Application of a Latent Trait Modeling Method for Missing Data Across Datasets: Guidance on Appropriate Factor Structure

Latent trait space can be leveraged to harmonize small data into big data when the constituent datasets measure the same underlying (latent) domains using a set of partially overlapping measurement instruments in each domain. The latent trait space then acts as a common metric space for each dataset, thus ensuring the same scale for the latent traits across datasets, despite the use of non-identical sets of measurement instruments within datasets. This approach, as originally published, only applied to a narrow set of circumstances, namely, that each measurement instrument occurred in more than one dataset. Here, we extend the latent trait approach to drop this requirement by using matrix completion methods. Using a simulation study, we evaluate the reliability of this extension and offer guidance on circumstances when the latent trait approach to missing data is robust and practical on real datasets.