Table of Contents

Random coefficients LCSM

NLSY97 data

Real data analysis

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##Model part
model{
   for (i in 1:N){
       LS[i,1:2]~dmnorm(mu[1:2], inv_sig_LS[1:2,1:2])
       Y[i,1]~dnorm(y[i,1],inv_sig_e2)

       y[i,1]<-LS[i,1]

        for (t in 2:T){
             Y[i,t]~dnorm(y[i,t], inv_sig_e2)
             d[i,t-1]<-gamma[i,t-1]*y[i,t-1]+LS[i,2]
             y[i,t]<-d[i,t-1]+y[i,t-1]
				
				## another way to deal this
				gamma[i, t-1]~dnorm(mugamma[i,t-1], inv_sig_v2)
				mugamma[i, t-1]<-beta[1]*X[i,t-1] + beta[2]*(Z[i]-0.6442308)
			}
    }

       inv_sig_e2~dgamma(.001,.001)
       inv_sig_v2~dgamma(.001,.001)

    for (i in 1:2){
       beta[i]~dnorm(0,.00001)
       par[i]<-beta[i]
    }
      
       mu[1]~dnorm(0,.00001)
       mu[2]~dnorm(0,.00001)
      par[3]<-mu[1]
      par[4]<-mu[2]

      inv_sig_LS[1:2,1:2]~dwish(sigs[1:2,1:2],2)
       sigs[1,1]<-1
       sigs[2,2]<-1
       sigs[1,2]<-sigs[2,1]
       sigs[2,1]<-0
      
       par[5]<-1/inv_sig_e2
       par[6]<-1/inv_sig_v2
       sig_LS[1:2,1:2]<-inverse(inv_sig_LS[1:2,1:2])
       par[7]<-sig_LS[1,1]
       par[8]<-sig_LS[1,2]
       par[9]<-sig_LS[2,2]
}

## Starting values
list(beta=c(0,0),inv_sig_e2=1,inv_sig_v2=1, mu=c(1,1), inv_sig_LS=structure(.Data=c(1,0,0,1),.Dim=c(2,2)))

list(
N
=
104, T
=
5.00000E+00, Y
= structure(.Data= c(
1.17000E+01, 8.60000E+00, 7.10000E+00, 7.60000E+00, 8.50000E+00, 9.50000E+00, 8.90000E+00, 7.60000E+00, 8.00000E+00, 8.50000E+00, 9.00000E+00, 9.40000E+00, 8.60000E+00, 8.80000E+00,     NA,     NA, 8.30000E+00,     NA, 8.00000E+00, 8.30000E+00, 1.10000E+01, 1.05000E+01,     NA, 9.60000E+00, 9.70000E+00, 1.35000E+01, 1.24000E+01, 1.21000E+01, 1.17000E+01, 1.20000E+01, 1.15000E+01, 1.18000E+01, 1.19000E+01, 1.21000E+01, 1.09000E+01,     NA,     NA, 1.20000E+01, 9.60000E+00, 8.60000E+00, 1.01000E+01, 8.30000E+00, 9.00000E+00,     NA, 7.70000E+00, 9.40000E+00, 1.15000E+01, 1.10000E+01, 1.00000E+01, 1.39000E+01, 8.40000E+00, 6.60000E+00,     NA, 7.80000E+00, 8.20000E+00, 8.30000E+00, 8.50000E+00, 1.00000E+01, 8.50000E+00, 8.20000E+00, 7.40000E+00, 7.50000E+00, 5.50000E+00, 6.90000E+00,     NA, 1.03000E+01, 1.07000E+01, 9.70000E+00, 8.70000E+00, 8.50000E+00, 9.50000E+00, 8.30000E+00, 9.40000E+00, 9.10000E+00, 9.10000E+00, 1.21000E+01, 1.14000E+01, 1.18000E+01, 1.22000E+01, 1.20000E+01, 8.00000E+00,     NA, 6.90000E+00, 8.60000E+00, 7.90000E+00, 1.27000E+01, 1.17000E+01, 1.17000E+01, 1.07000E+01, 1.09000E+01, 8.40000E+00, 8.20000E+00, 8.30000E+00, 9.20000E+00, 9.20000E+00, 8.80000E+00, 1.01000E+01, 6.60000E+00,     NA, 7.70000E+00, 1.24000E+01, 1.15000E+01, 1.12000E+01, 1.01000E+01, 1.02000E+01,     NA, 1.00000E+01, 9.30000E+00, 8.50000E+00, 1.04000E+01, 1.03000E+01, 5.50000E+00, 8.60000E+00, 8.30000E+00, 9.80000E+00, 1.03000E+01, 9.40000E+00, 9.70000E+00, 7.80000E+00, 1.00000E+01, 9.10000E+00, 1.06000E+01, 1.08000E+01, 9.40000E+00, 9.50000E+00, 1.20000E+01, 1.13000E+01, 1.10000E+01, 1.04000E+01, 9.70000E+00, 9.10000E+00, 9.70000E+00, 1.08000E+01, 1.03000E+01, 8.80000E+00, 1.03000E+01, 1.16000E+01, 1.17000E+01, 1.01000E+01, 1.09000E+01, 8.90000E+00, 1.05000E+01, 9.80000E+00, 9.40000E+00, 8.60000E+00, 1.05000E+01, 8.40000E+00, 1.11000E+01, 9.40000E+00, 8.70000E+00, 1.01000E+01,     NA, 9.80000E+00, 8.20000E+00, 8.30000E+00, 1.24000E+01, 1.17000E+01, 1.15000E+01, 1.09000E+01, 1.07000E+01, 8.60000E+00, 8.20000E+00, 7.00000E+00, 8.50000E+00, 8.10000E+00, 1.01000E+01, 1.17000E+01, 8.90000E+00, 8.70000E+00, 8.30000E+00, 1.12000E+01,     NA, 8.90000E+00, 8.80000E+00,     NA, 9.80000E+00, 1.03000E+01, 8.20000E+00, 8.90000E+00,     NA, 1.03000E+01, 1.17000E+01, 1.13000E+01, 1.00000E+01, 1.05000E+01, 7.00000E+00, 8.60000E+00, 7.30000E+00, 7.50000E+00, 7.80000E+00, 1.23000E+01, 1.10000E+01, 1.13000E+01, 1.06000E+01, 1.14000E+01, 1.17000E+01, 1.13000E+01,     NA, 1.03000E+01, 1.04000E+01, 1.03000E+01, 9.10000E+00, 1.04000E+01, 9.50000E+00, 1.02000E+01, 1.11000E+01, 8.60000E+00, 1.04000E+01, 8.50000E+00, 9.00000E+00, 1.24000E+01, 1.04000E+01, 1.03000E+01, 1.13000E+01,     NA, 1.08000E+01, 1.00000E+01, 9.50000E+00, 8.00000E+00, 7.50000E+00, 1.22000E+01, 1.12000E+01, 1.09000E+01, 1.03000E+01, 1.07000E+01, 9.40000E+00, 9.00000E+00, 1.01000E+01, 8.50000E+00, 8.50000E+00, 9.70000E+00, 8.10000E+00, 1.24000E+01, 8.30000E+00, 7.00000E+00, 9.90000E+00, 8.50000E+00, 1.01000E+01, 8.30000E+00, 9.90000E+00, 1.14000E+01, 1.12000E+01,     NA, 1.13000E+01, 1.02000E+01, 1.13000E+01, 1.13000E+01, 1.10000E+01, 1.10000E+01, 9.90000E+00, 1.06000E+01, 9.70000E+00, 8.80000E+00, 8.40000E+00, 9.30000E+00, 1.24000E+01, 1.02000E+01, 9.50000E+00,     NA, 1.12000E+01, 1.02000E+01, 1.04000E+01, 9.70000E+00, 9.40000E+00, 1.02000E+01, 1.16000E+01, 1.15000E+01, 9.30000E+00, 1.07000E+01, 1.30000E+01, 1.12000E+01, 1.10000E+01, 1.08000E+01, 1.02000E+01, 1.09000E+01, 1.08000E+01, 1.15000E+01, 1.14000E+01, 1.10000E+01, 1.08000E+01, 9.30000E+00, 1.10000E+01, 7.10000E+00, 8.70000E+00, 7.90000E+00, 6.10000E+00, 6.40000E+00, 8.90000E+00, 8.20000E+00, 7.30000E+00, 1.11000E+01, 1.05000E+01, 1.15000E+01, 1.19000E+01, 1.04000E+01, 7.80000E+00, 8.30000E+00, 9.20000E+00, 8.50000E+00, 7.90000E+00, 1.09000E+01, 1.15000E+01, 1.14000E+01, 1.03000E+01, 1.05000E+01, 1.08000E+01, 1.16000E+01, 1.18000E+01, 9.80000E+00, 9.60000E+00, 1.16000E+01, 1.03000E+01, 1.04000E+01, 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), .Dim=c(
104, 5
)), X
= structure(.Data= c(
-1.17282E+00, -1.02367E+00, -1.09825E+00, -1.17282E+00, -1.09825E+00, 1.06440E+00, 1.06440E+00, -4.27081E-01, -1.17282E+00, -1.17282E+00, -1.02367E+00, -1.17282E+00, -1.17282E+00, 1.06440E+00, 1.06440E+00, 1.06440E+00, -1.17282E+00, -5.01655E-01, 1.06440E+00, 8.40681E-01, -1.17282E+00, -1.17282E+00, -1.17282E+00, -8.74526E-01, -1.17282E+00, -1.17282E+00, -7.99952E-01, -7.25378E-01, -1.17282E+00, -1.17282E+00, -1.09825E+00, -4.27081E-01, -1.17282E+00, -7.25378E-01, 1.06440E+00, 1.06440E+00, -1.17282E+00, -1.09825E+00, -1.02367E+00, -8.74526E-01, -1.17282E+00, 1.06440E+00, 1.06440E+00, 1.06440E+00, -1.17282E+00, -8.74526E-01, 1.06440E+00, 1.06440E+00, -1.17282E+00, -1.09825E+00, -1.17282E+00, 1.06440E+00, -6.50804E-01, 1.06440E+00, 1.06440E+00, 1.06440E+00, -7.99952E-01, 1.06440E+00, 1.06440E+00, 1.06440E+00, -1.17282E+00, -1.09825E+00, -1.17282E+00, -1.02367E+00, -1.17282E+00, -1.17282E+00, 1.06440E+00, 1.06440E+00, -1.17282E+00, -1.02367E+00, 1.06440E+00, 9.89830E-01, -1.17282E+00, 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-1.17282E+00, -1.17282E+00, 1.06440E+00, 1.06440E+00, -1.17282E+00, -9.49101E-01, 1.06440E+00, 1.06440E+00, -1.17282E+00, -9.49101E-01, -1.09825E+00, -1.17282E+00, -1.17282E+00, -1.17282E+00, -1.09825E+00, -1.09825E+00, -1.17282E+00, 1.06440E+00, -7.99952E-01, 6.91533E-01, -1.17282E+00, -1.02367E+00, -9.49101E-01, -1.17282E+00, -1.09825E+00, -1.09825E+00, 1.06440E+00, 3.18661E-01, -1.17282E+00, -1.17282E+00, -1.02367E+00, -1.02367E+00, -4.27081E-01, 3.93236E-01, 1.06440E+00, -1.17282E+00, -1.17282E+00, -7.99952E-01, -7.25378E-01, -5.42097E-02, 6.91533E-01, 1.06440E+00, 1.06440E+00, 1.06440E+00, -1.02367E+00, -6.50804E-01, -1.17282E+00, -1.09825E+00
), .Dim=c(
104, 4
)), Z
=c(
1, 1, 0, 0, 1, 1, 1, 0, 1, 0, 1, 0, 1, 1, 0, 1, 1, 1, 0, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 0, 1, 0, 0, 0, 1, 0, 0, 1, 1, 0, 1, 1, 0, 1, 1, 0, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 0, 1, 1, 0, 0, 1, 0, 0, 1, 0, 1, 1, 1, 1, 1, 1, 1, 0, 0, 1, 0, 1, 1, 1, 0, 1, 1, 1, 0, 0, 1, 0, 0, 0, 0, 1, 0, 1, 1, 1, 1, 1, 1, 0
)
)

Simulation