In this article, we show that the underlying dimensions obtained when factor analyzing cross-sectional data actually form a mix of within-person state dimensions and between-person trait dimensions. We propose a factor analytical model that distinguishes between four independent sources of variance: common trait, unique trait, common state, and unique state. We show that by testing whether there is weak factorial invariance across the trait and state factor structures, we can tackle the fundamental question first raised by Cattell; that is, are within-person state dimensions qualitatively the same as between-person trait dimensions? Furthermore, we discuss how this model is related to other trait-state factor models, and we illustrate its use with two empirical data sets. We end by discussing the implications for cross-sectional factor analysis and suggest potential future developments.
Hamaker, E. L., Schuurman, N. K., & Zijlmans, E. A. O. (2017). Using a few snapshots to distinguish mountains from waves: Weak factorial invariance in the context of trait-state research. Multivariate Behavioral Research, 52(1), 47-60. https://doi.org/10.1080/00273171.2016.1251299