Using a Few Snapshots to Distinguish Mountains from Waves: Weak Factorial Invariance in the Context of Trait-State Research

Abstract

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.

A Review of Current Ambulatory Assessment Studies in Adolescent Samples and Practical Recommendations

“…Relatedly, more work needs to be done on how best to assess reliability and validity for measures that are used in intensive longitudinal designs. For instance, tools are needed that allow researchers to control for and deal with different sources of measurement error, including the person and the occasion (e.g., Hamaker, Schuurman, & Zijlmans, ; Vogelsmeier, Vermunt, Van Roekel, & De Roover, ). A strong alliance between methodologists and applied researchers may be a fruitful approach, allowing methodologists to invest their time in developing techniques that can aid the advancement of psychological theories, and applied researchers to learn and apply the most innovative methods before they are implemented in standard software.…”

The Factor Structure of Big Five Personality Trait Measures at the Between- and Within-Person Levels

“…A limitation of the current work is that I did not investigate individual differences in within-person factor structures. The obtained within-person factor structures reflect an average across individuals (Hamaker et al, 2017). The natural next steps would be to probe for idiosyncrasies in the within-person structures and to test for factorial invariance across individuals.…”

“…Yet, like any cross-sectional data analysis, cross-sectional factor analysis is unable to partition the variance into (a) time-invariant between-person variation and (b) within-person variation over time (e.g., Borsboom, Mellenbergh, & van Heerden, 2003;Cattell, 1955;Hamaker, Schuurman & Zijlmans, 2017;Molenaar, 2004). The cross-sectional factor structure is a weighted blend of the between-and within-person factor structures (Hamaker et al, 2017). Hence, it is unclear whether the common factor structure found in cross-sectional factor analyses holds on the between-person level, on the within-person level, on both levels, or on neither of them.…”

“…Hence, it is unclear whether the common factor structure found in cross-sectional factor analyses holds on the between-person level, on the within-person level, on both levels, or on neither of them. For example, a longitudinal data analysis of the Social Provision Scale suggested that the between-person variance of the scale is characterized by one common factor, whereas the within-person variance of the scale is characterized by two common factors (Hamaker et al, 2017). Similarly, the common factor structure of the Big Five scales might differ across the two levels.…”

“…To investigate whether the Big Five factor structure would hold on the between-and within-person levels, I used the common and unique trait-state (CUTS) model (Hamaker et al, 2017). The CUTS model decomposes the variance in item response behavior into four parts: (a) time-invariant variance that is common to more than one item, called common trait variance, (b) time-invariant variance that is common to only one item, called unique trait variance (see also personality nuances or method effects; e.g., Mõttus, Kandler, Bleidorn, Riemann, & McCrae, 2017;Geiser & Lockhart, 2012), (c) time-varying variance that is common to more than one item, called common state variance, and (d) time-varying variance that is common to only one item, called unique state variance.…”