The name is absent

multinomial logit model are popular model choices for implementing regression for
categorical outcomes. However, the computational burden associated with imple-
menting full posterior inference hinders the routine application of these models in
applied work. In recent years, there have been some advances using classical and
Bayesian approaches. In particular, the method of simulated moments by McFad-
den (1989), and Gibbs sampling with data augmentation as discussed in Albert and
Chib (1993) and McCulloch and Rossi (1994), have made the required computations
in the multinomial probit model more practical.

For inference with ordinal data, many authors have proposed methods in a clas-
sical (McCullagh, 1980) and Bayesian (Albert and Chib, 1993; Doss, 1994; Cowles,
1996) framework. A natural way to model ordinal data is to introduce an underlying
continuous latent variable. The ordinal outcome is linked with the latent variable
through a set of cutpoints. The probability of an ordinal outcome is represented by
the probability that this latent continuous variable falls within a given interval de-
fined by the cutpoints. The ordinal probit model is characterized by the assumption
that this latent variable follows a normal distribution.

Albert and Chib (1993) proposed Bayesian inference for the ordinal probit re-
gression parameters. The model includes a diffuse prior on the cutpoint parameters.
Cowles (1996) proposed improved posterior simulation with a hybrid Gibbs/Metropolis-
Hastings sampling scheme which updates the cutpoint parameters jointly with the
other parameters. This approach reduces the high auto-correlation and achieves prac-
tical convergence within a reasonable number of iterations of the MCMC simulation.

We propose a mixture model which can model ordinal data without the need to
estimate cutpoint parameters. We show that in the proposed mixture model, the
cutpoints can be fixed without loss of generality. While standard ordinal models
assume that the regression lines which characterize the ordinal outcomes are parallel
(thus leading to the proportional odds assumption when using a logistic link), our
model is flexible in the sense that it is able to fit data when this parallel regressions

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