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Application of a Hierarchical Model Incorporating Intrafamily Correlation and Cluster Effects

Cheng, An-Lin; Kelly, Patricia J.

doi: 10.1097/NNR.0b013e31820a3dbe

Background: Research interventions at the family level often include individual- and group-level data that can present an analytic challenge. The study that motivated this article was an intervention study conducted with elementary school children and their parents. Randomization occurred at the school level, with families nested within schools. Repeated measurements collected from children and parents at different time points presented modeling challenges, including how to specify the covariance structure correctly among all measurements.

Objectives: The aim of this study was to introduce a mixed model with random effects to model the correlations among family members, repeated measures, and the grouping effect.

Methods: A hierarchical random-effect model was used that included both fixed and random effects; time and intervention-by-time variables were included as fixed effects, the school-specific variable was included as random effect, and the intrafamily correlation was modeled through a spatial autoregression covariance matrix. Comparisons were made between the performance of the proposed modeling method and that of other parsimony models using Akaike's Information Criterion (AIC).

Results: The proposed modeling method produced a 3% and 9% reduction in AIC values, respectively, compared with the two other models. The likelihood ratio test further confirmed that the full model was better than the other two models (p < .0001 for both models).

Discussion: The data suggest that using the proposed mixed model technique will produce a significantly better model fit for intrafamily correlation with a nested study design.

An-Lin Cheng, PhD, is Assistant Professor; and Patricia J. Kelly, PhD, MPH, APRN, is Professor, School of Nursing, University of Missouri-Kansas City.

Accepted for publication December 6, 2010.

Funding for this work was received from the National Institute of Health, National Institute of Nursing Research (Grant R01NR8565-4).

Corresponding author: An-Lin Cheng, PhD, University of Missouri-Kansas City School of Nursing, 2464 Charlotte Street, Kansas City, MO 64108 (e-mail:

© 2011 Lippincott Williams & Wilkins, Inc.