Semiparametric errors-in-variables models: A Bayesian approach
Regression models incorporating measurement error have received much attention in the recent literature. Measurement error can arise both in the explanatory variables and in the response. We introduce a fairly general model which permits both types of errors. The model naturally arises as a hierarchical structure involving three distinct regressions. For each regression, a semiparametric generalized linear model is introduced utilizing an unknown monotonic function. By transformation, such a function can be viewed as a c.d.f. We model an unknown c.d.f. using mixtures of Beta c.d.f.'s, noting that such mixtures are dense within the class of all continuous distributions on [0, 1]. Thus, the overall model incorporates nonparametric links or calibration curves along with customary regression coefficients clarifying its semiparametric nature. Fully Bayesian fitting of such a model using sampling-based methods is proposed. We indicate numerous attractive advantages which our model and its fitting provide. A simulation example demonstrates quantitatively the potential benefit.
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