Factor analysis of multiple batteries by maximum likelihood

McDonald's (1970) generalization of Tucker's (1958) inter-battery factor analysis model to multiple batteries is considered. The identification of parameters is examined and an iterative algorithm for obtaining maximum-likelihood estimates is provided. Consideration of the relationship between inter-battery factor analysis and canonical correlation analysis in the case of two batteries suggests a generalization of canonical coefficients to the situation where there are several batteries. Examples of the application of the procedure are given.