Extending the trait-state-occasion model: How important is within-wave measurement equivalence?

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.