ODRPACK:
Software for Orthogonal Distance Regression
ODRPACK is
a portable collection of Fortran subroutines
designed to solve the Orthogonal Distance Regresson (ODR) problem, that
is, to find parameter estimates that minimize the sum of the squares of
the weighted orthogonal distances between each observed data point and the
curve described by a nonlinear equation. A
highly efficient and stable algorithm
for solving this problem was developed in collaboration between NIST's
Mathematical and Computational Sciences Division and the University of
Colorado at Boulder. This collaboration was undertaken in order to
provide NIST scientists the means to analyze high precision measurements
where both the explanatory and the response variables have errors that are
comparable in magnitude. Using this algorithm, an ODR problem can be
solved as efficiently as an ordinary least squares (OLS) problem where the
explanatory variables are treated as exact. This is the algorithm
implemented in ODRPACK.
ODRPACK is publically available and has proved to be as useful to industry
as it is to NIST scientists. It has been used to successfully solve
problems on machine architectures ranging from PCs to supercomputers.
ODRPACK accomodates
- many levels of user sophistication and problem difficulty;
- implicit as well as explicit orthogonal distance regression models;
- complex and other types of multiresponse data; and
- correlation within the components of a multidimensional observation.
The existence of ODRPACK means that solving an ODR problem is just as easy
as solving a nonlinear OLS problem, and that useful statistical
information can be readily produced.
Available from
http://www.netlib.org/netlib/odrpack/
References:
- Paul T. Boggs, Richard H. Byrd, Janet E. Rogers and Robert B. Schnabel
(1992),
``User's Reference Guide for
ODRPACK Version 2.01 -- Software for Weighted Orthogonal Distance Regression,''
NIST IR 4834,
U.S. Government Printing Office.
- Paul T. Boggs and Janet E. Rogers (1990),
``Orthogonal Distance Regression,''
Contemporary Mathematics, Volume 112:
Statistical Analysis of Measurement Error Models and their Applications,
P. J. Brown and Wayne A. Fuller, Editors,
pp. 183-194, American Mathematical Society, Providence, Rhode Island.
(Also published as NIST IR 89-4197, U.S. Government Printing Office.)
- Paul T. Boggs and Janet E. Rogers
(1990),
``The Computation and Use of the Asymptotic Covariance Matrix for
Measurement Error Models,''
NIST IR 89-4102, U.S. Government Printing Office.
- Paul T. Boggs, Richard H. Byrd, Janet Rogers Donaldson and Robert B. Schnabel
(1989),
``ODRPACK -- Software for Weighted Orthogonal Distance Regression,''
ACM Transactions on Mathematical Software,
Vol. 15, No. 4, pp 348-364.
- Paul T. Boggs, Janet Rogers Donaldson, Robert B. Schnabel and C. H. Spiegelman
(1988),
``A Computational Examination of Orthogonal Distance Regression,''
Journal of Econometrics,
Vol. 38, No. 1/2, pp. 169-201.
- Paul T. Boggs, Richard H. Byrd, and Robert B. Schnabel (1987),
``A stable and efficient algorithm for nonlinear orthogonal distance
regression,''
SIAM Journal of Scientific and Statistical Computing, 8, 6, 1052--1078.
Back:
Janet E Rogers
7/30/1997