## data generation model{ for (i in 1:n){ y[i]~dnorm(muy[i], pre_y) muy[i]<-iy + b*m[i] + c*x[i] m[i]~dnorm(mum[i], pre_m) mum[i]<-im + a*x[i] x[i]~dnorm(0,1) } } ## population parameter values list(n=500, iy=0, im=0, a=.39, b=.39, c=0, pre_y=1, pre_m=1) ## parameter estimation model{ for (i in 1:n){ y[i]~dnorm(muy[i], pre_y) muy[i]<-iy + b*m[i] + c*x[i] m[i]~dnorm(mum[i], pre_m) mum[i]<-im + a*x[i] } iy~dnorm(0, 1.0E-6) im~dnorm(0, 1.0E-6) a~dnorm(0, 1.0E-6) b~dnorm(0, 1.0E-6) c~dnorm(0, 1.0E-6) pre_y~dgamma(.001,.001) pre_m~dgamma(.001,.001) tau<-a*b } ## initial values list(iy=0, im=0, a=.39, b=.39, c=0, pre_y=1, pre_m=1) ## parameter estimation model{ for (i in 1:n){ y[i]~dnorm(muy[i], pre_y) muy[i]<-iy + tau/a*m[i] + c*x[i] m[i]~dnorm(mum[i], pre_m) mum[i]<-im + a*x[i] } iy~dnorm(0, 1.0E-6) im~dnorm(0, 1.0E-6) a~dnorm(0, 1.0E-6) tau~dnorm(0, 1.0E-6) c~dnorm(0, 1.0E-6) pre_y~dgamma(.001,.001) pre_m~dgamma(.001,.001) } ## initial values list(iy=0, im=0, a=.39, tau=.39, c=0, pre_y=1, pre_m=1) ## generated data list(n=500, m = c( 1.436,-1.171,-0.4665,0.9741,-0.8708, -2.092,-0.2641,-0.5893,0.1589,-0.6167, 1.899,0.3424,0.9494,0.02347,0.7029, 0.1858,0.1829,-1.777,-0.1004,0.8475, 0.4793,-1.098,-0.03153,2.309,0.95, -1.04,1.257,0.601,-1.145,-3.434, -0.6539,1.162,-1.53,0.5234,-1.886, 0.1827,1.447,-1.006,0.1696,-0.3526, -0.1517,1.01,-0.08137,0.1517,-1.289, -2.058,0.6589,-1.483,0.2432,-0.3459, -1.128,0.1029,0.2404,0.3797,0.03015, -0.6454,0.4905,-0.6488,-0.06781,-1.888, -0.223,-0.8946,1.317,-2.638,1.366, -0.8151,2.078,0.5277,0.2458,0.4059, -1.282,-0.9085,-0.5928,-2.242,-0.4842, 1.211,0.2836,0.3711,-0.8948,0.3163, -1.298,-0.0884,0.8404,-0.9896,-0.683, 0.1628,-1.63,-0.5291,1.804,-0.8317, 0.3505,0.8275,-0.8784,-0.5764,1.318, -0.3594,-0.1715,-0.7472,-2.555,-0.1681, 0.3191,-0.4486,-0.5813,-0.1759,-0.67, 1.331,1.458,0.8451,-1.177,0.1344, 1.263,-0.4336,-1.29,-0.07023,-2.041, 0.5815,-0.6285,-2.148,-0.7123,2.436, 1.503,-0.5858,0.832,-0.9761,1.043, 0.1624,-0.769,-0.3482,-1.923,0.1463, -0.7484,1.751,-0.8561,1.436,-0.7891, -0.2492,-0.3818,-0.1747,-1.277,0.4514, 0.7822,0.397,0.4374,0.2577,-0.01581, -1.326,-0.5177,-1.525,-0.2938,1.988, -0.3295,-0.1371,0.3817,2.287,1.689, 0.4547,1.312,2.366,-0.8429,0.7685, 0.4464,0.1602,-0.3536,-0.873,-0.09389, 2.085,0.6627,0.9558,0.2005,0.08684, -1.078,-0.7545,0.07803,-1.45,0.3453, -0.825,-0.5384,-0.1143,0.3356,-0.6841, 0.2168,2.384,-0.7358,0.5576,2.102, -1.307,-2.119,-1.075,-1.404,0.2923, 0.336,1.545,1.118,0.48,0.4341, -1.934,-0.8378,-1.609,-2.705,0.1818, -0.9606,-0.7144,-0.5728,-0.4411,0.3711, -0.5734,0.4098,-1.068,-1.25,0.7149, -1.229,2.342,1.002,0.3504,0.8357, -1.778,-0.6546,-0.9983,0.6044,1.238, 0.9593,-0.6025,-0.9919,1.978,0.1085, 0.1952,0.755,-0.6017,-1.099,1.007, 1.628,0.4166,-0.2523,0.3353,-0.5746, 0.9491,1.057,-1.443,0.5035,-0.9151, 1.096,0.6101,-0.5985,-0.2317,-0.7585, -2.043,1.597,0.6273,-0.5031,0.4019, 0.1514,-0.8808,0.9534,0.9813,1.126, 0.4795,1.874,-1.425,-1.108,-0.7763, -3.364,-1.855,-0.5678,0.3117,0.1886, 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-1.004,-0.01064,-0.8496,-0.591,1.479, -0.7221,0.04977,-0.6239,1.66,-1.266, 1.195,-1.524,0.6237,0.6426,1.224, 0.3781,-1.4,-0.3907,0.4814,-0.5582, -0.218,-0.8199,-0.1623,0.1989,1.577, -1.642,1.04,1.068,-0.3191,0.9234, -1.838,1.771,1.492,-1.35,0.2338, -1.027,0.03282,-0.8525,-2.146,1.058, -1.825,-0.5398,-1.39,0.4023,-1.186, 0.4817,0.2259,-1.091,-0.6104,-0.5527, 1.245,-0.2359,-0.7365,2.101,-2.181, 0.3038,-0.2463,-1.523,2.341,0.1595, -0.7703,1.585,0.6356,0.902,-1.494, -2.572,0.04389,1.041,0.1249,0.6624, 0.2911,0.6164,-1.73,0.0205,-0.8785, 2.054,1.108,-0.4087,2.172,-1.411, -1.512,1.362,-0.4606,-0.1589,-0.2338, -2.262,-0.09985,-1.549,-0.9966,0.5889, -2.487,1.984,-2.071,1.094,-1.75, -0.1514,-0.6988,0.6209,-1.315,0.9067), x = c( 0.7268,-1.347,0.6934,-1.222,-0.7298, -1.966,0.2762,1.136,1.054,-0.7137, 0.9273,1.049,2.14,-0.2541,0.08295, 1.407,-0.9553,-0.8873,-0.1775,0.4261, 1.722,0.6593,-0.7972,0.7611,1.461, -0.2778,-0.8848,0.9539,0.4193,-0.4277, 1.842,-0.1409,-2.647,0.75,-0.4147, 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