  In this paper, we propose a general framework for combining evidence of
varying quality to estimate underlying binary latent variables in the presence
of restrictions imposed to respect the scientific context. The resulting
algorithms cluster the multivariate binary data in a manner partly guided by
prior knowledge. The primary model assumptions are that 1) subjects belong to
classes defined by unobserved binary states, such as the true presence or
absence of pathogens in epidemiology, or of antibodies in medicine, or the
"ability" to correctly answer test questions in psychology, 2) a binary design
matrix $\Gamma$ specifies relevant features in each class, and 3) measurements
are independent given the latent class but can have different error rates.
Conditions ensuring parameter identifiability from the likelihood function are
discussed and inform the design of a novel posterior inference algorithm that
simultaneously estimates the number of clusters, design matrix $\Gamma$, and
model parameters. In finite samples and dimensions, we propose prior
assumptions so that the posterior distribution of the number of clusters and
the patterns of latent states tend to concentrate on smaller values and sparser
patterns, respectively. The model readily extends to studies where some
subjects' latent classes are known or important prior knowledge about
differential measurement accuracy is available from external sources. The
methods are illustrated with an analysis of protein data to detect clusters
representing auto-antibody classes among scleroderma patients.
