Platonic and Operational True Scores in Covariance Structure Analysis

Abstract

Bielby (1986) argues that conventional practices for normalizing latent variable models can lead the applied researcher astray. He presents two examples to show how this may occur. In the first example, he considers the regression of income on education. In the second, he considers a panel model of attitude stability. He concludes that “explicit calibration of measurements” is as critical in sociological work as it is in the physical sciences. The primary purpose of this note is to distinguish between Platonic and operational true scores, to discuss the implications of this distinction in factor analysis, and to show how external information can be brought to bear on some of the problems raised by Bielby. Specifically, we show how external information can be incorporated into a covariance structure model to identify and estimate the parameters of the structural model linking education and income. Secondarily, we briefly discuss Bielby's panel model of attitude stability. Bielby tends to treat this example as if the true scores of interest are conceptually the same as those in the education-income example. If this is the case, he is arguing for a Platonic conception of attitude, an argument he should explicitly acknowledge and make, because this is not the usual conception of attitude in empirical research. If this is not the case, however, Bielby's example is not convincing.