ABSTRACT
If the errors are small enough to be ignored, we can take S=? ? '. From this point of view factor analysis is outwardly similar to finding the principal components of S since both procedures start with a linear model and end up with matrix factorization. However, the model for principal component analysis must be linear by the very fact that it refers to a rigid rotation of the original coordinate axes, whereas in the factor analysis model the linearity is as much a part of our hypothesis about the dependence structure as the choice of exactly m common factors. The linear model in factor analysis allows us to interpret ?ij as correlation coefficients but if the covariances reproduced by the m-factor linear model fail to fit the linear model adequately, it is as proper to reject linearity as to advance the more usual finding that m common factors are inadequate to explain the correlation structure.
