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Hi. I’m fitting a hierarchical logistic regression model
and am interested in calculating a variance partition coefficient to estimate the
variance attributable to the higher-level term. This is a straightforward
matter when both the response and the higher-level term are linear, but I am
uncertain how to address it in the case of a non-linear response. I understand
there are approximations available, (e.g those described by Goldstein, Brown
and Rasbash) but how would they be implemented in WinBUGS? Is this
an issue with which anyone is familiar?
Also, I’ve come across references to the fact that placing normal
priors with large variances on fixed effect terms in logistic models may lead
to less than satisfactory results. I’ve not had any obvious
problems with this model, but is this most folks experience? Are there more
appropriate priors than those I’ve chosen?
Many thanks
Charles DiMaggio
model
# likelihood for observed data
{ for( i in 1 : Nobs ) {
y[i] ~ dbern(p[i])
logit(p[i]) <- alpha0
+ alpha1 * exp[i] + alpha2 * sex[i] + alpha3*age[i]
alpha4*race[i] +
alpha5*married[i] + alpha6*educ[i]
+ b[cty[i]] # county
term for random
effects
}
for (j in 1:Ncty){
b[j] ~ dnorm(0.0,tau.b)
}
# priors for coefficients
for (k in 1:6)
# prior for random effects term
tau.b ~ dgamma(0.001,0.001)
# variance random effect term
sigma2.b <- 1 / tau.b
}