lab:projects:12bayesian_random_coefficients

Random coefficients LCSM
- NLSY97 data
Real data analysis
- Simulation
Random coefficients LCSM

NLSY97 data

Data set
Variables in the data set
- Outcome: piat1-piat5: PIAT math test standard score from Year 1998-2002
- Time varying covariates: smoke1-smoke5: # of days smoked in last 30 days Year 1998-2002
- Time invariant covariates: op: optimistic about the future (1997), depress: depression at 2002
Real data analysis

BUGS code
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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(
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), .Dim=c(
104, 5
)), X
= structure(.Data= c(
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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
)
)
Table of Contents

Random coefficients LCSM

NLSY97 data

Real data analysis

Simulation
