Agreement on the Classification of Latent Class Membership Between Different Identification Constraint Approaches in the Mixture Rasch Model

When using the mixture Rasch model, the model identification constraints are either to set the equal means for all classes in the assumed normal ability distributions (equal ability mean constraint in short), or to set the sum of item difficulties to be zero for each class. In real data analysis, however, both constraints are not always sufficient to establish a common scale across latent classes unless some items are specified as anchor items in the estimation. If these two conventional constraint approaches recover the class membership as good as the anchor item constraint approach, the conventional constraint approaches may be considered useful for the purpose of class membership classification. This study investigated agreement on class membership between one conventional constraint (the equal ability mean) and the anchor item constraint approaches. Results showed high agreement between these two constraint approaches, indicating that the conventional constraint of the equal mean ability approach may be used to recover the latent class membership although item profiles are not correctly estimated across latent classes.