Representing sources of error in the common-factor model: Implications for theory and practice.

In the traditional presentation of the common-factor model, measured variables are represented as exact linear combinations of common and unique factors. From the perspective that no mathematical model will fit real-world phenomena perfectly, it is suggested that this representation is problematic. It is not consistent with the phenomena it is intended to model, and it does not provide an adequate basis for understanding some issues inherent in factor analysis. An alternative representation of the model that incorporates a «lack-of-fit» term into the initial equation for the measured variables is proposed. Subsequent derivation of the covariance form of the model in the population and the sample yields a framework that alloys for differentiation of various sources of error that arise in applications of the model. These developments provide a basis for study of some important issues such as model definition, parameter estimation, and sample size