The article introduces a new method called the mixture of latent trait analyzers model for clustering categorical data. This method combines a categorical latent class and a continuous latent trait variable to better capture group structures and dependencies within these groups. By using a variational approach for model fitting, the researchers applied this method to data from the National Long Term Care Survey and voting in the U.S. Congress. The results showed that the mixture of latent trait analyzers model produced more intuitive clustering results and a better fit compared to other existing methods.