A general solution for the latent class model of latent structure analysis

Abstract

For the point distribution model of Lazarsfeld's latent structure analysis, the general matrix equation is stated which relates the manifest data in the form of joint occurrence matrices to the latent parameters. The relationship of the item responses and these joint occurrence matrices is also indicated in matrix form. A general solution for the latent parameters is then presented, which is based on the notion of factoring two joint occurrence matrices. The solution is valid under certain conditions which will usually be fulfilled. The solution assumes that estimates are available for the elements in the joint occurrence matrices with recurring subscripts, analogous to item communality or reliability. Some alternative methods of obtaining these estimates are discussed. Finally a fictitious 3-class, 8-item example is presented in detail.