MAXIMUM LIKELIHOOD ESTIMATION IN A LATENT VARIABLE PROBLEM

Abstract

This chapter discusses the maximum likelihood estimation in a latent variable problem. Latent variates are random variables, which cannot be measured directly, but play essential roles in the description of observable quantities. They occur in a broad range of statistical problems. In the case that the dependent variate y is discrete, latent structure models play an important role, arising in connection with ability tests. Computing uniform residuals is an effective general means to proceed in latent variable problems. In some cases, the subject's ability can be eliminated by conditioning on an appropriate statistic. Maximum likelihood estimation is a viable approach to a broad class of latent variable problems. Generalized linear interactive modeling (GLIM) is an effective tool for carrying out the needed computations. GLIM also contains a high-level syntax for handling variables with factorial structure, vectors, and nonfull rank models. Its powerful directives shorten the length of the program considerably and allow simple simulation of the whole situation for checking programs and logic.