FUNCTIONAL COMPARATIVE CALIBRATION USING AN EM ALGORITHM

For many measurements made on processes and individuals, the true value being measured is unknown or unknowable. When data consist of two or more distinct methods of measurement, the problem of comparing measurements is often referred to as comparative calibration. A provisional analysis of such data can be made assuming one method or set of measurements is unbiased, by means of the classic functional relationship model. Assuming normality in the multivariate case (i.e., more than two methods of measurement), maximum likelihood estimates are usually calculated using generalized eigenvalues and eigenvectors. We propose calculating the same maximum likelihood estimates using a simple EM algorithm. The problems of estimating the variance of parameter estimates and testing the hypothesis of equal calibration lines are considered. An alternative error assumption for the basic model is also explored. The proposed methods are validated using simulation.