model{
#Model specification
for (i in 1: 300 ) {
m[i]~ dnorm(mum[i], Inv_sig2_em)
mum[i]<-im+a*x[i]
y[i]~dnorm(muy[i], Inv_sig2_ey)
muy[i]<-iy+c*x[i]+b*m[i]
}

#priors

a~dnorm(0, 1.0E-6)
b~dnorm(0, 1.0E-6)
c~dnorm(0, 1.0E-6)
im~dnorm(0, 1.0E-6)
iy~dnorm(0, 1.0E-6)
Inv_sig2_ey~dgamma(1.0E-3, 1.0E-3)
Inv_sig2_em~dgamma(1.0E-3, 1.0E-3)

#parameter transformation
Sig2_ey<-1/Inv_sig2_ey
Sig2_em<-1/Inv_sig2_em
product<-a*b
Para[1]<-a
Para[2]<-b
Para[3]<-c
Para[4]<-product
Para[5]<-im
Para[6]<-iy
Para[7]<-Sig2_ey
Para[8]<-Sig2_em
}

## initial values
list(im=0, iy=0, a=0, b=0, c=0, Inv_sig2_ey=1,Inv_sig2_em=1 )

## data
list(
x=c(76, 67, 67, 72, 69, 70, 77, 79, 73, 69, 78, 69, 75, 81, 72, 
78, 75, 84, 79, 79, 68, 77, 73, 82, 73, 68, 68, 81, 86, 72, 65, 
75, 71, 72, 72, 71, 72, 74, 79, 73, 71, 71, 70, 70, 76, 75, 67, 
75, 67, 77, 73, 67, 73, 71, 66, 77, 71, 79, 79, 76, 88, 69, 69, 
78, 82, 65, 75, 80, 81, 69, 79, 71, 66, 72, 69, 73, 80, 71, 77, 
84, 69, 73, 70, 76, 79, 75, 69, 71, 81, 67, 78, 67, 65, 82, 68, 
81, 76, 72, 72, 83, 69, 70, 75, 66, 69, 76, 68, 71, 67, 65, 84, 
67, 72, 80, 67, 69, 80, 85, 72, 76, 69, 71, 67, 72, 70, 66, 68, 
65, 69, 71, 71, 75, 68, 72, 75, 68, 66, 87, 67, 74, 67, 87, 72, 
71, 75, 80, 78, 69, 72, 77, 79, 79, 67, 73, 78, 65, 68, 76, 72, 
70, 84, 69, 69, 75, 72, 66, 72, 70, 80, 74, 73, 84, 71, 70, 74, 
79, 75, 72, 75, 73, 68, 68, 80, 67, 85, 82, 80, 85, 87, 74, 67, 
65, 70, 68, 66, 65, 68, 66, 72, 68, 75, 70, 66, 78, 76, 65, 75, 
67, 76, 79, 68, 68, 81, 81, 68, 81, 67, 69, 85, 74, 82, 74, 71, 
66, 74, 79, 70, 69, 65, 71, 75, 65, 70, 69, 74, 83, 68, 70, 65, 
70, 65, 67, 85, 69, 70, 81, 76, 65, 66, 65, 82, 70, 71, 66, 68, 
67, 76, 67, 68, 70, 66, 68, 85, 75, 66, 71, 76, 70, 76, 67, 70, 
65, 65, 82, 78, 76, 73, 68, 72, 81, 79, 75, 75, 69, 73, 73, 85, 
85, 72, 68, 73, 70, 81, 71, 68, 65, 78, 76, 81, 73),

m=c(28, 13, 24, 33, 30, 35, 32, 38, 17, 56, 14, 32, 45, 11, 42, 
22, 26, 34, 42, 16, 28, 19, 14, 36, 31, 31, 22, 22, 25, 20, 53, 
35, 15, 15, 29, 53, 43, 45, 22, 22, 16, 33, 43, 42, 43, 40, 25, 
19, 33, 19, 36, 47, 24, 60, 40, 25, 31, 14, 30, 7, 29, 19, 19, 
27, 29, 47, 17, 16, 20, 26, 30, 55, 57, 46, 37, 11, 19, 47, 27, 
27, 33, 24, 10, 18, 39, 23, 27, 31, 23, 21, 33, 38, 56, 33, 31, 
24, 17, 44, 21, 15, 10, 23, 32, 56, 34, 8, 9, 20, 13, 64, 29, 
56, 37, 8, 32, 41, 18, 30, 50, 41, 55, 36, 25, 26, 13, 53, 39, 
33, 73, 52, 29, 16, 41, 40, 15, 31, 24, 9, 36, 47, 40, 35, 14, 
37, 14, 32, 20, 37, 9, 30, 17, 24, 43, 25, 28, 53, 27, 23, 27, 
40, 20, 33, 33, 16, 22, 34, 37, 38, 20, 17, 36, 20, 57, 38, 39, 
21, 33, 36, 30, 36, 36, 37, 22, 27, 35, 20, 48, 13, 10, 32, 40, 
44, 14, 19, 45, 43, 17, 43, 50, 34, 35, 30, 15, 7, 14, 25, 25, 
16, 19, 36, 21, 27, 22, 17, 25, 16, 30, 28, 10, 32, 16, 44, 50, 
27, 22, 16, 47, 24, 28, 31, 14, 47, 44, 48, 42, 39, 51, 29, 59, 
12, 46, 23, 12, 25, 16, 11, 33, 32, 39, 43, 43, 43, 48, 30, 27, 
16, 13, 39, 61, 43, 16, 47, 24, 7, 13, 40, 10, 55, 33, 34, 25, 
29, 37, 18, 48, 31, 42, 37, 17, 28, 19, 24, 27, 13, 11, 23, 42, 
17, 17, 22, 44, 47, 15, 44, 64, 47, 23, 11, 34, 32),

y=c(27, 15, 19, 27, 23, 14, 22, 10, 9, 27, 14, 19, 22, 12, 23, 
22, 14, 20, 24, 9, 24, 22, 17, 23, 23, 16, 20, 21, 13, 22, 26, 
15, 12, 23, 12, 26, 25, 24, 23, 21, 12, 20, 21, 21, 18, 23, 21, 
14, 19, 16, 18, 24, 15, 26, 23, 12, 19, 21, 22, 20, 15, 15, 13, 
16, 19, 25, 21, 16, 14, 12, 19, 24, 22, 25, 22, 13, 24, 19, 25, 
25, 22, 8, 13, 14, 18, 21, 23, 18, 18, 13, 25, 20, 26, 22, 20, 
17, 11, 22, 22, 18, 10, 16, 16, 23, 19, 9, 11, 15, 20, 26, 19, 
25, 19, 8, 22, 17, 17, 23, 28, 22, 28, 26, 24, 12, 16, 25, 22, 
19, 27, 24, 21, 16, 24, 21, 14, 25, 18, 8, 20, 22, 26, 20, 4, 
26, 13, 18, 17, 20, 3, 24, 18, 18, 19, 18, 23, 23, 20, 15, 24, 
24, 21, 25, 25, 9, 14, 22, 18, 22, 11, 21, 20, 17, 28, 22, 28, 
15, 22, 24, 19, 22, 13, 16, 11, 19, 26, 19, 23, 15, 6, 23, 25, 
21, 15, 13, 18, 24, 14, 21, 24, 24, 25, 24, 12, 14, 21, 25, 21, 
4, 20, 13, 20, 19, 25, 17, 22, 19, 20, 15, 14, 18, 15, 23, 26, 
15, 23, 13, 26, 12, 13, 28, 9, 21, 19, 24, 27, 21, 25, 20, 26, 
17, 26, 13, 14, 20, 6, 3, 24, 24, 23, 22, 27, 24, 25, 26, 23, 
18, 16, 26, 24, 20, 3, 24, 14, 2, 9, 17, 12, 23, 21, 22, 18, 
21, 23, 10, 25, 18, 22, 22, 11, 13, 23, 12, 14, 10, 8, 16, 22, 
15, 11, 19, 18, 27, 9, 24, 23, 25, 19, 13, 16, 18)

)