lab:projects:12bayesian_random_coefficients_lcsm:index
Table of Contents
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
Click to display ⇲
Click to hide ⇱
##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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), .Dim=c(
104, 4
)), Z
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)
)