Analysis of Latent Structure Models with Multidimensional Latent Variables
A. P. Dunmur, D. Michael Titterington · 2000
Abstract Within the total interface between statistics and neural computing, we shall concentrate in this chapter on the particular area of latent structure models, which has attracted considerable recent interest in the neural-computation literature. We shall review this activity and attempt to relate it to the statistical literature. There are new slants, especially in the form of new models and new computational ideas. The plan of the chapter is as follows. In Section 1 we outline the general framework of latent structure models, following this in Section 2 with statements of the structures associated with latent trait, latent profile and latent class models, with particular emphasis on the case of multidimensional latent variables. Section 3 discusses maximum likelihood estimation of the parameters in the models, using the EM algorithm, and identifies a problem of computational complexity in the E-step. Section 4 describes how so-called mean-field approximations have been developed in response to this difficulty. Bayesian approaches are described in Section 5, implemented mainly using versions of the Gibbs sampler.