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Assessing interaction effects in linear measurement error models
Author(s) -
Huang LiShan,
Wang Hongkun,
Cox Christopher
Publication year - 2005
Publication title -
journal of the royal statistical society: series c (applied statistics)
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.205
H-Index - 72
eISSN - 1467-9876
pISSN - 0035-9254
DOI - 10.1111/j.1467-9876.2005.00467.x
Subject(s) - categorical variable , observational error , mathematics , statistics , errors in variables models , linear model , corollary , linear regression , variables , variable (mathematics) , variance (accounting) , econometrics , mathematical analysis , accounting , pure mathematics , business
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.