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Centering lower-level interactions in multilevel models

(2017)
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Abstract
In hierarchical designs, the effect of a lower level predictor on an outcome may oftentimes be confounded by an (un)measured upper level variable. When such confounding is left unaddressed, the effect of the lower level predictor will be estimated with bias. As to remove any such bias in a linear random intercept model, researchers often separate the lower level effect into a within- and between-component (under a specific set of confounding-assumptions). When the effect of the lower level predictor is additionally moderated by another lower level predictor, an interaction between both predictors needs to be included into the model. To again address any possible unmeasured upper level confounding, this interaction term also requires partitioning into a within- and between- cluster component. This can be achieved by first multiplying both predictors and to consequently centering that product term, or vice versa. We demonstrate that the former centering approach proves much more efficient and robust against misspecification of cross- and upper-level effects, compared to the latter.
Keywords
Centering, Interactions, Multilevel data, Confounding

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Please use this url to cite or link to this publication:

MLA
Josephy, Haeike, and Tom Loeys. Centering Lower-Level Interactions in Multilevel Models. 2017.
APA
Josephy, H., & Loeys, T. (2017). Centering lower-level interactions in multilevel models. Presented at the International Meetings of the Psychometric Society 2017, Zürich.
Chicago author-date
Josephy, Haeike, and Tom Loeys. 2017. “Centering Lower-Level Interactions in Multilevel Models.” In . Zürich.
Chicago author-date (all authors)
Josephy, Haeike, and Tom Loeys. 2017. “Centering Lower-Level Interactions in Multilevel Models.” In . Zürich.
Vancouver
1.
Josephy H, Loeys T. Centering lower-level interactions in multilevel models. In Zürich; 2017.
IEEE
[1]
H. Josephy and T. Loeys, “Centering lower-level interactions in multilevel models,” presented at the International Meetings of the Psychometric Society 2017, University of Zürich, Switzerland, 2017.
@inproceedings{8544394,
  abstract     = {{In hierarchical designs, the effect of a lower level predictor on an outcome may oftentimes be confounded by an (un)measured upper level variable. When such confounding is left unaddressed, the effect of the lower level predictor will be estimated with bias. As to remove any such bias in a linear random intercept model, researchers often separate the lower level effect into a within- and between-component (under a specific set of confounding-assumptions). When the effect of the lower level predictor is additionally moderated by another lower level predictor, an interaction between both predictors needs to be included into the model. To again address any possible unmeasured upper level confounding, this interaction term also requires partitioning into a within- and between- cluster component. This can be achieved by first multiplying both predictors and to consequently centering that product term, or vice versa. We demonstrate that the former centering approach proves much more efficient and robust against misspecification of cross- and upper-level effects, compared to the latter.}},
  author       = {{Josephy, Haeike and Loeys, Tom}},
  keywords     = {{Centering,Interactions,Multilevel data,Confounding}},
  language     = {{eng}},
  location     = {{University of Zürich, Switzerland}},
  pages        = {{39}},
  title        = {{Centering lower-level interactions in multilevel models}},
  year         = {{2017}},
}