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Estimation of an errors‐in‐variables regression model when the variances of the measurement errors vary between the observations
Author(s) -
Kulathinal S. B.,
Kuulasmaa Kari,
Gasbarra Dario
Publication year - 2002
Publication title -
statistics in medicine
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.996
H-Index - 183
eISSN - 1097-0258
pISSN - 0277-6715
DOI - 10.1002/sim.1062
Subject(s) - statistics , observational error , multivariate statistics , regression analysis , regression , correction for attenuation , errors in variables models , mathematics , econometrics , attenuation , physics , optics
It is common in the analysis of aggregate data in epidemiology that the variances of the aggregate observations are available. The analysis of such data leads to a measurement error situation, where the known variances of the measurement errors vary between the observations. Assuming multivariate normal distribution for the ‘true’ observations and normal distributions for the measurement errors, we derive a simple EM algorithm for obtaining maximum likelihood estimates of the parameters of the multivariate normal distributions. The results also facilitate the estimation of regression parameters between the variables as well as the ‘true’ values of the observations. The approach is applied to re‐estimate recent results of the WHO MONICA Project on cardiovascular disease and its risk factors, where the original estimation of the regression coefficients did not adjust for the regression attenuation caused by the measurement errors. Copyright © 2002 John Wiley & Sons, Ltd.