Double instrumental variable estimation of interaction models with big data

The factor analysis of a (n,m) matrix of observations Y is based on the joint spectral decomposition of the matrix squares YY′ and Y′Y for Principal Component Analysis (PCA). For very large matrix dimensions n and m, this approach has a high level of numerical complexity. The big data feature suggests new estimation methods with a smaller degree of numerical complexity. The double Instrumental Variable (IV) approach uses row and column instruments to estimate consistently the factors via an averaging method. We compare the double IV approach to PCA in terms of numerical complexity and statistical efficiency. The double IV approach can be used for the analysis of recommender systems and provides a new collaborative filtering approach.