Matrix-variate data analysis by two-way factor model with replicated observations

Motivated by recent work on matrix-variate data analysis in various scientific domains, we propose a two-way factor model (2wFMs) to capture the separable effects of row and column attributes. This paper studies the identification conditions of 2wFMs and develops a block alternative optimization algorithm for maximum likelihood estimation (MLE). The asymptotic theories for the maximum likelihood estimators are established. Monte Carlo simulations show that the method we propose is effective and robust.