dear saengla,
for small values of the sd parameter, these inverse-gamma prior
distributions do not work so well, both for computational and modeling
reasons. i recommend using a uniform or, more generally, half-t prior
distribution that can be implemented using a multiplicative
parameterization. you can see the paper
http://www.stat.columbia.edu/~gelman/research/unpublished/tau7.pdf
for details and further references.
good luck!
yours
andrew
(p.s. message forwarded to the bugs list since others might be interested)
Saengla Chaimongkol wrote:
>Dear BUGSlisters,
>
>I am fitting the multilevel logistic regression by using WinBUGS. I have a
>problem that the variance is very slow mixing when its value is lower than
>1. I use the default gamma(0.001, 0.001) as the prior distribution. I also
>vary as dgamma(0.01,0.01), dgamma(.1,.1) but it does not much improve.
>However, when I use dgamma(1,1) or dgamma(.5,.5), it is fast mixing but it
>is over-estimate.
>
>My model is
> y[i] ~ dbin(p[i],1)
> logit(p[i]) = beta[k] + gamma[k]*group[i] + u2[i] + u3[i] +
> u4[i,k]*group[i]
>
>beta[k] ~ dnorm(0, 1.0E-6) # the difficult of item k
>gamma[k] ~ dnorm(0,1.0E-6) # the differecnce difficulty between group
>u2[i] ~ dnorm(0, tau2) # level-2 random effect (student)
>tau2 ~ dgamma(0.001, 0.001)
>u3[i] ~ dnorm(0, tau3) # level-3 random effect (school)
>tau3 ~ dgama(0.001,0.001)
>
>u[i,k] ~ dnorm(0, tau[k]) # interaction random effect of item and level-3
>indicating that variance of each item vary across schools.
>
>tau[k] ~ dgamma(0.001,0.001)
>
>
>I assume that tau[k] is small such as .1,.2 for some k that I have a
>problem that it is very slow mixing but for tau[k] are 1 or 2, it does not
>have any problem.
>
>Does anyone give me any suggestion of improving the mixing of such small
>variance in WinBUGS?
>
>Thank you very much in advance for any comment,
>saengla
>
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--
Andrew Gelman
Professor, Department of Statistics
Professor, Department of Political Science
Social Work Building (Amsterdam Ave. and 122 St.), Room 1016
Columbia University
New York, NY 10027
(o) 212-851-2142
(o-fax) 212-851-2164
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www.stat.columbia.edu/~gelman
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