Analysis of multivariate reliability structures and the induced bias in linear model estimation

Area of Science:

• Biostatistics
• Epidemiology
• Biomedical Research

Background:

• Least squares regression assumes accurate predictor measurements.
• Unreliable measurements (X) instead of true values (x) induce bias in regression coefficients (beta).
• This bias is complex and unpredictable in multivariate settings.

Purpose of the Study:

• To characterize the estimation bias caused by measurement error in regression models.
• To present and review a simple adjustment procedure to correct this bias.
• To generalize univariate reliability concepts to multivariate cases.

Main Methods:

• Characterization of estimation bias in regression models with measurement error.
• Development and review of a bias adjustment procedure.
• Definition of three reliability coefficient matrices for multivariate data.

Main Results:

• The bias induced by measurement error does not consistently shrink coefficients toward zero in multivariate cases.
• Several intuitive conjectures about the bias were found to be false.
• The proposed adjustment procedure offers a way to correct for estimation bias.

Conclusions:

• Accurate estimation of regression coefficients requires addressing measurement error.
• The study provides a framework and methods for correcting bias in multivariate regression.
• The methods are illustrated using dietary intake data from a cancer prevention study.