,11.25,12.94,12.83,12.37,
7.341,8.644,9.471,10.69,10.78,
5.97,9.22,17.21,14.53,19.52,
8.119,11.73,11.69,14.67,15.29,
6.454,9.521,14.22,12.03,22.81,
5.253,9.432,13.26,15.8,17.29,
3.705,5.557,5.319,7.501,9.769,
7.096,5.311,5.793,5.8,5.531,
10.22,13.97,17.35,22.68,25.27,
6.687,7.265,7.91,9.513,10.88,
13.13,9.24,9.359,13.87,13.82,
5.972,7.768,12.21,11.02,11.9,
7.134,8.354,10.06,11.95,12.4,
6.82,6.696,14.41,13.21,16.61,
7.555,11.64,16.3,15.55,21.29,
9.202,7.785,12.23,13.55,17.08,
4.475,6.7,10.15,9.942,12.39,
5.155,5.567,5.345,8.752,10.74,
5.857,5.629,8.206,11.02,13.58,
7.167,11.53,15.18,15.47,18.14,
9.319,10.68,10.02,15.57,20.26,
8.728,11.06,13.76,19.58,21.99,
6.615,7.67,7.097,6.957,4.936,
7.253,10.58,16.1,19.4,24.19,
8.58,10.34,12.5,16.89,16.55,
5.01,9.503,8.964,12.74,15.53,
8.166,10.9,13.07,15.5,19.23,
5.981,8.438,15.96,14.03,15.88,
7.429,9.48,11.02,17.24,15.78,
4.993,12.18,18.07,22.74,24.87,
8.184,10.81,14.27,19.0,24.19),
.Dim = c(300,5)))

Analyze as T with estimated df

	mean	sd	MC_error	val2.5pc	median	val97.5pc	start	sample
Inv_Sig_e2	0.9526	0.07745	0.00612	0.8107	0.9489	1.11	1000	3001
Inv_cov[11]	1.196	0.3253	0.03368	0.7577	1.142	2.043	1000	3001
Inv_cov[12]	0.32	0.1149	0.007614	0.1234	0.3103	0.5668	1000	3001
Inv_cov[21]	0.32	0.1149	0.007614	0.1234	0.3103	0.5668	1000	3001
Inv_cov[22]	0.9321	0.07978	0.001836	0.7845	0.9291	1.096	1000	3001
bL[1]	4.82	0.09491	0.006034	4.629	4.822	5.008	1000	3001
bS[1]	2.059	0.06808	0.002225	1.928	2.061	2.193	1000	3001
k	4.244	0.5453	0.04638	3.28	4.2	5.373	1000	3001

#WinBUGS codes generated by BAUW: http://bauw.psychstat.org
#USE WITH CAUTION!

Model{
  # Model specification for linear growth curve model
  for (i in 1:N){
    LS[i,1:2]~dmnorm(muLS[i,1:2], Inv_cov[1:2,1:2])
    muLS[i,1]<-bL[1]
    muLS[i,2]<-bS[1]
    for (t in 1:5){
      y[i, t] ~ dt(muY[i,t], Inv_Sig_e2, k)
      muY[i,t]<-LS[i,1]+LS[i,2]*t
    }
  }

  k~dunif(3, 30)

  #Priors for model parameter
  for (i in 1:1){
    bL[i] ~ dnorm(0, 1.0E-6)
    bS[i] ~ dnorm(0, 1.0E-6)
  }
  Inv_cov[1:2,1:2]~dwish(R[1:2,1:2], 2)
  R[1,1]<-1
  R[2,2]<-1
  R[2,1]<-R[1,2]
  R[1,2]<-0
  Inv_Sig_e2 ~ dgamma(.001, .001)
  Sig_e2 <- 1/Inv_Sig_e2
  Cov[1:2,1:2]<-inverse(Inv_cov[1:2,1:2])
  Sig_L2 <- Cov[1,1]
  Sig_S2 <- Cov[2,2]
  Cov_LS <- Cov[1,2]
  rho_LS <- Cov[1,2]/sqrt(Cov[1,1]*Cov[2,2])
}

# The (naive) starting values for model parameters.
list(k=4, bL=c(5), bS = c(2), Inv_Sig_e2 = 1, Inv_cov= structure(.Data = c(1,0,0,1),.Dim=c(2,2)),LS = structure(.Data = c(
4.566,1.296,5.097,1.591,5.169,
0.2067,4.221,1.752,7.714,0.05158,
4.08,0.8305,6.492,2.576,2.957,
2.289,4.33,2.634,5.698,0.9366,
3.032,2.831,3.752,3.166,4.13,
2.936,4.758,3.296,5.104,1.947,
5.585,0.3074,2.933,1.625,3.385,
2.499,4.996,1.862,4.851,3.503,
4.011,3.282,3.771,1.866,7.545,
0.7209,4.677,3.086,4.66,1.711,
5.522,0.8198,5.294,2.812,4.001,
0.9769,5.26,2.406,5.248,1.716,
4.763,1.472,3.802,1.811,5.598,
1.175,3.664,3.627,5.227,1.966,
4.348,2.246,5.761,1.038,4.725,
0.9613,7.291,1.845,4.503,1.986,
5.549,1.017,4.482,3.032,4.835,
2.42,4.757,1.839,3.154,3.117,
5.096,3.68,6.292,1.698,4.133,
2.911,6.694,1.267,2.638,2.96,
5.153,2.161,4.265,1.439,6.239,
0.5326,4.424,3.33,8.357,1.119,
5.076,3.825,3.696,3.836,6.229,
2.629,4.735,1.436,4.355,4.295,
4.083,0.587,4.017,2.176,3.932,
2.548,5.382,3.254,7.278,-1.7,
5.075,2.704,3.276,2.462,3.789,
2.759,4.188,1.682,5.856,-0.02246,
5.626,2.911,5.25,0.6643,3.518,
0.6248,5.568,-0.3362,5.113,1.026,
5.483,3.262,4.109,-0.224,5.263,
1.267,4.328,3.363,3.826,2.93,
5.072,3.007,5.006,0.1496,5.6,
3.097,3.43,2.453,3.853,1.895,
5.529,5.122,4.729,0.5532,5.483,
1.195,5.297,2.667,7.458,-0.3812,
4.517,3.327,6.143,1.963,4.166,
1.747,6.654,1.149,5.48,2.751,
4.676,3.682,4.741,0.9135,6.634,
0.9691,3.015,3.719,5.544,0.3026,
8.473,-0.05376,5.445,0.3776,5.872,
2.752,5.374,1.754,4.358,1.564,
3.614,1.932,3.819,2.293,5.234,
2.287,5.715,0.8591,4.266,1.628,
4.407,1.63,6.875,1.901,6.601,
1.814,5.26,3.401,6.045,1.512,
6.384,1.931,4.397,2.575,5.621,
2.068,3.955,2.035,3.963,4.335,
3.606,2.753,5.423,3.229,3.365,
3.694,3.162,2.068,3.245,1.526,
5.707,2.17,6.89,1.269,6.366,
1.796,5.205,2.657,2.983,2.237,
3.839,1.395,4.987,1.982,3.602,
1.472,6.281,1.734,5.184,0.6604,
5.378,0.5802,4.991,0.9695,5.066,
1.348,5.603,2.043,5.809,2.801,
5.842,2.676,3.675,3.962,3.662,
3.824,5.224,0.6743,4.469,2.333,
6.069,0.7096,4.616,-0.3334,5.343,
2.654,6.237,0.7163,4.499,2.653,
5.281,1.838,5.133,0.2718,4.094,
2.853,5.302,1.162,6.507,2.464,
5.323,2.076,5.524,1.388,4.234,
1.791,5.422,1.293,4.803,1.833,
5.437,2.918,6.329,1.807,3.844,
2.078,4.942,1.421,4.532,2.335,
4.09,3.212,4.584,1.893,4.075,
2.785,4.994,2.086,7.62,0.5028,
6.183,1.687,4.81,1.701,4.524,
2.823,4.52,1.151,4.888,2.011,
5.29,0.6222,3.902,3.948,4.576,
3.595,3.173,1.963,6.568,1.8,
4.766,4.369,5.271,2.561,2.708,
3.804,3.051,3.742,5.848,3.619,
4.575,2.68,4.086,2.482,4.773,
1.855,4.998,0.3159,5.192,1.249,
4.623,2.551,5.218,1.702,5.596,
1.383,8.594,-0.873,3.893,3.145,
5.6,2.44,2.998,2.888,4.313,
2.296,5.155,0.7865,5.493,1.181,
2.937,3.038,4.175,2.596,5.03,
0.1572,3.831,2.44,4.101,4.121,
3.439,3.192,3.721,1.967,5.265,
1.435,7.236,-0.2765,4.912,2.113,
2.975,4.473,4.462,3.098,6.984,
1.585,4.883,3.923,6.182,2.541,
5.125,4.306,5.548,1.39,3.717,
2.873,4.944,1.392,5.838,1.452,
4.414,1.325,4.637,1.496,6.23,
1.862,7.584,2.173,4.429,1.053,
3.849,4.382,6.643,1.903,5.058,
1.959,5.117,1.555,2.459,2.857,
5.061,4.801,3.284,2.263,6.385,
0.6228,5.92,1.156,3.589,2.291,
4.59,0.9942,4.94,2.276,4.362,
2.559,4.001,1.483,5.137,2.422,
6.083,1.122,4.837,0.7332,3.471,
2.692,3.333,1.38,5.112,3.04,
4.956,3.464,3.974,0.3202,5.573,
0.663,5.527,1.23,7.411,-0.7974,
5.998,2.797,6.369,1.766,4.378,
0.8029,3.94,3.282,2.703,2.085,
4.728,2.277,6.481,0.5644,4.386,
1.66,4.666,2.983,5.682,-0.1715,
3.265,3.664,3.934,3.127,5.824,
1.332,4.981,1.84,4.306,2.155,
4.282,1.269,6.326,3.538,4.848,
2.82,4.157,3.037,7.543,1.356,
5.415,1.109,3.575,2.992,6.756,
1.863,3.931,3.358,2.441,3.141,
3.26,1.156,5.415,0.1014,5.434,
4.087,4.757,0.9659,5.034,1.92,
5.907,1.306,3.807,2.066,4.787,
2.371,5.426,2.611,5.231,2.609,
4.228,1.401,5.619,0.6223,4.014,
1.677,4.832,2.845,4.735,3.127,
3.778,3.568,6.182,-0.02521,2.452,
4.343,5.177,2.523,3.454,2.347,
6.209,2.281,3.053,2.934,5.425,
2.055,3.311,4.488,4.457,3.744),
.Dim = c(300,2)))

# Please put your data here. Remeber you can convert your data by BAUW--Convert Data. :)
list(N=300,

y = structure(.Data = c(
5.434,6.667,9.555,9.774,8.141,
6.031,9.47,8.635,12.03,13.33,
4.388,5.667,6.048,7.182,5.825,
7.696,7.657,7.235,13.66,13.95,
6.763,6.758,9.775,9.979,9.139,
5.388,7.156,6.545,7.241,7.986,
9.913,12.75,13.99,17.48,15.57,
4.457,8.631,9.998,12.95,15.71,
10.78,9.27,10.28,18.82,17.15,
5.851,7.179,9.009,9.739,10.41,
7.267,9.782,11.46,16.16,17.98,
7.062,10.26,13.08,15.88,19.96,
5.28,10.33,12.66,15.06,18.82,
8.238,10.49,15.67,13.88,21.3,
8.211,8.457,9.681,12.83,14.86,
7.032,5.918,6.141,5.725,7.737,
4.502,4.673,6.797,9.571,11.42,
5.346,6.334,10.96,11.18,13.32,
7.327,9.246,8.09,11.0,13.72,
8.312,11.22,14.16,21.47,21.87,
7.561,8.409,16.16,19.37,20.62,
6.398,7.642,9.167,11.01,12.26,
8.197,7.792,9.609,9.222,13.0,
6.475,10.13,14.86,17.08,20.62,
6.518,13.3,10.87,12.87,12.74,
4.8,4.236,7.493,8.459,8.67,
8.294,10.87,14.88,15.09,18.64,
4.955,6.128,8.075,7.82,8.608,
8.83,12.34,13.19,16.03,18.8,
10.04,9.023,9.447,12.78,14.41,
-24.34,5.734,8.996,12.1,12.09,
5.237,7.455,8.778,10.16,13.19,
6.836,10.12,9.678,11.0,10.07,
6.129,12.67,14.28,17.8,21.36,
6.873,8.877,10.08,14.91,15.32,
6.897,8.645,8.155,11.67,16.04,
5.242,7.948,9.34,6.176,10.17,
5.867,5.296,7.69,8.587,11.1,
10.32,11.15,12.86,14.5,15.71,
6.092,7.549,10.65,10.15,14.42,
6.437,9.938,8.223,10.25,12.8,
8.851,10.88,14.62,15.65,19.21,
5.78,10.9,11.17,17.78,17.1,
7.626,11.15,10.92,12.74,17.14,
5.077,10.14,8.602,18.68,18.6,
10.28,12.74,16.09,21.09,21.87,
8.132,11.75,11.93,10.52,15.0,
4.784,9.41,10.95,14.35,19.41,
5.098,10.41,11.77,11.07,11.23,
3.681,6.731,12.31,15.98,16.5,
4.656,8.072,12.01,13.01,16.22,
5.526,7.743,10.1,9.762,11.08,
8.501,8.554,9.194,7.784,10.77,
8.816,11.4,16.14,18.19,23.55,
5.883,9.943,10.81,11.47,12.73,
9.612,10.21,16.01,20.61,23.51,
9.509,10.77,15.08,17.02,22.13,
9.213,10.69,14.47,18.04,19.01,
5.157,7.923,7.131,9.302,12.41,
9.781,12.61,15.93,20.92,25.0,
4.803,5.907,6.863,5.865,6.197,
7.346,10.09,10.4,14.55,15.09,
6.725,10.25,12.0,13.91,14.71,
10.44,10.65,13.8,19.52,22.26,
5.968,3.309,1.568,0.2516,0.1415,
4.673,10.31,14.23,15.65,16.5,
6.411,8.871,10.33,13.7,16.38,
6.634,9.475,13.84,14.62,17.73,
5.316,8.731,9.563,10.23,11.96,
4.682,3.747,3.121,5.813,5.657,
8.405,10.61,14.22,15.12,19.34,
5.413,3.841,5.177,7.947,8.173,
4.855,4.056,4.441,5.631,9.194,
3.873,7.993,5.764,4.727,1.546,
5.951,7.452,8.943,8.472,10.3,
9.364,13.85,14.13,17.16,21.13,
3.568,5.008,4.208,2.201,2.549,
2.506,8.606,9.179,10.47,10.94,
6.344,8.923,16.07,17.2,23.8,
7.278,10.83,12.02,14.46,19.86,
10.23,9.773,15.0,17.81,18.78,
4.633,6.487,5.389,6.911,3.369,
8.313,11.64,14.52,17.68,21.59,
6.772,4.514,11.26,13.64,14.54,
5.864,6.61,7.421,11.08,12.04,
11.97,16.87,23.24,25.97,30.85,
-0.5038,4.44,4.22,6.721,7.38,
6.895,8.83,9.489,9.843,13.0,
6.465,10.77,11.66,14.46,18.55,
6.786,5.029,6.812,6.548,5.732,
5.149,10.8,16.43,18.8,21.16,
11.16,10.13,12.67,14.52,16.22,
5.936,7.817,8.495,11.34,13.41,
7.996,7.868,8.386,9.717,12.55,
8.164,10.55,10.91,16.22,19.63,
7.101,12.95,15.79,19.48,23.44,
5.681,5.933,5.652,8.134,9.741,
9.843,8.478,10.4,9.713,12.11,
7.08,12.07,13.46,16.58,20.57,
4.86,5.75,6.042,7.756,7.575,
7.606,7.478,9.364,7.974,8.443,
5.821,4.091,6.345,5.65,6.517,
9.533,15.47,14.35,17.7,19.74,
7.027,9.603,10.15,13.86,15.88,
5.381,7.223,7.76,10.78,10.56,
7.076,7.102,10.03,11.96,13.96,
2.82,8.425,10.58,12.48,16.25,
7.635,10.25,12.55,15.47,18.3,
6.139,7.936,8.559,10.13,11.75,
5.944,7.622,7.68,12.14,11.6,
6.227,8.782,6.851,11.54,11.28,
7.478,10.48,14.38,14.15,17.43,
7.579,9.177,12.32,15.73,16.2,
8.949,12.31,15.46,19.42,22.36,
7.438,9.246,11.24,12.1,15.6,
6.016,9.548,12.03,14.71,15.81,
5.553,8.987,12.16,15.23,16.85,
5.745,9.478,11.86,13.47,15.23,
2.34,6.687,9.96,10.91,11.8,
9.228,12.75,16.27,21.87,25.32,
7.269,9.609,12.39,14.01,15.96,
7.854,11.73,14.32,15.9,19.84,
9.874,9.001,15.56,16.94,24.02,
4.125,6.003,8.816,12.77,13.34,
5.34,7.042,5.239,10.05,10.52,
8.706,8.111,11.41,12.81,17.63,
7.381,9.335,11.17,13.08,13.41,
8.069,10.97,11.04,13.64,18.91,
6.873,8.726,14.4,16.95,16.84,
1.507,8.334,10.86,11.39,12.86,
3.916,6.754,-4.17,10.71,8.455,
8.119,7.972,11.12,11.56,16.59,
6.8,5.647,8.667,9.273,12.48,
7.471,8.88,12.64,14.1,14.83,
5.876,9.407,6.248,8.864,7.71,
2.832,6.472,9.658,7.678,8.599,
5.55,7.267,5.662,6.33,9.457,
7.009,7.084,5.089,10.99,12.44,
7.434,11.18,12.83,14.06,14.32,
9.934,11.44,13.04,17.48,20.45,
8.497,10.06,14.94,16.2,19.88,
7.185,11.53,17.84,20.28,23.17,
5.919,12.17,16.17,16.21,22.54,
2.448,6.455,10.18,8.362,9.384,
6.235,8.462,10.79,12.18,16.95,
6.352,8.181,9.213,8.034,10.25,
2.528,3.022,5.37,3.118,2.576,
8.712,10.74,14.13,16.2,17.79,
6.809,8.895,10.3,9.686,8.94,
6.772,11.86,13.09,12.84,17.77,
7.698,6.951,9.389,11.73,12.73,
5.356,5.389,6.481,6.061,5.376,
6.781,11.51,13.48,17.17,19.35,
6.555,7.473,8.024,10.53,11.92,
10.99,11.04,14.81,16.94,21.18,
5.117,11.69,10.0,14.13,19.68,
8.911,9.806,9.551,10.05,12.9,
5.736,9.307,10.54,14.28,12.85,
8.198,9.182,9.134,11.14,11.58,
6.646,8.469,10.06,11.14,14.05,
7.1,11.33,14.35,17.35,19.08,
6.422,8.741,11.81,13.36,13.83,
4.895,8.199,9.752,11.63,14.05,
7.992,8.197,9.102,11.31,13.81,
6.947,10.99,14.49,12.22,13.84,
7.657,11.41,15.33,17.01,20.3,
7.358,8.334,10.49,10.9,15.71,
6.263,8.972,12.22,16.55,19.1,
6.096,10.49,12.11,10.3,16.28,
7.869,6.923,8.674,8.931,10.41,
8.518,8.2,10.23,16.18,13.47,
4.797,7.408,8.641,11.4,11.84,
8.714,9.693,12.21,15.25,20.65,
5.422,5.882,7.475,12.47,10.4,
7.396,9.947,11.17,13.76,13.46,
5.534,6.94,7.093,8.603,9.94,
9.473,9.452,16.18,19.46,22.55,
7.274,12.06,15.95,18.4,24.71,
5.006,8.394,8.229,11.01,13.45,
8.301,9.131,13.06,13.05,14.92,
6.933,13.12,15.4,22.77,27.63,
7.733,10.95,14.95,16.71,17.51,
4.47,10.03,13.38,18.11,22.31,
7.032,9.203,15.19,16.56,24.07,
10.76,14.43,19.01,19.14,24.53,
9.229,10.17,14.37,13.85,19.83,
5.513,4.403,14.26,15.59,16.8,
7.328,11.57,11.69,11.57,13.53,
5.106,6.43,5.393,6.543,4.928,
6.95,7.191,11.69,10.59,10.55,
3.387,9.406,11.83,14.42,17.95,
5.401,8.521,7.748,12.3,13.83,
6.988,7.986,8.281,10.35,10.6,
6.593,7.007,7.834,6.37,1.273,
7.387,7.677,11.48,17.18,18.62,
6.541,9.619,13.69,16.3,16.9,
3.309,6.234,12.53,15.27,17.6,
5.742,5.249,11.37,12.68,16.93,
6.748,7.126,7.033,7.74,10.33,
7.179,7.816,9.063,10.1,11.9,
6.404,10.95,10.41,13.13,16.84,
5.672,10.12,14.67,13.62,17.58,
4.771,6.432,6.369,5.669,7.253,
7.145,7.742,10.8,13.81,15.49,
8.415,13.01,16.21,20.89,25.69,
7.593,7.019,13.28,17.3,17.55,
6.861,9.019,8.923,12.65,14.2,
7.225,8.06,8.523,12.96,11.23,
5.838,5.307,3.137,5.966,5.733,
6.698,6.683,9.619,12.97,15.29,
8.003,9.819,16.31,20.78,26.22,
7.36,12.18,12.93,17.32,18.24,
8.476,11.13,13.83,15.22,14.67,
9.214,16.88,16.93,19.53,24.77,
7.873,10.17,13.86,17.95,18.31,
9.825,13.19,17.9,21.87,27.02,
6.503,8.272,10.38,11.32,12.3,
5.713,9.24,12.5,19.91,17.91,
5.669,8.369,10.28,9.336,11.01,
3.304,8.64,10.39,10.37,10.68,
6.711,8.024,10.46,10.57,10.36,
6.061,7.026,8.748,10.24,12.29,
9.735,7.702,13.02,14.52,14.68,
10.65,13.16,15.36,15.04,18.04,
4.662,6.66,6.267,6.982,9.401,
8.676,11.88,17.85,18.89,26.64,
6.097,9.547,10.87,13.3,15.76,
7.416,7.924,12.76,14.42,15.27,
7.699,8.195,8.15,12.82,12.43,
4.947,9.174,12.94,11.82,17.08,
10.11,14.72,21.19,24.82,30.36,
6.302,10.62,9.888,12.43,15.85,
8.102,14.87,8.236,8.541,9.303,
7.164,8.132,10.78,7.605,10.83,
4.26,6.816,13.92,12.01,11.7,
6.859,6.343,6.755,8.088,10.43,
4.805,9.792,15.83,15.22,15.48,
7.461,8.11,10.43,14.63,17.16,
4.439,6.938,8.087,10.56,11.83,
7.752,10.35,13.16,13.6,16.53,
7.643,8.692,6.851,11.25,12.38,
4.561,4.756,6.962,7.052,6.557,
5.119,8.035,10.99,13.78,14.84,
4.156,4.583,5.151,7.597,10.54,
8.037,11.46,15.22,17.49,24.09,
8.413,10.13,15.37,18.96,20.91,
10.42,6.146,2.242,6.541,7.009,
6.362,6.485,6.432,8.463,5.419,
7.497,8.186,11.13,11.84,11.11,
4.435,5.679,3.287,3.384,3.693,
6.438,11.33,14.83,18.87,21.76,
9.431,9.189,12.45,13.52,15.47,
4.991,7.784,6.671,7.192,8.837,
7.683,11.1,12.71,16.06,21.32,
5.288,8.055,10.34,11.47,13.86,
6.203,10.63,11.5,14.02,18.17,
6.897,7.86,7.677,9.414,7.718,
6.469,9.631,8.004,9.888,11.34,
6.438,10.21,13.33,17.89,18.96,
6.056,3.898,3.166,3.9,4.645,
7.503,9.75,14.11,17.82,19.17,
6.194,11.45,12.82,16.52,21.22,
6.879,9.928,10.37,11.0,12.54,
7.443,8.96,9.996,13.68,14.86,
6.192,8.718,8.559,12.6,14.62,
6.088,5.052,7.752,10.2,11.4,
8.152,14.4,18.46,19.96,22.65,
8.109,9.924,13.25,17.64,18.15,
7.536,12.1,12.87,14.86,19.17,
9.759,11.25,12.94,12.83,12.37,
7.341,8.644,9.471,10.69,10.78,
5.97,9.22,17.21,14.53,19.52,
8.119,11.73,11.69,14.67,15.29,
6.454,9.521,14.22,12.03,22.81,
5.253,9.432,13.26,15.8,17.29,
3.705,5.557,5.319,7.501,9.769,
7.096,5.311,5.793,5.8,5.531,
10.22,13.97,17.35,22.68,25.27,
6.687,7.265,7.91,9.513,10.88,
13.13,9.24,9.359,13.87,13.82,
5.972,7.768,12.21,11.02,11.9,
7.134,8.354,10.06,11.95,12.4,
6.82,6.696,14.41,13.21,16.61,
7.555,11.64,16.3,15.55,21.29,
9.202,7.785,12.23,13.55,17.08,
4.475,6.7,10.15,9.942,12.39,
5.155,5.567,5.345,8.752,10.74,
5.857,5.629,8.206,11.02,13.58,
7.167,11.53,15.18,15.47,18.14,
9.319,10.68,10.02,15.57,20.26,
8.728,11.06,13.76,19.58,21.99,
6.615,7.67,7.097,6.957,4.936,
7.253,10.58,16.1,19.4,24.19,
8.58,10.34,12.5,16.89,16.55,
5.01,9.503,8.964,12.74,15.53,
8.166,10.9,13.07,15.5,19.23,
5.981,8.438,15.96,14.03,15.88,
7.429,9.48,11.02,17.24,15.78,
4.993,12.18,18.07,22.74,24.87,
8.184,10.81,14.27,19.0,24.19),
.Dim = c(300,5)))

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Analyze data as student-t data

Analyze data as normal data

Analyze as T with estimated df

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