Locally ancillary quasi-score models for errors-in-covariates

Paul J. Rathouz, Kung Yee Liang

Research output: Contribution to journalArticlepeer-review

Abstract

We use the notion of locally ancillary estimating functions to develop a quasi-score method for fitting regression models containing measurement error in the covariates. Suppose that interest is on the model E(Y|u, w) for response Y, the observed data are (y, x, w), and X is a mismeasured surrogate for u. We take a functional modeling approach, treating the u as a fixed nuisance parameter. Beginning with quasi-scores for the regression parameter and the unknown u, we derive a bias-corrected quasi-score for the regression parameter that is second-order locally ancillary for the nuisance u. Our method for this requires only the correct specification of the mean and variance functions for Y and X in terms of u, w, and the regression parameter. When an estimator for u is plugged into the corrected quasi-score, local approximations show that the bias is small. We present simulations verifying this result and an example from child psychiatry, both using log-linear regression models.

Original languageEnglish (US)
Pages (from-to)1004-1013
Number of pages10
JournalJournal of the American Statistical Association
Volume96
Issue number455
DOIs
StatePublished - Sep 1 2001

Keywords

  • Ancillarity
  • Measurement error
  • Nuisance parameter
  • Quasi-likelihood
  • Semiparametric model

ASJC Scopus subject areas

  • Statistics and Probability
  • Statistics, Probability and Uncertainty

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