Incomplete Corrections for Regressor Unreliabilities

When the independent variables in a regression model are measured with error, the least squares estimates of the regression coefficients are not consistent. This article shows that correcting for the known unreliabilities may yield more misleading estimates than an ordinary (uncorrected) regression analysis because correction for attenuation uniformly improves the coefficient estimates only if all the predictor variances are adjusted for measurement error. In the absence of known reliabilities for some predictors, the analyst is well-advised to attempt an analysis of the sensitivity of the coefficient estimates to variations in the unknown reliabilities. However, some notions about the unknown reliabilities are required in order to assess the relative errors of the partially corrected and ordinary estimates.