, Volume 75, Issue 3, pp 347–365 | Cite as

On the detectability of different forms of interaction in regression models

  • Juxin LiuEmail author
  • Paul Gustafson


We consider the ability to detect interaction structure from data in a regression context. We derive an asymptotic power function for a likelihood-based test for interaction in a regression model, with possibly misspecified alternative distribution. This allows a general investigation of different types of interactions which are poorly or well detected via data. Principally we contrast pairwise-interaction models with ‘diffuse interaction models’ as introduced in Gustafson et al. (Stat Med 24:2089–2104, 2005).


Interaction Misspecified model Score function Wald test-statistic Pairwise interaction models Diffuse interaction models 


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Copyright information

© Springer-Verlag 2010

Authors and Affiliations

  1. 1.Department of Mathematics and StatisticsUniversity of SaskatchewanSaskatchewanCanada
  2. 2.Department of StatisticsUniversity of British ColumbiaVancouverCanada

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