Factor analysis is a statistical technique that explains correlations among observed random variables with the help of a smaller number of unobserved factors. In traditional full-factor analysis, each observed variable is influenced by every factor. However, many applications exhibit interesting sparsity patterns, that is, each observed variable only depends on a subset of the factors. In this talk, we will discuss parameter identifiability of sparse factor analysis models. In particular, we present a sufficient condition for parameter identifiability that generalizes the well-known Anderson-Rubin condition and is tailored to the sparse setup. This is joint work with Mathias Drton, Miriam Kranzlmüller, and Irem Portakal.