Double Decomposition of Level-1 Variables in Multilevel Models: An Analysis of the Flynn Effect in the NSLY Data

ABSTRACT

This paper introduces an extension of cluster mean centering (also called group mean centering) for multilevel models, which we call “double decomposition (DD).” This centering method separates between-level variance, as in cluster mean centering, but also decomposes within-level variance of the same variable. This process retains the benefits of cluster mean centering but allows for context variables derived from lower level variables, other than the cluster mean, to be incorporated into the model. A brief simulation study is presented, demonstrating the potential advantage (or even necessity) for DD in certain circumstances. Several applications to multilevel analysis are discussed. Finally, an empirical demonstration examining the Flynn effect (Flynn, 1987), our motivating example, is presented. The use of DD in the analysis provides a novel method to narrow the field of plausible causal hypotheses regarding the Flynn effect, in line with suggestions by a number of researchers (Mingroni, 2014; Rodgers, 2015).

KEYWORDS:

• Centering
• Flynn effect
• multilevel modeling
• within- versus between-level variance

Article information

Conflict of interest disclosures: Each author signed a form for the 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 by a grant.

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.

Acknowledgments: The authors would like to thank Dr. Kris Preacher for a comment early in the course of this research that helped in motivating some of their thinking.

The authors would like to thank Conor Dolan, Ellen Hamaker, and Lesa Hoffman for their comments on prior versions of this manuscript. The ideas and opinions expressed herein are those of the authors alone, and the endorsement by the authors’ institution is not intended and should not be inferred.