Taking the Error Term of the Factor Model Into Account

Abstract

The problem of factor score indeterminacy implies that the factor and the error scores cannot be completely disentangled in the factor model. It is therefore proposed to compute Harman’s factor score predictor that contains an additive combination of factor and error variance. This additive combination is discussed in the framework of classical test theory. On this basis, a definition of reliability, standard error of measurement, and confidence intervals for the factor score predictor are proposed. It is argued that factor score predictor intervals should be used instead of single score predictors to account for the error term in the factor model. The calculation of reliabilities and factor score predictor intervals is illustrated by means of a small simulation study and an empirical example.