Measurement error models with interactions

Douglas Midthune, Raymond J. Carroll, Laurence S. Freedman, Victor Kipnis

Research output: Contribution to journalArticlepeer-review

5 Scopus citations


An important use of measurement error models is to correct regression models for bias due to covariate measurement error. Most measurement error models assume that the observed error-prone covariate ($W$) is a linear function of the unobserved true covariate ($X$) plus other covariates ($Z$) in the regression model. In this paper, we consider models for $W$ that include interactions between $X$ and $Z$. We derive the conditional distribution of $X$ given $W$ and $Z$ and use it to extend the method of regression calibration to this class of measurement error models. We apply the model to dietary data and test whether self-reported dietary intake includes an interaction between true intake and body mass index. We also perform simulations to compare the model to simpler approximate calibration models.

Original languageEnglish
Pages (from-to)277-290
Number of pages14
Issue number2
StatePublished - 1 Apr 2016
Externally publishedYes

Bibliographical note

Funding Information:
R.J.C.'s research was supported by a grant from the National Cancer Institute (U01-CA057030).

Publisher Copyright:
© 2015 Published by Oxford University Press 2015.


  • Interactions
  • Measurement error
  • Mixed models
  • Nonlinear mixed models
  • Nutritional epidemiology


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