Inverse Regression from Longitudinal Data

Inverse regression, or statistical calibration, uses the estimated relationship between a response Y and a covariate x to infer the values of unknown x’s from their observed Y’s. Typically x is univariate but Y may be multivariate. A brief review of the basic theory will be given, followed by consideration of the problems involved in extending these approaches to longitudinal data, i.e. where the training data consists of groups of observations on distinct individuals. A Bayesian analysis using MCMC is shown to give a flexible framework for solving these problems. An example concerning the age determination of tern chicks from their wingspan and weight measurements will be used for illustration.