title: Application of a hierarchical model incorporating intrafamily correlation and cluster effects.
abstract: 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.
  
  
  OBJECTIVE
  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).
  
  
  CONCLUSIONS
  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.
authors.affiliation: School of Nursing, University of Missouri-Kansas City, MO 64108, USA. chenga@umkc.edu
authors.forename: An-Lin
authors.initials: AL
authors.lastname: Cheng
authors.forename: Patricia J
authors.initials: PJ
authors.lastname: Kelly
mesh_terms: D002648:Child; D006801:Humans; D016013:Likelihood Functions; D016294:Models, Nursing; D015233:Models, Statistical; D010290:Parents; D016032:Randomized Controlled Trials as Topic