Determining the Number of Factors in High-dimensional Generalised Latent Factor Models
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As a generalisation of the classical linear factor model, generalised latent factor models are a useful tool for analysing multivariate data of different types, including binary choices and counts. In this paper, we propose an information criterion to determine the number of factors in generalised 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. To establish this consistency result, an error bound is established for the parameter estimates that improves the existing results and may be of independent theoretical interest. Simulation shows that the proposed criterion has good finite sample performance. An application to Eysenck's personality questionnaire confirms the three-factor structure of this personality survey.
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