Dear All,
I have a questions about uniformative prior in the context of small size data:
I have 72 observations (panel data: 9 countries and 8 years). all the variables are log transformed. I would like to estimate the following model:
The model is (nonparametrically panel data regression functions in the instrumental variable context):
S_it = alpha_i + theta_1 *Yd_it + f(Bt_it) + theta_2 *Pe_it + epsilon_it (1) Principal equation
B_it = delta_i + gamma_1*Yd_it + D_it*gamma_2 + gamma_3*Pe_it + mu_it (2) Instrumental variable equation
S[i, t] < suicides[i,t]
Yd[i,t]< yields[i,t]
Bt[i,t]< BtCotton[i,t]
Pe[i,t] < pesticides[i,t]
Dt[i,t] < debt[i,t]
f is nonparametric function
I specified an unformative prior to the unknown parameters (please find the winbugs code bellow). My questions:
what uninformative prior should I specify?
How to resolve the high autocorrolation problem?
Regards,
**********************************************************************************************
model {
for (i in 1:9){
for (t in 1:8){
Y[i,t,1] <suicides[i,t]
X[i,t,1] <yields[i,t]
Y[i,t,2] <BtCotton[i,t]
X[i,t,2] <pesticides[i,t]
X[i,t,3] <debt[i,t]
Y[i,t,1:2] ~ dmnorm(mu[i,t,1:2], tau[1:2,1:2])
mu[i, t,1] < theta[1,i]* H[i,t,1] + beta[1,i]*mu[i,t,2] + beta[2,i]*pow(mu[i,t,2],2) + theta[2,i]* H[i,t,2] + alpha[i]
mu[i, t, 2] < gamma[1,i]* H[i,t,1] + gamma[2,i]* H[i,t,2] + gamma[3,i]*H[i,t,3] + lambda[i]
H[i,t,1]<(X[i,t,1]mean(X[,,1]))/sd(X[,t,1])
H[i,t,2]<(X[i,t,2]mean(X[,,2]))/sd(X[,t,2])
H[i,t,3]<(X[i,t,3]mean(X[,, 3]))/sd(X[,t, 3])
}
}
for (i in 1:9){
alpha[i]~ dnorm(mu.alpha[i], tau.alpha[i])
lambda[i]~ dnorm(mu.lambda[i], tau.lambda[i])
theta[1,i]~ dnorm(mu.theta1[i], tau.theta1[i])
theta[2,i]~ dnorm(mu.theta2[i], tau.theta2[i])
beta[1,i]~dnorm(mu.beta1[i],tau.beta1[i])
beta[2,i]~dnorm(mu.beta2[i],tau.beta2[i])
gamma[1,i]~ dnorm(mu.gamma1[i],tau.gamma1[i])
gamma[2,i]~ dnorm(mu.gamma2[i],tau.gamma2[i])
gamma[3,i]~ dnorm(mu.gamma3[i],tau.gamma3[i])
tau.alpha[i] < pow(sigma.alpha[i], 2)
tau.lambda[i]< pow(sigma.lambda[i], 2)
tau.theta1[i]< pow(sigma.theta1[i], 2)
tau.theta2[i]< pow(sigma.theta2[i], 2)
tau.beta1[i]< pow(sigma.beta1[i], 2)
tau.beta2[i]< pow(sigma.beta1[i], 2)
tau.gamma1[i]< pow(sigma.gamma1[i], 2)
tau.gamma2[i]< pow(sigma.gamma2[i], 2)
tau.gamma3[i]< pow(sigma.gamma3[i], 2)
mu.alpha[i]~ dnorm(0, 0.0001)
mu.lambda[i]~ dnorm(0, 0.0001)
mu.theta1[i]~ dnorm(0, 0.0001)
mu.theta2[i]~ dnorm(0, 0.0001)
mu.beta1[i]~ dnorm(0, 0.0001)
mu.beta2[i]~ dnorm(0, 0.0001)
mu.gamma1[i]~ dnorm(0, 0.0001)
mu.gamma2[i]~ dnorm(0, 0.0001)
mu.gamma3[i]~ dnorm(0, 0.0001)
sigma.alpha[i] ~ dunif (0, 100)
sigma.lambda[i] ~ dunif (0, 100)
sigma.theta1[i] ~ dunif (0, 100)
sigma.theta2[i] ~ dunif (0, 100)
sigma.beta1[i]~ dunif (0, 100)
sigma.beta2[i] ~ dunif (0, 100)
sigma.gamma1[i] ~ dunif (0, 100)
sigma.gamma2[i] ~ dunif (0, 100)
sigma.gamma3[i] ~ dunif (0, 100)
}
tau[1:2,1:2] ~dwish(R[,],2)
R[1,1]< 0.01
R[1,2]< 0.0
R[2,1]<0.0
R[2,2]<0.01
sigma[1:2,1:2]<inverse(tau[1:2,1:2 ])
}

This list is for discussion of modelling issues and the BUGS software.
For help with crashes and error messages, first mail [log in to unmask]
To mail the BUGS list, mail to [log in to unmask]
Before mailing, please check the archive at www.jiscmail.ac.uk/lists/bugs.html
Please do not mail attachments to the list.
To leave the BUGS list, send LEAVE BUGS to [log in to unmask]
If this fails, mail [log in to unmask], NOT the whole list
