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Improved Regression Calibration

Published online by Cambridge University Press:  01 January 2025

Anders Skrondal  and
Jouni Kuha
Anders Skrondal*
Affiliation:
Division of Epidemiology, Norwegian Institute of Public Health
Jouni Kuha
Affiliation:
Department of Statistics, London School of Economics
*
Requests for reprints should be sent to Anders Skrondal, Division of Epidemiology, Norwegian Institute of Public Health, P.O. Box 4404, Nydalen, 0403 Oslo, Norway. E-mail: anders.skrondal@fhi.no
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Abstract

The likelihood for generalized linear models with covariate measurement error cannot in general be expressed in closed form, which makes maximum likelihood estimation taxing. A popular alternative is regression calibration which is computationally efficient at the cost of inconsistent estimation. We propose an improved regression calibration approach, a general pseudo maximum likelihood estimation method based on a conveniently decomposed form of the likelihood. It is both consistent and computationally efficient, and produces point estimates and estimated standard errors which are practically identical to those obtained by maximum likelihood. Simulations suggest that improved regression calibration, which is easy to implement in standard software, works well in a range of situations.

Keywords

covariate measurement errormeasurement modelgeneralized linear modelpseudo maximum likelihood estimationregression calibration
Type
Original Paper
Information
Psychometrika , Volume 77 , Issue 4 , October 2012 , pp. 649 - 669
Copyright
Copyright © 2012 The Psychometric Society

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