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| R has a Bayesian procedure, leiv, which uses a Cauchy prior for the slope combined with a likelihood function using the standard deviations of (predictor) x and (outcome) y and their correlation from the data to produce posterior distributions for the slope and intercept adjusted for measurement error. The procedure can also use these posterior distributions to produce median values and credible regions for the slope and intercept. | R has a Bayesian procedure, leiv, which uses a Cauchy prior for the slope combined with a likelihood function using the standard deviations of (predictor) x and (outcome) y and their correlation from the data to produce posterior distributions for the slope and intercept adjusted for measurement error. The procedure can also use these posterior distributions to produce median values and credible regions for the slope and intercept. The Bayesian procedure is described in [[attachment:leivpaper.pdf | Leonard D. (2011) Estimating a bivariate linear relationship]] ''Bayesian Analysis'' '''6(4)''' 727-754. |
Errors in variables when doing a regression
If there is measurement error in a predictor (x) it follows that the slope and intercept will not converge to their true values and be biasedly estimated. For example the slope will converge to slope / (Variance(x) + Variance(Measurement Error of x)) which will lead to an underestimate of the slope in the presence of measurement error since its variance will be non-zero.
Klauer KC, Draine SC and Greenwald A G (1998) An unbiased errors-in-variables approach to detecting unconscious cognition. British Journal of Mathematical and Statistical Psychology 51 253-267 present a method for estimating the slope and intercept and their standard errors adjusting for measurement error. This can be estimated using a FORTRAN program used by the authors.
R has a Bayesian procedure, leiv, which uses a Cauchy prior for the slope combined with a likelihood function using the standard deviations of (predictor) x and (outcome) y and their correlation from the data to produce posterior distributions for the slope and intercept adjusted for measurement error. The procedure can also use these posterior distributions to produce median values and credible regions for the slope and intercept. The Bayesian procedure is described in Leonard D. (2011) Estimating a bivariate linear relationship Bayesian Analysis 6(4) 727-754.