Common, Specific, and Error Variance Components of Factor Models

Abstract

In the classic factor-analysis model, the total variance of an item is decomposed into common, specific, and random error components. Since with cross-sectional data it is not possible to estimate the specific variance component, specific and random error variance are summed to the item's uniqueness. This procedure imposes a downward bias to item reliability estimates, however, and results in correlated item uniqueness in longitudinal models. In this article, we describe a method for estimating common, specific, and random error variance with longitudinal data. An empirical example demonstrates the specification and testing of hypotheses regarding the temporal invariance of common, specific, and error components, and the practical utility of our approach. This example makes clear the limitations of combining specific and random error components. The assumption that all unique variance is random error is shown to be untenable.