UC Davis

Measurement invariance (MI) is an important assumption in testing group-mean differences. MI describes the conditions where the measurement model of a latent construct is equivalent across different groups. Despite the importance of establishing full MI, it is unrealistic to fulfill all levels of MI (i.e., pattern, weak, strong, strict) in the real world. Alternatively, researchers may choose to fit partially invariant models. Yet, this popular approach requires the exact identification of non-invariance and leaves the question open about which model fitting strategies should be selected. Thus, the current dissertation seeks to answer two related questions via simulation studies: (1) How to use sparse Bayesian estimation methods (i.e., the Horseshoe prior) for detecting non-invariant items; (2) Can we improve the predictive performance of partially invariant models using the horseshoe (HS) prior? The first study aims to demonstrate how to use the HS prior for detecting non-invariant items. I discuss how to approach the identification of non-invariant items as a variable selection problem and I describe how to identify non-invariant items within a Bayesian framework relying on the HS prior used in Bayesian model selection. A simulation study is introduced to investigate the performance of the HS priors in identifying non-invariant items under various conditions. The simulation conditions include sample size, parameter difference, scale length, and item reliability. The results showed that the HS prior approach almost always accurately identified non-invariant items. A large sample size and a high item-reliability can facilitate the identification of non-invariant items even when the amount of non-invariance was small. For identifying invariant items, the HS prior approach exhibited an almost perfect performance. The second study seeks to improve the predictive performance of partially invariant models. Common model solutions for partially invariant models usually focus on explaining the underlying mechanism of psychological phenomena. Current approaches may not generalize well to new and unseen data since MI is only considering the characteristics of the current sample at hand. Recently, the field has seen an increase in the interest in evaluating psychological assessments based on out-of-sample performance. Here, I evaluate an out-of-sample prediction-focused strategy based on partially invariant items. I employed a HS prior model to mimic the idea of Bayesian-Model-Averaging for improving the predictive performance of partially invariant models. The results of a simulation study indicated that the HS prior model outperformed the other commonly used model fitting strategies (i.e., fully constrained model, partially constrained model, freely estimated model) under most conditions. Sample size, parameter differences and item-reliability showed differential impacts on models’ predictive performance. The third study illustrated with an example how to use the HS prior approach for empirical analyses. First, the DERS-9 scale was assessed for item-level MI between genders and between two measurement occasions with a sample of 300 for each group. Next, a partially invariant SEM model was fitted with a sample of 728 college students, where the partially invariant status of the self-esteem scale between genders was confirmed, and then the HS prior model and the freely estimated model were fitted for comparison where peer victimization was regressed on self-esteem between genders. The results indicated that the HS prior performed well in terms of predictions with empirical data. In conclusion, this dissertation discussed and explored potential solutions of two major issues with measurement invariance: non-invariant item detections, and the predictive performance of partially invariant models. The results of two simulation studies indicated that the HS prior approach is a viable alternative to traditional methods for identifying non-invariant items and fitting partially invariant models. Finally, the implications and limitations of this set of studies, along with recommendations for future studies were discussed.