Hi All,
I'm trying to fit a finite mixture of multinomial logit model in WinBUGS.
The model looks like the following.
Assume S mixture components with mixing proportions pi_1, ... , pi_S. There
are K categories in the multinomial distribution. The conditional
distribution of Y is f_s(Y=k) = exp(a_sk)/sum_{k'=1}^K exp(a_sk'). a_sk can
be a function of covariates.
The problem I'm encountering is that the estimation never converges. I
suspect that nonconvergence is due to label switching. But I did enforce
identification restrictions. Below are the two methods I tried.
1. Imposing an order restriction on mixing proportions pi_1, ... , pi_S.
Instead of giving pi_1, ... , pi_S a Dirichlet prior, I model them as
multinomial logit too. pi_s = exp(b_s)/sum_{s'=1}^S exp(b_s'), b_1 = 0 for
identification purposes. {b_s, s=2,...,S} are given normal priors. The
order restriction is implemented through b_1 <= b_2 <= ... <= b_S.
2. Imposing an order restriction on {a_sk, s=1, ..., S}. {a_sk} are given
normal priors and a_11 <= a_21 <= ... <= a_S1.
These two mothods didn't work. I don't understand why.
Any advice would be highly appreciated.
Regards,
Yuanping
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