Fitting a linear model to survey data when the long-term average daily
intake of a dietary component is an explanatory variable

Abstract

The National Health and Nutrition Examination Survey (NHANES) collects information on both dietary intake and health conditions from a complex sample of individuals in the US. Instrumental-variable regression can be used to model an individual’s health-related attribute as a linear function of explanatory variables including the average daily intake of dietary components. This overcomes the apparent limitation of the NHANES collecting dietary intake data on only two days per sampled individual because the averages of two days per individual exhibit considerable intra-individual variability. Readily available software routines can perform
survey-sensitive instrumental-variable regression with data like that collected by the NHANES, but the relevant quantitative literature is not clear about what parameters these routines are actually estimating. We fit the long-term (usual) serum beta-carotene level of a population of women aged 20-64 to a linear function of each woman’s long-term average (usual) daily betacarotene intake from food and other explanatory variables using survey-sensitive instrumental regression and provide two interpretations of the results. Keywords: extended linear model, instrumental-variable regression, measurement error, standard linear model, usual daily intake.