Dear Bugs
users,
I am running
a multinomial logit model and using the estimated parameters to compute a multy
party equilibria algorithm (Adams, Merrill, and Grofmanl; 2005). The
multinomial model is stochastic but the nested nash model is just an
iterative algorithm that maximizes the location of the parties given the true
voter's location but has no distribution. I have two
questions:
1.- For a long time
I have been running multinomial logit models in Bugs will all categories rather
than J-1. Identification has not being a problem in bugs and the
multinomial model with all J categories converges without problem. Still, the
"Alligators" example fixes the parameters of the first category to zero (alpha[1] <- 0). Is there some particular reason to estimate the
multinomial in Bugs with J-1 categories? I could fix one category and back
transform the model to obtain the parameters of interest, but seems utterly
unnecessary.
2.- Second, I am
using the results of the multinomial to iteratively search for multiple parties
Nash equilibria (nested in the code). In the model, the parameters of the
multinomial are fitted to the nash algorithm which tricks bugs into compiling by
adding an intermediate parameter (nash[t]~dnorm(nash.mu[t],100)) which fits the
mean of the derivative with a high precision, Tau=100. Does anyone knows a more
elegant way to use Bugs Random Walk to fit data to an analytical algorithm?
The
code for the model is below:
model
{
for (t in 1:K)
{
#Nash
Equilibrium Algorithm
nash[t]~dnorm(nash.mu[t],100)
nash.mu[t] <-
mean(w1[,t])/mean(w2[,t])+xbar
probp[t]<-
mean(p[,t])
A[t] <-
A.s[t]
B[t] <- B.s[t]
#Party Location priors for
Multinomial
model
A.s[t]~dnorm(.5,.001)
B.s[t]~dnorm(.5,.001)
probz[t]<-
mean(z[,t])
}
for (i in 1 : I) { # Loop around
groups
Y[i,1:K] ~ dmulti( z[i,1:K] , 1)
for (k in 1
: K) { # Multinomial Choice
Model
z[i,k] <- phi.s[i,k] /
sum(phi.s[i,])
log(phi.s[i,k]) <-
B.s[k]*valence[i,k]-A.s[k]*(pow(x[i]-s[i,k],2))
#Nash
Model
p[i,k] <- phi[i,k] /
sum(phi[i,])
log(phi[i,k]) <-
B[k]*valence[i,k]-A[k]*(pow(x[i]-nash[k],2))
w1[i,k] <-
p[i,k]*(1-p[i,k])*(x[i]-xbar)
w2[i,k] <- p[i,k]*(1-p[i,k])
}
}
}
}
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