AJP - Regulatory, Integrative and Comparative Physiology, Vol 245, Issue 2 135-R142, Copyright © 1983 by American Physiological Society
Parameter estimation in linear functional relationships
E. M. Haacke and M. D. Goldman
We present the application of a weighted least-squares technique to extract
parameter estimates in linear models when all variables are subject to
error and the goal of the investigation is the value of the parameters
themselves. We assume that the relative variances of the variables are
known and that the errors between variables are independent. The method of
parameter estimation for linear functional relationships is presented, and
we describe its differences from linear regression. We discuss how to
obtain confidence intervals for the parameter estimates with an emphasis on
computer Monte Carlo simulations. An explicit example related to
measurements of lung volume changes is presented. An eigenvalue analysis of
the data pertaining to the number of independent variables and a physical
interpretation of the data space are also discussed.
