Highly Nonlinear Measurement Error Models in Nutritional Epidemiology
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This dissertation consists of two main projects in the area of measurement error models with application in nutritional epidemiology. The first project studies the application of moment reconstruction and moment- adjusted imputation in the context of nonlinear Berkson-type measurement error. The idea of moment reconstruction and moment adjusted imputation, like regression calibration, is to replace the unobserved variable of interest which is subject to measurement error with a proxy, which can be used in a variety of subsequent analyses, without redoing the measurement error model each time a different downstream analysis is performed. However, both methods essentially require the homoscedastic classical measurement error model or non-classical model that can be easily reduced to a classical one. In the first project, we deal with a case where the measurement error structure is of nonlinear Berkson-type, and develop analogues of moment reconstruction and moment-adjusted imputation for this case. We use National Institutes of Health-AARP Diet and Health Study, where the latent variable is a dietary pattern score called the Healthy Eating Index-2005, and simulations to illustrate the methods. The numerical results show the promise of these methods in the nonlinear Berkson-type measurement error context. In the second project, we consider measurement error models for two variables observed repeatedly and subject to measurement error. One variable is continuous but positive, while the other variable is a mixture of continuous and zero measurements. This second variable has two sources of zeros. The first source is episodic zeros, wherein some of the measurements for an individual may be zero and others positive. The second source is hard zeros, i.e., some individuals will always report zero. An example is the consumption of alcohol from alcoholic beverages: some individuals consume alcoholic beverages episodically, while others never consume alcoholic beverages. However, with a small number of repeated measurements from individuals, it is not possible to determine those that are episodic zeros and those that are hard zeros. We develop a new measurement error model for this problem, and use Bayesian methods to t it. We also contrast our approach for a single variable which is subject to excess zeros, with those methods that have been developed for a single variable and proven to be somewhat numerically unstable. Simulations and data analyses of two studies are used to show that the new method gives more realistic and numerically stable results than the maximum likelihood approach.
Latent variable models
Wei, Rubin (2014). Highly Nonlinear Measurement Error Models in Nutritional Epidemiology. Doctoral dissertation, Texas A & M University. Available electronically from