Multiplicative-Form CERs: A Progress Review
Exponential and power functions, y = abcx and y = ax , have significant currency as CER
functional forms; and the ready accessibility of the Excel Solver has put a tool for fitting them to data in everyone’s hands. However, compared to their linear cousins, the mathematics of these “multiplicative CERs” is less easy and knowledge of their fundamentals is less widespread. It is thus a good time to improve our understanding of them, to ground future development and application firmly. We speak here to our initial efforts.
In one line of work, we use the Excel Solver to determine “best” constants “a” and “b” from noiseless data comprising varying “a”/”b”/”x” triples – e.g., y = ax exactly, for each triple. We report on the behavior of Solver-determined “best” values for “a” and “b” over different
methodologies for finding them. To provide immediate utility for the community, we look at
“learning curve variants” of the multiplicative forms, y = abx and y = ax , where the exponents are base 2 logs of the numbers we control in the experimental design.
In a second line of research, we discuss concepts for identifying when the multiplicative CER form is appropriate.
Dr. Robinson is a space systems cost estimator with Wyle. He holds a SCEA certification, a BA in psychology from Rutgers University, and a doctorate in operations research from the George Washington University. As part of his doctoral preparations he studied decision theory with Richard Soland, statistical models with Nozer Singpurwalla, and measurement theory with Fred Roberts (in absentia at Rutgers).
Mr. Mosier currently estimates space systems costs for Wyle, and previously worked on issues of transportation security economics.
He received his BS in economics from the American University in 2004. While at American, he received a grant from the School of Arts and Sciences to research and present findings on the politicization of White House economic forecasting, under the guidance of Kara Olson. He also researched the determinants of household relocation, under the guidance of Robert Lerman.