Adjustment of measuring devices with linear models

We consider the problem of linear calibration or adjustment of two measuring devices based on a sample of replicated measurements. Linear adjustments are routinely used in the pavement industry. A simple solution based on linear regression of the average measurements of one device on the other has been used by field engineers. To address the statistical concern that the regression parameter estimates are biased due to attenuation, we consider a more sophisticated multivariate model to obtain asymptotically unbiased estimates of the calibration parameters. The maximum likelihood estimates (MLEs) of the multivariate model are computed with the EM algorithm. Simulation studies and asymptotic calculations are used to compare properties of the MLE with the simple regression method. Data from two measuring devices used for determining asphalt pavement density, coring and nuclear gauge, are used in an example. We find that the superiority in parameter estimation of the MLE does not always result in better adjustments. In typical applications, such as determining pavement density, the simple regression method is highly competitive and often performs better than the multivariate MLE in adjusting the measurements from a cruder device despite its bias problem.