Semiparametric errors-in-variables models: A Bayesian approach

Journal Article (Journal Article)

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.

Full Text

Duke Authors

Cited Authors

  • Mallick, BK; Gelfand, AE

Published Date

  • July 1, 1996

Published In

Volume / Issue

  • 52 / 3

Start / End Page

  • 307 - 321

International Standard Serial Number (ISSN)

  • 0378-3758

Digital Object Identifier (DOI)

  • 10.1016/0378-3758(95)00139-5

Citation Source

  • Scopus