on the above argument, we have that for each j , as the sample size n → ∞ . Hence, the estimation of equivalence classes is the same as the true one up to a permutation. We now present the sliced sampler for the simulation from the posterior distribution of model (7), (8), and (9). The likelihood function is For each observation, we augment an independent index u$_{i}$ following the uniform distribution in [0 , 1]. Thus, the complete data likelihood is With this augmentation scheme, a Gibbs sampler iterates according the following conditional dis- tributions. A Sliced sampler for latent class model P ( 〈 α 〉 j = [ α ]$_{j}$) → 1 n ∏ i =1 { ∞ ∑ α =1 π α J ∏ j =1 k$_{j}$ ∏ y =1 ( p y j $_{α}$) I ( y$_{ij}$ = y ) } . L ( p , π ; y$_{1}$ , ..., y$_{n}$ , α $_{1}$, ..., α $_{n}$, u ) = n ∏ i =1 { I ( u$_{i}$ < π α $_{i}$) J ∏ j =1 k$_{j}$ ∏ y =1 ( p y j $_{α}$) I ( y$_{ij}$ = y ) } . Dirichlet ( 1 + ∑ i : α $_{i}$= α I ( y$_{ij}$ = 1) , ..., 1 + ∑ i : α $_{i}$= α I ( y$_{ij}$ = k$_{j}$ ) 1. Update u$_{i}$ , for i = 1 , ..., n , by sampling from the conditional posterior, U (0 , π α $_{i}$). 2. For h = 1 , ..., M where M = max { α $_{1}$, ..., α n } , update p$_{j}$ α from the full conditional posterior distribution 3. For h = 1 , ..., M , update V α from the conditional distribution that is Beta(1 , β ) truncated to 41