Dear BUGS users,
I would like to share my modelling problem in WinBUGS. The model is the
"unbalanced and unequally-spaced" panel data model with serially
correlated errors, especially with first-order autocorrelation errors.
The term "unbalanced and unequally-spaced" means that for each
individual in panel data, the number of observations is different and
also observations are missing (on both dependent and independent
variables) in different time.
For simplicity, the problem can be regarded as modelling a linear
y[i] = x[i]*beta + u[i] with u[i] = rho*u[i-1] + e[i], -1<rho<1, e
~ N(0, 1).
When "equally-spaced" case (that is, without missing observations), its
modelling is straightforward: the usual steps are (1) to make the error
terms uncorrelated as well as homoscedastic and then (2) the
distribution of y can be modeled as follows:
y[i] ~ dnorm (mu[i], tau)
mu[i] <- rho*y[i-1] + beta*x[i] – rho*beta*x[i-1]
A Difficulty seems to be in modelling when observations are missing. One
possibility seems to apply the steps in "equally-spaced" case. It,
however, does not work in WinBUGS. The reason is that after making the
error terms uncorrelated and homoscedastic, the distribution of y itself
is not possible. Instead the likelihood can be expressed for only a
function of y with parameter rho estimated, which implies that modelling
needs "data transformation with parameter". As mentioned in WinBUGS user
guide, however, it is not possible within WinBUGS framework.
I am looking for other possible modelling methods within WinBUGS. I
would greatly appreciate any comment.
Department of Economics
SUNY at Stony Brook
Stony Brook, NY 11794-4384
Phone: (631) 807-9033
e-mail: [log in to unmask]
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