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Assessing interaction effects in linear measurement error models

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  • Li‐Shan Huang
  • Hongkun Wang
  • Christopher Cox

Abstract

Summary. 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.

Suggested Citation

  • Li‐Shan Huang & Hongkun Wang & Christopher Cox, 2005. "Assessing interaction effects in linear measurement error models," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 54(1), pages 21-30, January.
    • Handle: RePEc:bla:jorssc:v:54:y:2005:i:1:p:21-30
    DOI: 10.1111/j.1467-9876.2005.00467.x
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    Cited by:

    1. Barros, Michelli & Giampaoli, Viviana & Lima, Claudia R.O.P., 2007. "Hypothesis testing in the unrestricted and restricted parametric spaces of structural models," Computational Statistics & Data Analysis, Elsevier, vol. 52(2), pages 1196-1207, October.
    2. Brisa N. Sánchez & Shan Kang & Bhramar Mukherjee, 2012. "A Latent Variable Approach to Study Gene–Environment Interactions in the Presence of Multiple Correlated Exposures," Biometrics, The International Biometric Society, vol. 68(2), pages 466-476, June.

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