Accommodating and Extending Various Models for Special Effects Within the Generalized Partially Confirmatory Factor Analysis Framework

Special measurement effects including the method and testlet effects are common issues in educational and psychological measurement. They are typically covered by various bifactor models or models for the multiple traits multiple methods (MTMM) structure for continuous data and by various testlet effect models for categorical data. However, existing models have some limitations in accommodating different type of effects. With slight modification, the generalized partially confirmatory factor analysis (GPCFA) framework can flexibly accommodate special effects for continuous and categorical cases with added benefits. Various bifactor, MTMM and testlet effect models can be linked to different variants of the revised GPCFA model. Compared to existing approaches, GPCFA offers multidimensionality for both the general and effect factors (or traits) and can address local dependence, mixed-type formats, and missingness jointly. Moreover, the partially confirmatory approach allows for regularization of the loading patterns, resulting in a simpler structure in both the general and special parts. We also provide a subroutine to compute the equivalent effect size. Simulation studies and real-data examples are used to demonstrate the performance and usefulness of the proposed approach under different situations.