Programs

Factor Analysis - Peking University

This program delves into Factor Analysis, a statistical method originating from early work on intelligence measurement. Its primary goal, similar to Principal Component Analysis, is to reduce the dimensionality of data by compressing information from multiple variables into a smaller set of derived variables called 'factors'. These factors are designed to represent underlying structures and group original variables, aiming for a more parsimonious and interpretable model. The course explores both R-type factor analysis, which reduces the number of variables while keeping observations constant, and Q-type factor analysis, which reduces the number of observations while preserving the variables. The curriculum covers the theoretical underpinnings of factor analysis, including the orthogonal factor model, its mathematical formulation, assumptions, and the interpretation of its components. Students will learn about factor loadings, commonalities, unique variances, and how these relate to the covariance structure of the observed variables. The program also examines the relationship between factor analysis and linear models, highlighting key differences in their coefficients and the nature of latent variables. Further modules address the estimation of factor models, including methods like Principal Component Method and Maximum Likelihood Estimation. Students will gain insights into the process of identifying and estimating factor loadings and unique variances, as well as techniques for rotating factors to achieve more meaningful interpretations. The course also draws comparisons with Principal Component Analysis, distinguishing their objectives, interpretations, and mathematical properties.