Leonard A. Stefanski is Professor of Statistics at North Carolina State University. He is an elected Fellow of the American Statistical Association. He served as Associate Editor for the Journal of the American Statistical Association for fourteen years, and now serves as Editor. With several co-authors he has published over sixty articles as well as the book, Regression and Measurement Error in Nonlinear Models.

Abstract

Measurement Error Models for Variance Predictors

Laine Elliott and Len Stefanski (presenter)

Commonly measurement error models assume a relationship between a response Y and an error-prone predictor X, where the measured predictor W = X + U and U is the measurement error (Carroll et al., 2005). The problem is to infer E(Y|X) from data (Wi, Yi) and an estimate of the measurement error variance, possible calculated from replicate measurements Wij (in which case Wi is the mean of the replicate measurements). Implicit in this setup is the assumption that the response depends only on the subject-specific mean measurement X=E(W). Because replicate measurements frequently arise in longitudinal studies, where variation around the mean is intrinsic, not instrumental (e.g. blood pressure, weight, cholesterol) it is reasonable to question whether the response might also depend on the intrinsic variation. Such models were studied by Iribarren et al. (1995), Grove et al. (1997) and recently by Yang et al. (2007). The problem of measurement error in these models was addressed by Lyles et al. (1997). This talk will highlight some of the problems unique to modeling with subject-specific variances and summarize results obtained by tackling these problems using standard measurement error modeling approaches.