  Statistical latent class models are widely used in social and psychological
researches, yet it is often difficult to establish the identifiability of the
model parameters. In this paper we consider the identifiability issue of a
family of restricted latent class models, where the restriction structures are
needed to reflect pre-specified assumptions on the related assessment. We
establish the identifiability results in the strict sense and specify which
types of restriction structure would give the identifiability of the model
parameters. The results not only guarantee the validity of many of the
popularly used models, but also provide a guideline for the related
experimental design, where in the current applications the design is usually
experience based and identifiability is not guaranteed. Theoretically, we
develop a new technique to establish the identifiability result, which may be
extended to other restricted latent class models.
