Assessing interaction effects in linear measurement error models

Li Shan Huang, Hongkun Wang, Christopher Cox

Research output: Contribution to journalArticlepeer-review

11 Scopus citations


In a linear model, the effect of a continuous explanatory variable may vary across groups defined by a categorical variable, and the variable itself may be subject to measurement error. This suggests a linear measurement error model with slope-by-factor interactions. The variables that are defined by such interactions are neither continuous nor discrete, and hence it is not immediately clear how to fit linear measurement error models when interactions are present. This paper gives a corollary of a theorem of Fuller for the situation of correcting measurement errors in a linear model with slope-by-factor interactions. In particular, the error-corrected estimate of the coefficients and its asymptotic variance matrix are given in a more easily assessable form. Simulation results confirm the asymptotic normality of the coefficients in finite sample cases. We apply the results to data from the Seychelles Child Development Study at age 66 months, assessing the effects of exposure to mercury through consumption of fish on child development for females and males for both prenatal and post-natal exposure.

Original languageEnglish (US)
Pages (from-to)21-30
Number of pages10
JournalJournal of the Royal Statistical Society. Series C: Applied Statistics
Issue number1
StatePublished - 2005
Externally publishedYes


  • Asymptotic normality
  • Interaction
  • Regression calibration
  • Simulation extrapolation

ASJC Scopus subject areas

  • Statistics and Probability
  • Statistics, Probability and Uncertainty


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