Deming regression

Deming regression is an errors-in-variables model that fits a line describing the relationship between two variables. Unlike ordinary linear regression, it is suitable when there is measurement error in both variables.

Deming regression (Cornbleet & Gochman, 1979) finds the line of best fit by minimizing the sum of the distances between the measured values and the regression line, at an angle specified by the variance ratio. It assume both variables are measured with error. The variance ratio of the errors in the X / Y variable is required and assumed to be constant across the measuring interval. If you measure the items in replicate, the measurement error of each method is estimated from the data and the variance ratio calculated.

In the case where the variance ratio is equal to 1, Deming regression is equivalent to orthogonal regression. When only single measurements are made by each method and the ratio of variances is unknown, a variance ratio of 1 is sometimes used as a default. When the range of measurements is large compared to the measurement error this can be acceptable. However in cases where the range is small the estimates are biased and the standard error underestimated, leading to incorrect hypothesis tests and confidence intervals (Linnet, 1998).

Weighted Deming regression (Linnet, 1990) is a modification of Deming regression that assumes the ratio of the coefficient of variation (CV), rather than the ratio of variances, is constant across the measuring interval.

Confidence intervals for parameter estimates use a t-distribution and the standard errors are computed using a Jackknife procedure (Linnet, 1993).