Equate groups: An innovative method to link multi-item instruments across studies

Background: Combining existing data sets for meta-analyses enables analyses across multiple contexts and conditions. However, the use of different measurement instruments in different studies hampers comparability. This paper proposes a novel method to link tools administered across multiple studies. Methods: : The proposed methodology starts by forming equate groups, i.e., sets of items from different instruments with similar meanings. We fit the Rasch model to all data, with the additional restriction that items within the same equate group obtain identical difficulty estimates. The main modelling task is to divide equate groups into active (where the restriction holds) and passive (without the restriction) groups. We studied the method's performance in a simulation study and illustrated its practical application to early childhood development. Results: : If we treat all equate groups as passive, the difficulty estimates of the identical items are unduly affected by differences in abilities between the study samples. On the other hand, when abilities are similar across samples, it is safer to set all equate groups to passive because any mis-specified equate groups can lead the restricted model to underperform. Our method deals with the common case between these two extremes where 1) we suspect a priori ability differences between samples, and 2) at least some of the items are equivalent across instruments. Conclusions: : Our equating method presents a flexible alternative to the classic common-item nonequivalent-group design for existing data. We conclude that equate groups are an economical and exciting concept that enables insightful statistical analysis from seemingly disparate data sources.