Calibration with random slopes

Abstract

We consider the following linear calibration problem. Two scalar quantities X and Y are related by a simple linear regression of Y on X , and at the calibration step repeated measurements on both X and Y are available for a number of sampling units. At the prediction step a Y measurement, possibly together with previously obtained Y measurements, is available for a new sampling unit, and we wish to estimate the corresponding unknown X . Both the intercept and the slope of the regression are allowed to vary between units, resulting in a random regression coefficient model at the calibration step. As a result, at the prediction step the unknown X affects both the mean and covariance structure of Y . Point and interval estimates for X are obtained and illustrated on a set of biomedical data.