Latent Factor Models for Large-scale Data
Latent factor models are widely used to measure unobserved latent traits in social and behavioral sciences, including psychology, education, and marketing. Motivated by the applications of latent factor models to large-scale measurements which consist of many manifest variables (e.g. test items) and a large sample size, we study the properties of latent factor models under an asymptotic setting where both the number of manifest variables and the sample size grows to infinity. In this talk, I will introduce generalized latent factor models under exploratory and confirmatory settings. For the exploratory setting, we propose a constrained joint maximum likelihood approach for model estimation and investigate its theoretical properties. For the confirmatory setting, we study how the design information affects the identifiability and estimability of the model, and propose a rate-optimal estimator when the model is identifiable. The estimators can be efficiently computed through parallel computing. Our results provide insights on the design of large-scale measurement and have important implications on measurement validity.