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lab:projects:12bayesian_random_coefficients_lcsm:index

Random coefficients LCSM

NLSY97 data

• 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(
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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), .Dim=c(
104, 4
)), Z
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)
)