  As a generalization of the classical linear factor model, generalized latent
factor models are useful for analyzing multivariate data of different types,
including binary choices and counts. This paper proposes an information
criterion to determine the number of factors in generalized latent factor
models. The consistency of the proposed information criterion is established
under a high-dimensional setting where both the sample size and the number of
manifest variables grow to infinity, and data may have many missing values. An
error bound is established for the parameter estimates, which plays an
important role in establishing the consistency of the proposed information
criterion. This error bound improves several existing results and may be of
independent theoretical interest. We evaluate the proposed method by a
simulation study and an application to Eysenck's personality questionnaire.
