Extending the Trait?State?Occasion Model: How Important Is Within-Wave Measurement Equivalence?

Abstract

Trait-State-Occasion (TSO) covariance models represent an important advance in methods for studying the longitudinal stability of latent constructs. Such models have only been examined under fairly restricted conditions (e.g., having only 2 tau-equivalent indicators per wave). In this study, Monte Carlo simulations revealed the effects of having 2 versus 3 indicators per wave and relaxing the within-wave tau equivalence. These modifications were examined under conditions that varied with regard to the within-wave trait variance and the cross-wave stability of occasion influences. In general, the TSO model performed well (i.e., few convergence problems or out-of-range parameter estimates) under most of these conditions; however, the likelihood of improper solutions increased when only 2 indicators were used per wave, when factor loadings were small, when the proportion of trait variance was either very high or very low, and when the occasion factor was highly stable. Based on these findings, recommendations are made for successful use of TSO models with real data.The relative consistency or stability of individual differences is an important concern in the behavioral sciences, particularly in longitudinal research. The degree to which a construct changes or remains stable over time may provide important clues about its causes, correlates, and effects. Information regarding the stability of a construct can also inform decisions about research design (Cole, 2006) and statistical methodology (Collins & Sayer, 2001). Cole, Martin, and Steiger (2005) recently introduced the Trait-State-Occasion (TSO) model for STRUCTURAL EQUATION MODELING, 14(1),

Gender differences in the longitudinal structure of cognitive diatheses for depression in children and adolescents

“…To examine the longitudinal structure of positive and negative cognitions, we used confirmatory factor analysis to test a series of trait-state-occasion models (Ciesla et al, 2007; Cole et al, 1005; Lagrange & Cole, 2008). The general form of this model is depicted in Figure 3.…”

“…They also differ with regard to the assumptions they make about the underlying pattern of covariances. In a series of articles, Cole and colleagues show that their model has a lower rate of problematic solutions, makes fewer assumptions about the underlying covariances, and can be expanded to accommodate complex multi-method designs (Ciesla, Cole, & Steiger, 2007; Cole et al, 2005; LaGrange & Cole, 2008). In the current article, we applied Cole et al’s method to a four-wave, two-cohort data set containing repeated measures of both the CTI-C and the SPPC.…”

Distinguishing state variability from trait change in longitudinal data: The role of measurement (non)invariance in latent state-trait analyses

“…We recommend that researchers include at least three indicators in their analyses and collect data for the same indicators on four or more time points (Ciesla et al, 2007). Such larger designs allow for more powerful tests of the assumption that the process under investigation is a pure state-variability (state-trait) process.…”

“…Even though several methodological papers discussed MI in the context of LST models (Alessandri, Caprara, & Tisak, 2012; Baumgartner & Steenkamp, 2006; Ciesla, Cole, & Steiger, 2007; Tisak & Tisak, 2000), most methodological work in this area has not explicitly addressed whether MI is at all relevant to LST analyses and what the consequences of measurement non-invariance might be. Although Baumgartner and Steenkamp (2006) advocated a model-building procedure for establishing MI based on the item loadings and intercepts, in which loadings and intercepts are systematically released from invariance (see also Alessandri et al, 2012), they did not specifically discuss the relevance of these issues to LST analyses or for the separation of state-variability from trait-change processes.…”

Fighting for Intelligence: A Brief Overview of the Academic Work of John L. Horn

“…This computer-simulation approach has certainly increased in popularity in psychometric and statistical research, and of course Horn was not alone in understanding these topics (e.g., Ciesla, Cole, & Steiger, 2007; L. K. Muthén & Muthén, 2005).…”