October 2002 | Technical Memorandum NTIA TM-03-397
An Iterated Nested Least-Squares Algorithm for Fitting Multiple Data Sets
Cite This Publication
Stephen D. Voran, “An Iterated Nested Least-Squares Algorithm for Fitting Multiple Data Sets,” Technical Memorandum NTIA TM-03-397, U.S. Department of Commerce, National Telecommunications and Information Administration, Institute for Telecommunication Sciences, October 2002.
Stephen D. Voran 
Abstract:
A multiple data set fitting problem often arises in conjunction with the development of objective estimators of perceived audio or video quality. In such development work, we often seek the best linear relationship between a set of objective audio or video quality estimation parameters and a set of subjective audio or video quality scores. In order to find the most robust and reliable relationship, we prefer to perform a least-squares fit using as many audio or video data points as possible. This motivates us to combine scores from different subjective tests. Unfortunately, scores from different subjective tests or data sets can differ in significant ways due to differing test procedures, environments, languages, and other sources. We develop a solution to this multiple data set fitting problem: the iterated nested least-squares (INLS) algorithm. This algorithm iterates between two least-squares steps. One step attempts to homogenize heterogeneous data sets through the use of a single first-order correction for all of the data points in each data set. The other least-squares step solves for the appropriate linear combination of the parameters, across all data sets. We also offer example INLS algorithm results using simulation data and data from telephone-bandwidth speech quality tests. For convenience we have written this memorandum in the language of objective estimation of perceived audio and video quality but the results are completely general and can be used to fit other types of data sets as well.
Keywords: audio quality estimation; speech quality estimation; video quality estimation; data set fitting; least-squares fitting; linear regression; meta-analysis
For technical information concerning this report, contact:
Stephen D. Voran
Institute for Telecommunication Sciences
(303) 497-3839
svoran@ntia.gov
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