Hello BUGS users!
I am having a hard time with dummy coding and representation of results.
This is rather basic, but I just can not find the solution anywhere. I
hope someone can help me with this. Here is the model I would like to fit
y_i ~ N(mu_i, sigma^2)
mu_i = intercept + beta_j + gamma_k,
where beta and gamma are two factors, each with say 3 levels. Now I
write the following model, where I use "double indexing" feature and
corner constraint i.e. "treatment contrast"
for (i in 1:N) {
y[i] ~ dnorm(mu[i], tau2)
mu[i] <- alpha + beta[b[i]] + gamma[g[i]]
}
alpha ~ dunif(-100, 100)
beta[1] <- 0 # corner constraint
beta[2] ~ dunif(-100, 100)
beta[3] ~ dunif(-100, 100)
gamma[1] <- 0 # corner constraint
gamma[2] ~ dunif(-100, 100)
gamma[3] ~ dunif(-100, 100)
After compiling and running I get the following coefficients in result
alpha, beta[2], beta[3], gamma[2] and gamma[3]
and if I am right the meaning of coefficients is
alpha = intercept + beta[1] + gamma[1]
beta[2] = alpha - beta[2]
...
However, for presentation of results I would like to get "true" beta
coefficients i.e. beta_j "marginal" to gamma_k - LSM (Least Square
Means) in SAS parlance. How can I construct these quantities in BUGS?
--
Lep pozdrav / With regards,
Gregor Gorjanc
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University of Ljubljana PhD student
Biotechnical Faculty
Zootechnical Department URI: http://www.bfro.uni-lj.si/MR/ggorjan
Groblje 3 mail: gregor.gorjanc <at> bfro.uni-lj.si
SI-1230 Domzale tel: +386 (0)1 72 17 861
Slovenia, Europe fax: +386 (0)1 72 17 888
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"One must learn by doing the thing; for though you think you know it,
you have no certainty until you try." Sophocles ~ 450 B.C.
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