  Factor models are widely used across diverse areas of application for
purposes that include dimensionality reduction, covariance estimation, and
feature engineering. Traditional factor models can be seen as an instance of
linear embedding methods that project multivariate observations onto a lower
dimensional Euclidean latent space. This paper discusses a new class of
geometric embedding models for multivariate binary data in which the embedding
space correspond to a spherical manifold, with potentially unknown dimension.
The resulting models include traditional factor models as a special case, but
provide additional flexibility. Furthermore, unlike other techniques for
geometric embedding, the models are easy to interpret, and the uncertainty
associated with the latent features can be properly quantified. These
advantages are illustrated using both simulation studies and real data on
voting records from the U.S. Senate.
