Incorporating Mobility in Growth Modeling for Multilevel and Longitudinal Item Response Data

ABSTRACT

Multilevel data often cannot be represented by the strict form of hierarchy typically assumed in multilevel modeling. A common example is the case in which subjects change their group membership in longitudinal studies (e.g., students transfer schools; employees transition between different departments). In this study, cross-classified and multiple membership models for multilevel and longitudinal item response data (CCMM-MLIRD) are developed to incorporate such mobility, focusing on students' school change in large-scale longitudinal studies. Furthermore, we investigate the effect of incorrectly modeling school membership in the analysis of multilevel and longitudinal item response data. Two types of school mobility are described, and corresponding models are specified. Results of the simulation studies suggested that appropriate modeling of the two types of school mobility using the CCMM-MLIRD yielded good recovery of the parameters and improvement over models that did not incorporate mobility properly. In addition, the consequences of incorrectly modeling the school effects on the variance estimates of the random effects and the standard errors of the fixed effects depended upon mobility patterns and model specifications. Two sets of large-scale longitudinal data are analyzed to illustrate applications of the CCMM-MLIRD for each type of school mobility.

KEYWORDS:

• Item response theory
• longitudinal data analysis
• multilevel modeling
• school mobility

Article information

Conflict of Interest Disclosures: Each author signed a form for disclosure of potential conflicts of interest. No authors reported any financial or other conflicts of interest in relation to the work described.

Ethical Principles: The authors affirm having followed professional ethical guidelines in preparing this work. These guidelines include obtaining informed consent from human participants, maintaining ethical treatment and respect for the rights of human or animal participants, and ensuring the privacy of participants and their data, such as ensuring that individual participants cannot be identified in reported results or from publicly available original or archival data.

Funding: This work was not supported.

Role of the Funders/Sponsors: None of the funders or sponsors of this research had any role in the design and conduct of the study; collection, management, analysis, and interpretation of data; preparation, review, or approval of the manuscript; or decision to submit the manuscript for publication.

Acknowledgements: The authors thank the two anonymous reviewers and the editor for their comments on prior versions of this manuscript. The ideas and opinions expressed herein are those of the authors alone, and endorsement by the authors' institutions is not intended and should not be inferred.