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Subject:

uninformative prior (small sample size data)

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Thu, 11 Oct 2012 11:19:53 +0100

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 ```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]<- Bt-Cotton[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 ```