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On the detectability of different forms of interaction in regression models

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Abstract

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).

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Authors and Affiliations

  1. Department of Mathematics and Statistics, University of Saskatchewan, Saskatchewan, Canada

    Juxin Liu

  2. Department of Statistics, University of British Columbia, Vancouver, Canada

    Paul Gustafson

Authors
  1. Juxin Liu
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  2. Paul Gustafson
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Correspondence to Juxin Liu.

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Liu, J., Gustafson, P. On the detectability of different forms of interaction in regression models. Metrika 75, 347–365 (2012). https://doi.org/10.1007/s00184-010-0330-8

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  • DOI: https://doi.org/10.1007/s00184-010-0330-8

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