Latent ordered class analysis

Abstract

The problem of deriving latent ordered classes is discussed in the latent structure analysis, where these classes are assumed to be ordered based on binary items which are regarded as indexes for one latent trait. Up to now, the problem of ordered classes has been discussed only as the result of interpretation of the derived latent classes in the general latent class analysis. Thus, the ordinary latent class model does not have any concepts of latent ordered classes. In this paper, the assumption of latent ordered classes or unidimensional concepts is incorporated into the model itself. Unlike the ordinary latent class model, the aim of this paper is to analyze data by the aid of a structured model. As the structured model, a logistic model is adopted and the algorithm of ML estimation for this model is constructed based on EM algorithm.