This paper by T. W. Anderson and Herman Rubin discusses methods and mathematical problems related to factor analysis, focusing on a general probability model. The authors aim to provide a unified exposition of factor analysis from a mathematical statistician's perspective, addressing issues such as model existence, identification, determination of the structure, parameter estimation, hypothesis testing, and the determination of the number of factors. They explore the conditions under which the model can generate a given covariance matrix and the conditions necessary for unique identification of the model parameters. The paper also delves into various restrictions on the factor loadings that can help in identifying the model and determining the structure. Additionally, it discusses methods for solving the model given the population data and provides conditions for local identification. The authors emphasize the importance of these theoretical considerations for practical applications in statistics and psychology.This paper by T. W. Anderson and Herman Rubin discusses methods and mathematical problems related to factor analysis, focusing on a general probability model. The authors aim to provide a unified exposition of factor analysis from a mathematical statistician's perspective, addressing issues such as model existence, identification, determination of the structure, parameter estimation, hypothesis testing, and the determination of the number of factors. They explore the conditions under which the model can generate a given covariance matrix and the conditions necessary for unique identification of the model parameters. The paper also delves into various restrictions on the factor loadings that can help in identifying the model and determining the structure. Additionally, it discusses methods for solving the model given the population data and provides conditions for local identification. The authors emphasize the importance of these theoretical considerations for practical applications in statistics and psychology.