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

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 Flynn, J. R. (1987). Massive IQ gains in 14 nations: What IQ tests really measure. Psychological Bulletin, 101(2), 171. https://doi.org/10.1037/h0090408.Crossref], Web of Science ®] , Google Scholar]), 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 Mingroni, M. A. (2014). Future efforts in Flynn effect research: Balancing reductionism with holism. Journal of Intelligence, 2(4), 122. https://doi.org/10.3390/jintelligence2040122.Crossref] , Google Scholar]; Rodgers, 2015 Rodgers, J. L. (2015). Methodological issues associated with studying the Flynn effect: Exploratory and confirmatory efforts in the past, present, and future. Journal of Intelligence, 3(4), 111. https://doi.org/10.3390/jintelligence3040111. Crossref] , Google Scholar]).